Chin. Phys. B

Soliton interactions and asymptotic state analysis in a discrete nonlocal nonlinear self-dual network equation of reverse-space type

Cui-Lian Yuan(袁翠连) and Xiao-Yong Wen(闻小永)

Chin. Phys. B, 2021, 30 (3): 030201. DOI: 10.1088/1674-1056/abc2ba

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We propose a reverse-space nonlocal nonlinear self-dual network equation under special symmetry reduction, which may have potential applications in electric circuits. Nonlocal infinitely many conservation laws are constructed based on its Lax pair. Nonlocal discrete generalized (m, N-m)-fold Darboux transformation is extended and applied to solve this system. As an application of the method, we obtain multi-soliton solutions in zero seed background via the nonlocal discrete N-fold Darboux transformation and rational solutions from nonzero-seed background via the nonlocal discrete generalized (1, N-1)-fold Darboux transformation, respectively. By using the asymptotic and graphic analysis, structures of one-, two-, three-and four-soliton solutions are shown and discussed graphically. We find that single component field in this nonlocal system displays unstable soliton structure whereas the combined potential terms exhibit stable soliton structures. It is shown that the soliton structures are quite different between discrete local and nonlocal systems. Results given in this paper may be helpful for understanding the electrical signals propagation.

Discontinuous event-trigger scheme for global stabilization of state-dependent switching neural networks with communication delay

Yingjie Fan(樊英杰), Zhen Wang(王震), Jianwei Xia(夏建伟), and Hao Shen(沈浩)

Chin. Phys. B, 2021, 30 (3): 030202. DOI: 10.1088/1674-1056/abc541

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This paper is concerned with the global stabilization of state-dependent switching neural networks (SDSNNs) via discontinuous event-triggered control with network-induced communication delay. Aiming at decreasing triggering times, a discontinuous event-trigger scheme is utilized to determine whether the sampling information is required to be sent out or not. Meanwhile, under the effect of communication delay, the trigger condition and SDSNNs are transformed into two tractable models by designing a fictitious delay function. Then, using the Lyapunov-Krasovskii stability theory, some inequality estimation techniques, and extended reciprocally convex combination method, two sufficient criteria are established for ensuring the global stabilization of the resulting closed-loop SDSNNs, respectively. A unified framework is derived that has the ability to handle the simultaneous existence of the communication delay, the properties of discontinuous event-trigger scheme, as well as feedback controller design. Additionally, the developed results demonstrate a quantitative relationship among the event trigger parameter, communication delay, and triggering times. Finally, two numerical examples are presented to illustrate the usefulness of the developed stabilization scheme.

Model predictive inverse method for recovering boundary conditions of two-dimensional ablation

Guang-Jun Wang(王广军), Ze-Hong Chen(陈泽弘), Guang-Xiang Zhang(章广祥), and Hong Chen(陈红)

Chin. Phys. B, 2021, 30 (3): 030203. DOI: 10.1088/1674-1056/abc2b6

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A model predictive inverse method (MPIM) is presented to estimate the time-and space-dependent heat flux on the ablated boundary and the ablation velocity of the two-dimensional ablation system. For the method, first of all, the relationship between the heat flux and the temperatures of the measurement points inside the ablation material is established by the predictive model based on an influence relationship matrix. Meanwhile, the estimation task is formulated as an inverse heat transfer problem (IHTP) with consideration of ablation, which is described by an objective function of the temperatures at the measurement point. Then, the rolling optimization is used to solve the IHTP to online estimate the unknown heat flux on the ablated boundary. Furthermore, the movement law of the ablated boundary is reconstructed according to the estimation of the boundary heat flux. The effects of the temperature measurement errors, the number of future time steps, and the arrangement of the measurement points on the estimation results are analyzed in numerical experiments. On the basis of the numerical results, the effectiveness of the presented method is clarified.

Constructing reduced model for complex physical systems via interpolation and neural networks Suggested by editors

Xuefang Lai(赖学方), Xiaolong Wang(王晓龙, and Yufeng Nie(聂玉峰)

Chin. Phys. B, 2021, 30 (3): 030204. DOI: 10.1088/1674-1056/abd92e

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The work studies model reduction method for nonlinear systems based on proper orthogonal decomposition (POD) and discrete empirical interpolation method (DEIM). Instead of using the classical DEIM to directly approximate the nonlinear term of a system, our approach extracts the main part of the nonlinear term with a linear approximation before approximating the residual with the DEIM. We construct the linear term by Taylor series expansion and dynamic mode decomposition (DMD), respectively, so as to obtain a more accurate reconstruction of the nonlinear term. In addition, a novel error prediction model is devised for the POD-DEIM reduced systems by employing neural networks with the aid of error data. The error model is cheaply computable and can be adopted as a remedy model to enhance the reduction accuracy. Finally, numerical experiments are performed on two nonlinear problems to show the performance of the proposed method.

Delta-Davidson method for interior eigenproblem in many-spin systems ^Hot!

Haoyu Guan(关浩宇) and Wenxian Zhang(张文献)

Chin. Phys. B, 2021, 30 (3): 030205. DOI: 10.1088/1674-1056/abd74a

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Many numerical methods, such as tensor network approaches including density matrix renormalization group calculations, have been developed to calculate the extreme/ground states of quantum many-body systems. However, little attention has been paid to the central states, which are exponentially close to each other in terms of system size. We propose a delta-Davidson (DELDAV) method to efficiently find such interior (including the central) states in many-spin systems. The DELDAV method utilizes a delta filter in Chebyshev polynomial expansion combined with subspace diagonalization to overcome the nearly degenerate problem. Numerical experiments on Ising spin chain and spin glass shards show the correctness, efficiency, and robustness of the proposed method in finding the interior states as well as the ground states. The sought interior states may be employed to identify many-body localization phase, quantum chaos, and extremely long-time dynamical structure.

Hierarchical simultaneous entanglement swapping for multi-hop quantum communication based on multi-particle entangled states

Guang Yang(杨光, Lei Xing(邢磊), Min Nie(聂敏), Yuan-Hua Liu(刘原华), and Mei-Ling Zhang(张美玲)

Chin. Phys. B, 2021, 30 (3): 030301. DOI: 10.1088/1674-1056/abcf3d

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Entanglement swapping is a key technology for multi-hop communication based on entanglement in quantum networks. However, the end-to-end delay of the traditional sequential entanglement swapping (SEQES) grows rapidly with the increase of network scale. To solve this problem, we first propose a low-delay multi-particle simultaneous entanglement swapping (SES) scheme to establish the remote four-particle Greenberger-Horne-Zeilinger (GHZ) channel states for the bidirectional teleportation of three-particle GHZ states, in which the intermediate nodes perform Bell state measurements, send the measurement results and the Bell state type to the user node Bob (or Alice) through classical channel simultaneously. Bob (or Alice) only needs to carry out a proper unitary operation according to the information he (or she) has received. Further, we put forward a hierarchical simultaneous entanglement swapping (HSES) scheme to reduce the classical information transmission cost, which is composed of level-1 SES and level-2 SES (schemes). The former is an inner segment SES, and the latter is an inter segments SES. Theoretical analysis and simulation results show the HSES can obtain the optimal performance tradeoff between end-to-end delay and classical cost.

Spin-orbit-coupled spin-1 Bose-Einstein condensates confined in radially periodic potential

Ji Li(李吉), Tianchen He(何天琛), Jing Bai(白晶), Bin Liu(刘斌), and Huan-Yu Wang(王寰宇)

Chin. Phys. B, 2021, 30 (3): 030302. DOI: 10.1088/1674-1056/abc53e

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We investigate the ground states of spin-1 Bose-Einstein condensates (BECs) with spin-orbit coupling in a radially periodic potential by numerically solving the coupled Gross-Pitaevskii equations. In the radially periodic potential, we first demonstrate that spin-orbit-coupled antiferromagnetic BECs support a multiring petal phase. Polar-core vortex can be observed from phase profiles, which is manifested as circularly symmetric distribution. We further show that spin-orbit coupling can induce multiring soliton structure in ferromagnetic BECs. It is confirmed especially that the wave-function phase of the ring corresponding to uniform distribution satisfies the rotational symmetry, and the wave-function phase of the ring corresponding to partial splitting breaks the rotational symmetry. Adjusting the spin-orbit coupling strength can control the number of petal in antiferromagnetic BECs and the winding numbers of wave-function in ferromagnetic BECs. Finally, we discuss effects of spin-independent and spin-dependent interactions on the ground states.

Majorana stellar representation for mixed-spin (s, 1/2) systems

Yu-Guo Su(苏玉国), Fei Yao(姚飞), Hong-Bin Liang(梁宏宾), Yan-Ming Che(车彦明), Li-Bin Fu(傅立斌), and Xiao-Guang Wang(王晓光)

Chin. Phys. B, 2021, 30 (3): 030303. DOI: 10.1088/1674-1056/abc2bc

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By describing the evolution of a quantum state with the trajectories of the Majorana stars on a Bloch sphere, Majorana's stellar representation provides an intuitive geometric perspective to comprehend the quantum system with high-dimensional Hilbert space. However, the representation of a two-spin coupling system on a Bloch sphere has not been solved satisfactorily yet. Here, a practical method is presented to resolve the problem for the mixed-spin (s, 1/2) system and describe the entanglement of the system. The system can be decomposed into two spins: spin-(s+1/2) and spin-(s-1/2) at the coupling bases, which can be regarded as independent spins. Besides, any pure state may be written as a superposition of two orthonormal states with one spin-(s+1/2) state and the other spin-(s-1/2) state. Thus, the whole initial state can be regarded as a state of a pseudo spin-1/2. In this way, the mixed spin decomposes into three spins. Therefore, the state can be represented by (2s+1)+(2s-1)+1=4s+1 sets of stars on a Bloch sphere. Finally, some examples are given to show symmetric patterns on the Bloch sphere and unveil the properties of the high-spin system by analyzing the trajectories of the Majorana stars on the Bloch sphere.

Deterministic nondestructive state analysis for polarization-spatial-time-bin hyperentanglement with cross-Kerr nonlinearity Suggested by editors

Hui-Rong Zhang(张辉荣), Peng Wang(王鹏), Chang-Qi Yu(于长琦), and Bao-Cang Ren(任宝藏)

Chin. Phys. B, 2021, 30 (3): 030304. DOI: 10.1088/1674-1056/abd7d5

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We present a deterministic nondestructive hyperentangled Bell state analysis protocol for photons entangled in three degrees of freedom (DOFs), including polarization, spatial-mode, and time-bin DOFs. The polarization Bell state analyzer and spatial-mode Bell state analyzer are constructed by polarization parity-check quantum nondemolition detector (P-QND) and spatial-mode parity-check quantum nondemolition detector (S-QND) using cross-Kerr nonlinearity, respectively. The time-bin Bell state analyzer is constructed by the swap gate for polarization state and time-bin state of a photon (P-T swap gate) and P-QND. The Bell states analyzer for one DOF will not destruct the Bell states of other two DOFs, so the polarization-spatial-time-bin hyperentangled Bell states can be determinately distinguished without destruction. This deterministic nondestructive state analysis method has useful applications in quantum information protocols.

Quantum walk under coherence non-generating channels

Zishi Chen(陈子石) and Xueyuan Hu(胡雪元)

Chin. Phys. B, 2021, 30 (3): 030305. DOI: 10.1088/1674-1056/abd74d

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We investigate the probability distribution of the quantum walk under coherence non-generating channels. We define a model called generalized classical walk with memory. Under certain conditions, generalized classical random walk with memory can degrade into classical random walk and classical random walk with memory. Based on its various spreading speed, the model may be a useful tool for building algorithms. Furthermore, the model may be useful for measuring the quantumness of quantum walk. The probability distributions of quantum walks are generalized classical random walks with memory under a class of coherence non-generating channels. Therefore, we can simulate classical random walk and classical random walk with memory by coherence non-generating channels. Also, we find that for another class of coherence non-generating channels, the probability distributions are influenced by the coherence in the initial state of the coin. Nevertheless, the influence degrades as the number of steps increases. Our results could be helpful to explore the relationship between coherence and quantum walk.

A proposal for preparation of cluster states with linear optics

Le Ju(鞠乐), Ming Yang(杨名), and Peng Xue(薛鹏)

Chin. Phys. B, 2021, 30 (3): 030306. DOI: 10.1088/1674-1056/abd74b

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Measurement-based quantum computation in an optical setup shows great promise towards the implementation of large-scale quantum computation. The difficulty of measurement-based quantum computation lies in the preparation of cluster state. In this paper, we propose the method of generating the large-scale cluster state, which is a platform for measurement-based quantum computation. In order to achieve more complex quantum circuits, the preparation protocol of N-photon cluster state will be proposed as a generalization of the preparation of four-and five-photon cluster states. Furthermore, our proposal is experimentally feasible.

Fast generation of W state via superadiabatic-based shortcut in circuit quantum electrodynamics

Xue-Mei Wang(王雪梅), An-Qi Zhang(张安琪), Peng Xu(许鹏, and Sheng-Mei Zhao(赵生妹)

Chin. Phys. B, 2021, 30 (3): 030307. DOI: 10.1088/1674-1056/abd75b

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We propose a scheme to fast prepare the three-qubit W state via superadiabatic-based shortcuts in a circuit quantum electrodynamics (circuit QED) system. We derive the effective Hamiltonian to suppress the unwanted transitions between different eigenstates by counterdiabatic driving, and obtain the W state with high-fidelity based on the superadiabatic passage. The numerical simulation results demonstrate that the proposed scheme can accelerate the evolution, and is more efficient than that with the adiabatic passage. In addition, the proposed scheme is robust to the decoherence caused by the resonator decay and qubit relaxation, and does not need additional parameters, which could be feasible in experiment.

Nonlocal advantage of quantum coherence in a dephasing channel with memory

Ming-Liang Hu(胡明亮), Yu-Han Zhang(张宇晗), and Heng Fan(范桁)

Chin. Phys. B, 2021, 30 (3): 030308. DOI: 10.1088/1674-1056/abcf4a

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We investigate nonlocal advantage of quantum coherence (NAQC) in a correlated dephasing channel modeled by the multimode bosonic reservoir. We obtain analytically the dephasing and memory factors of this channel for the reservoir having a Lorentzian spectral density, and analyze how they affect the NAQC defined by the l₁ norm and relative entropy. It is shown that the memory effects of this channel on NAQC are state-dependent, and they suppress noticeably the rapid decay of NAQC for the family of input Bell-like states with one excitation. For the given transmission time of each qubit, we also obtain the regions of the dephasing and memory factors during which there is NAQC in the output states.

Lagrangian analysis of the formation and mass transport of compressible vortex rings generated by a shock tube

Haiyan Lin(林海燕), Yang Xiang(向阳, Hong Liu(刘洪), and Bin Zhang(张斌)

Chin. Phys. B, 2021, 30 (3): 030501. DOI: 10.1088/1674-1056/abc67f

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In order to understand the mass transport and the dynamic genesis associated with a compressible vortex formation, a dynamic analysis of compressible vortex rings (CVRs) generated by shock tubes by using the framework of Lagrangian coherent structures (LCSs) and finite-time Lyapunov exponents field (FTLE) is performed. Numerical calculation is performed to simulate the evolution of CVRs generated by shock tubes with 70 mm, 100 mm, and 165 mm of the driver section at the circumstances of pressure ratio=3. The formation of CVRs is studied according to FTLE fields. The mass transport during the formation is obviously seen by the material manifold reveled by FTLE fields. A non-universal formation number for the three CVRs is obtained. Then the elliptic LCSs is implemented on three CVRs. Fluid particles separated by elliptic LCSs and ridges of FTLE are traced back to t=0 to identify the fluid that eventually forms the CVRs. The elliptic LCSs encompass around 60% fluid material of the advected bulk but contain the majority of the circulation of the ring. The other parts of the ring carrying almost zero circulation advect along with the ring. Combining the ridges of FTLE and the elliptic LCS, the whole CVR can be divided into three distinct dynamic parts: vortex part, entrainment part, and advected part. In addition, a criterion based on the vortex part formation is suggested to identify the formation number of CVRs.

Detailed structural, mechanical, and electronic study of five structures for CaF₂ under high pressure

Ying Guo(郭颖), Yumeng Fang(方钰萌), and Jun Li(李俊)

Chin. Phys. B, 2021, 30 (3): 030502. DOI: 10.1088/1674-1056/abc67d

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Detailed density functional theory (DFT) calculations of the structural, mechanical, thermodynamic, and electronic properties of crystalline CaF₂ with five different structures in the pressure range of 0 GPa-150 GPa are performed by both GGA (generalized gradient approximation)-PBE (Perdew-Burke-Ernzerhof) and LDA (local density approximation)-CAPZ (Cambridge Serial Total Energy Package). It is found that the enthalpy differences imply that the fluorite phase $ \to $ PbCl₂-type phase $ \to $ Ni₂In-type phase transition in CaF₂ occurs at P_GGA1 = 8.0 GPa, P_GGA2 = 111.4 GPa by using the XC of GGA, and P_LDA1 = 4.5 GPa, P_LDA2 = 101.7 GPa by LDA, respectively, which is consistent with previous experiments and theoretical conclusions. Moreover, the enthalpy differences between PbCl₂-type and Ni₂In-type phases in one molecular formula become very small at the pressure of about 100 GPa, indicating the possibility of coexistence of two-phase at high pressures. This may be the reason why the transition pressure of the second phase transition in other reports is so huge (68 GPa-278 GPa). The volume changed in the second phase transition are also consistent with the enthalpy difference result. Besides, the pressure dependence of mechanical and thermodynamic properties of CaF₂ is studied. It is found that the high-pressure phase of Ni₂In-type structure has better stiffness in CaF₂ crystal, and the hardness of the material has hardly changed in the second phase transition. Finally, the electronic structure of CaF₂ is also analyzed with the change of pressure. By analyzing the band gap and density of states, the large band gap indicates the CaF₂ crystal is always an insulator at 0 GPa-150 GPa.

Deformed two-dimensional rogue waves in the (2+1)-dimensional Korteweg-de Vries equation Suggested by editors

Yulei Cao(曹玉雷), Peng-Yan Hu(胡鹏彦), Yi Cheng(程艺), and Jingsong He(贺劲松)

Chin. Phys. B, 2021, 30 (3): 030503. DOI: 10.1088/1674-1056/abd15e

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Within the (2+1)-dimensional Korteweg-de Vries equation framework, new bilinear B\"acklund transformation and Lax pair are presented based on the binary Bell polynomials and gauge transformation. By introducing an arbitrary function φ(y), a family of deformed soliton and deformed breather solutions are presented with the improved Hirota's bilinear method. By choosing the appropriate parameters, their interesting dynamic behaviors are shown in three-dimensional plots. Furthermore, novel rational solutions are generated by taking the limit of the obtained solitons. Additionally, two-dimensional (2D) rogue waves (localized in both space and time) on the soliton plane are presented, we refer to them as deformed 2D rogue waves. The obtained deformed 2D rogue waves can be viewed as a 2D analog of the Peregrine soliton on soliton plane, and its evolution process is analyzed in detail. The deformed 2D rogue wave solutions are constructed successfully, which are closely related to the arbitrary function φ(y). This new idea is also applicable to other nonlinear systems.

Transport property of inhomogeneous strained graphene ^Hot!

Bing-Lan Wu(吴冰兰), Qiang Wei(魏强), Zhi-Qiang Zhang(张智强), and Hua Jiang(江华)

Chin. Phys. B, 2021, 30 (3): 030504. DOI: 10.1088/1674-1056/abe3e3

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In analogy to real magnetic field, the pseudo-magnetic field (PMF) induced by inhomogeneous strain can also form the Landau levels and edge states. In this paper, the transport properties of graphene under inhomogeneous strain are studied. We find that the Landau levels have non-zero group velocity, and construct one-dimensional conducting channels. In addition, the edge states and the Landau level states in PMF are both fragile under disorder. We also confirm that the backscattering of these states could be suppressed by applying a real magnetic filed (MF). Therefore, the transmission coefficient for each conducting channel can be manipulated by adjusting the MF strength, which indicates the application of switching devices.

Anti-parity-time symmetric phase transition in diffusive systems

Pei-Chao Cao(曹培超) and Xue-Feng Zhu(祝雪丰)

Chin. Phys. B, 2021, 30 (3): 030505. DOI: 10.1088/1674-1056/abd694

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Parity-time (PT) symmetry/anti-parity-time (APT) symmetry in non-Hermitian systems reveal profound physics and spawn intriguing effects. Recently, it has been introduced into diffusive systems together with the concept of exceptional points (EPs) from quantum mechanics and the wave systems. With the aid of convection, we can generate complex thermal conductivity and imitate various wavelike dynamics in heat transfer, where heat flow can be "stopped" or moving against the background motion. Non-Hermitian diffusive systems offer us a new platform to investigate the heat wave manipulation. In this review, we first introduce the construction of APT symmetry in a simple double-channel toy model. Then we show the phase transition around the EP. Finally, we extend the double-channel model to the four-channel one for showing the high-order EP and the associated phase transition. In a general conclusion, the phase difference of adjacent channels is always static in the APT symmetric phase, while it dynamically evolves or oscillates when the APT symmetry is broken.

Impact of counter-rotating-wave term on quantum heat transfer and phonon statistics in nonequilibrium qubit-phonon hybrid system

Chen Wang(王晨), Lu-Qin Wang(王鲁钦), and Jie Ren(任捷)

Chin. Phys. B, 2021, 30 (3): 030506. DOI: 10.1088/1674-1056/abcfa8

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Counter-rotating-wave terms (CRWTs) are traditionally viewed to be crucial in open small quantum systems with strong system-bath dissipation. Here by exemplifying in a nonequilibrium qubit-phonon hybrid model, we show that CRWTs can play the significant role in quantum heat transfer even with weak system-bath dissipation. By using extended coherent phonon states, we obtain the quantum master equation with heat exchange rates contributed by rotating-wave-terms (RWTs) and CRWTs, respectively. We find that including only RWTs, the steady state heat current and current fluctuations will be significantly suppressed at large temperature bias, whereas they are strongly enhanced by considering CRWTs in addition. Furthermore, for the phonon statistics, the average phonon number and two-phonon correlation are nearly insensitive to strong qubit-phonon hybridization with only RWTs, whereas they will be dramatically cooled down via the cooperative transitions based on CRWTs in addition. Therefore, CRWTs in quantum heat transfer system should be treated carefully.

Atomic magnetometer with microfabricated vapor cells based on coherent population trapping

Xiaojie Li(李晓杰), Yue Shi(史越), Hongbo Xue(薛洪波), Yong Ruan(阮勇), and Yanying Feng(冯焱颖)

Chin. Phys. B, 2021, 30 (3): 030701. DOI: 10.1088/1674-1056/abc2b9

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An atomic magnetometer based on coherent population trapping (CPT) resonances in microfabricated vapor cells is demonstrated. Fabricated by the micro-electro-mechanical-system (MEMS) technology, the cells are filled with Rb and Ne at a controlled pressure. An experimental apparatus is built for characterizing properties of microfabricated vapor cells via the CPT effects. The typical CPT linewidth is measured to be about 3 kHz (1.46 kHz with approximately zero laser intensity) for the rubidium D1 line at about 90 ^°C. The effects of pressure, temperature and laser intensity on CPT linewidth are studied experimentally. A closed-loop atomic magnetometer is finally finished with a sensitivity of 210.5 pT/Hz^1/2 at 1 Hz bandwidth. This work paves the way for developing an integrated chip-scale atomic magnetometer in the future.

CCSD(T) study on the structures and chemical bonds of AnO molecules (An=Bk-Lr)

Xiyuan Sun(孙希媛), Pengfei Yin(殷鹏飞), Kaiming Wang(王开明), and Gang Jiang(蒋刚)

Chin. Phys. B, 2021, 30 (3): 033101. DOI: 10.1088/1674-1056/abc3b1

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The molecular geometries and dissociation energies of AnO (An=Bk-Lr) molecules were first obtained at the coupled-cluster single-, double-, and perturbative triple-excitations [CCSD(T)] level of theory. Four hybrid functionals, B3LYP, M06-2X, TPSSh, and PBE0, were also employed in the calculations for the sake of comparison. In comparison of the CCSD(T) results, B3LYP, TPSSh, and PBE0 functionals can obtain more appropriate results than M06-2X and MP2. The analyses on molecular orbitals show that the 7s, 6d, and 5f atomic orbitals of actinide (An) atoms participate in the bonding of An-O bonds. The partial covalent nature between An and O atoms is revealed by QTAIM analyses.

Effect of radiation on compressibility of hot dense sodium and iron plasma using improved screened hydrogenic model with l splitting

Amjad Ali, G Shabbir Naz, Rukhsana Kouser, Ghazala Tasneem, M Saleem Shahzad, Aman-ur-Rehman, and M H Nasim

Chin. Phys. B, 2021, 30 (3): 033102. DOI: 10.1088/1674-1056/abccb9

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High pressure investigations of matter involve the study of strong shock wave dynamics within the materials which gives rise to many thermal effects leading to dissociation of molecules, ionization of atoms, and radiation emission, etc. The response of materials experiencing a strong shock can be determined by its shock Hugoniot calculations which are frequently applied in numerical and experimental studies in inertial confinement fusion, laboratory astrophysical plasma, etc. These studies involve high energy density plasmas in which the radiation plays an important role in determining the energy deposition and maximum compressibility achieved by the shock within material. In this study, we present an investigation for the effect of radiation pressure on the maximum compressibility of the material using shock Hugoniot calculations. In shock Hugoniot calculations, an equation of state (EOS) is developed in which electronic contributions for EOS calculations are taken from an improved screened hydrogenic model with -l splitting (I-SHML) [ High Energy Density Physics (2018) 26 48] under local thermodynamic equilibrium (LTE) conditions. The thermal ionic part calculations are adopted from the state of the art Cowan model while the cold ionic contributions are adopted from the scaled binding energy model. The Shock Hugoniot calculations are carried out for sodium and iron plasmas and our calculated results show excellent agreement with published results obtained by using either sophisticated self-consistent models or the first principle study.

Scheme to measure the expectation value of a physical quantity in weak coupling regime

Jie Zhang(张杰), Chun-Wang Wu(吴春旺), Yi Xie(谢艺), Wei Wu(吴伟), and Ping-Xing Chen(陈平形)

Chin. Phys. B, 2021, 30 (3): 033201. DOI: 10.1088/1674-1056/abd772

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In quantum mechanics, the expectation value of an operator can be measured by using the projective measurement, if the coupling between the measured system and pointer is strong enough. However in the weak coupling regime, the pointer can not show all the eigenvalue of the physical quantity directly due to the overlapping among the pointer states, which makes the measurement of the expectation value difficult. In this paper, we propose an expectation value measurement method in the weak coupling regime inspired by the weak measurement scheme. Compared to the projective measurement, our scheme has two obvious advantages. Experimentally we use the internal state and motional state of a single trapped ⁴⁰Ca⁺ to establish the measurement scheme and realize the proof of principle demonstration of the scheme.

Efficient loading of ultracold sodium atoms in an optical dipole trap from a high power fiber laser Suggested by editors

Jing Xu(徐静), Wen-Liang Liu(刘文良), Ning-Xuan Zheng(郑宁宣), Yu-Qing Li(李玉清), Ji-Zhou Wu(武寄洲), Peng Li (李鹏), Yong-Ming Fu(付永明), Jie Ma(马杰), Lian-Tuan Xiao(肖连团), and Suo-Tang Jia(贾锁堂)

Chin. Phys. B, 2021, 30 (3): 033701. DOI: 10.1088/1674-1056/abc678

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We report on a research of the loading of ultracold sodium atoms in an optical dipole trap, generated by two beams from a high power fiber laser. The effects of optical trap light power on atomic number, temperature and phase space density are experimentally investigated. A simple theory is proposed and it is in good accordance with the experimental results of the loaded atomic numbers. In a general estimation, an optimal value for each beam with a power of 9 W from the fiber laser is achieved. Our results provide a further understanding of the loading process of optical dipole trap and laid the foundation for generation of a sodium Bose-Einstein condensation with an optical dipole trap.

Reflectionless spatial beam benders with arbitrary bending angle by introducing optic-null medium into transformation optics

Fei Sun(孙非), Yi-Chao Liu(刘一超), Yi-Biao Yang(杨毅彪), Hong-Ming Fei(费宏明), Zhi-Hui Chen(陈智辉), and Sai-Ling He(何赛灵)

Chin. Phys. B, 2021, 30 (3): 034101. DOI: 10.1088/1674-1056/abd38b

Abstract ( 357 )

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By introducing an optic-null medium into the finite embedded transformation, a reflectionless spatial beam bender is designed, which can steer the output beam by a fixed pre-designed angle β for an arbitrary incident angle. The bending angle β of the beam bender is determined by the geometrical angle of the device, which can be changed by simply choosing different geometrical angles. For various bending angles, the designed spatial beam bender can be realized by the same materials (i.e., an optic-null medium), which is a homogenous anisotropic material. Numerical simulations verify the reflectionless bending effect and rotated imaging ability of the proposed beam bender. A reduction model of the optic-null medium is studied, which can also be used for a reflectionless spatial beam bender with a pre-designed bending angle.

Design and verification of a broadband highly-efficient plasmonic circulator

Jianfei Han(韩建飞), Shu Zhen(甄姝), Weihua Wang(王伟华), Kui Han(韩奎), Haipeng Li(李海鹏), Lei Zhao(赵雷), and Xiaopeng Shen(沈晓鹏)

Chin. Phys. B, 2021, 30 (3): 034102. DOI: 10.1088/1674-1056/abca23

Abstract ( 453 )

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Circulators play a significant role in radar and microwave communication systems. This paper proposes a broadband and highly efficient plasmonic circulator, which consists of spoof surface plasmon polaritons (SSPPs) waveguides and ferrite disks to support non-reciprocal mode coupling. The simulated performance of symmetrically designed circulator shows that it has an insertion loss of roughly 0.5 dB while the isolation and return loss is more than 12 dB in the frequency range of 6.0 GHz-10.0 GHz (relative bandwidth of 50%). Equivalent circuit model has been proposed to explain the operating mechanism of the plasmonic circulator. The equivalent circuit model, numerical simulations, and experimental results are consistent with each other, which demonstrates the good performance of the proposed plasmonic circulator.

Numerical simulation of super-continuum laser propagation in turbulent atmosphere

Ya-Qian Li(李雅倩), Wen-Yue Zhu (朱文越), and Xian-Mei Qian(钱仙妹)

Chin. Phys. B, 2021, 30 (3): 034201. DOI: 10.1088/1674-1056/abd38a

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Considering the atmospheric extinction and turbulence effects, we investigate the propagation performances of super-continuum laser sources in atmospheric turbulence statistically by using the numerical simulation method, and the differences in propagation properties between the super-continuum (SC) laser and its pump laser are also analyzed. It is found that the propagation characteristics of super-continuum laser are almost similar to those of the pump laser. The degradation of source coherence degree may cause the relative beam spreading and scintillation indexes to decrease at different propagation distances or different turbulence strengths. The root-mean-square value of beam wandering is insensitive to the variation of source correlation length, and less aperture averaging occurs when the laser source becomes less coherent. Additionally, from the point of view of beam wandering, the SC laser has no advantage over the pump laser. Although the pump laser can bring about a bigger aperture average, the SC laser has a lower scintillation which may be due to the multiple wavelength homogenization effects on intensity fluctuations. This would be the most important virtue of the SC laser that can be utilized to improve the performance of laser engineering.

Modulation and enhancement of photonic spin Hall effect with graphene in broadband regions

Peng Dong(董鹏), Gaojun Wang(王高俊), and Jie Cheng(程杰)

Chin. Phys. B, 2021, 30 (3): 034202. DOI: 10.1088/1674-1056/abccb2

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The photonic spin Hall effect (SHE) holds great potential applications in manipulating spin-polarized photons. However, the SHE is generally very weak, and previous studies of amplifying photonic SHE were limited to the incident light in a specific wavelength range. In this paper, we propose a four-layered nanostructure of prism-graphene-air-substrate, and the enhanced photonic SHE of reflected light in broadband range of 0 THz-500 THz is investigated theoretically. The spin shift can be dynamically modulated by adjusting the thickness of air gap, Fermi energy of graphene, and also the incident angle. By optimizing the structural parameter of this structure, the giant spin shift (almost equal to its upper limit, half of the incident beam waist) in broadband range is achieved, covering the terahertz, infrared, and visible range. The difference is that in the terahertz region, the Brewster angle corresponding to the giant spin shift is larger than that of infrared range and visible range. These findings provide us with a convenient and effective way to tune the photonic SHE, and may offer an opportunity for developing new tunable photonic devices in broadband range.

Modified scaling angular spectrum method for numerical simulation in long-distance propagation Suggested by editors

Xiao-Yi Chen(陈晓义), Ya-Xuan Duan(段亚轩), Bin-Bin Xiang(项斌斌), Ming Li(李铭), and Zheng-Shang Da(达争尚)

Chin. Phys. B, 2021, 30 (3): 034203. DOI: 10.1088/1674-1056/abd38d

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The angular method (AS) cannot be used in long-distance propagation because it produces severe numerical errors due to the sampling problem in the transfer function. Two ways can solve this problem in AS for long-distance propagation. One is zero-padding to make sure that the calculation window is wide enough, but it leads to a huge calculation burden. The other is a method called band-limited angular spectrum (BLAS), in which the transfer function is truncated and results in that the calculation accuracy decreases as the propagation distance increases. In this paper, a new method called modified scaling angular spectrum (MSAS) to solve the problem for long-distance propagation is proposed. A scaling factor is introduced in MSAS so that the sampling interval of the input plane can be adjusted arbitrarily unlike AS whose sampling interval is restricted by the detector's pixel size. The sampling interval of the input plane is larger than the detector's pixel size so the size of calculation window suitable for long-distance field propagation in the input plane is smaller than the size of the calculation window required by the zero-padding. Therefore, the method reduces the calculation redundancy and improves the calculation speed. The results from simulations and experiments show that MSAS has a good signal-to-noise ratio (SNR), and the calculation accuracy of MSAS is better than BLAS.

Bidirectional highly-efficient quantum routing in a T-bulge-shaped waveguide Suggested by editors

Jia-Hao Zhang(张家豪), Da-Yong He(何大永), Gang-Yin Luo(罗刚银), Bi-Dou Wang(王弼陡), and Jin-Song Huang(黄劲松)

Chin. Phys. B, 2021, 30 (3): 034204. DOI: 10.1088/1674-1056/abd38c

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Quantum routing in a T-bulge-shaped waveguide system coupled with a driven cyclic three-level atom and a two-level atom is investigated theoretically. By employing the discrete-coordinate scattering method, exact expressions of the transport coefficients along three ports of the waveguide channels are derived. Our results show that bidirectional high transfer-rate single-photon routing between two channels can be effectively implemented, with the help of the effective potential generated by two atoms and the external driving. Moreover, multiple band zero-transmission emerges in the scattering spectra, arising from the quantum interferences among photons scattered by the boundary and the bulged resonators. The proposed system may suggest an efficient duplex router with filtering functions.

Dissipative dynamics of an entangled three-qubit system via non-Hermitian Hamiltonian: Its correspondence with Markovian and non-Markovian regimes

M Rastegarzadeh and M K Tavassoly

Chin. Phys. B, 2021, 30 (3): 034205. DOI: 10.1088/1674-1056/abc2c3

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We investigate an entangled three-qubit system in which only one of the qubits experiences the decoherence effect by considering a non-Hermitian Hamiltonian, while the other two qubits are isolated, i.e., do not interact with environment, directly. Then, the time evolution of the density matrix (for the pure as well as mixed initial density matrix) and the corresponding reduced density matrices are obtained, by which we are able to utilize the dissipative non-Hermitian Hamiltonian model with Markovian and non-Markovian regimes via adjusting the strange of the non-Hermitian term of the total Hamiltonian of the under-considered system.

Comparative study of pulsed laser diode end-pumped thulium-doped 2-μm Q-switched lasers

Ya Wen(温雅), Zhen Fan(范震), Lin-Hao Shang(尚林浩), Guang-Yong Jin(金光勇), Wang Chao(王超), Xin-Yu Chen(陈薪羽), and Chun-Ting Wu(吴春婷)

Chin. Phys. B, 2021, 30 (3): 034206. DOI: 10.1088/1674-1056/abca21

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We report pulsed laser diode (LD) end-pumped acoustic Q-switched Tm:YAG laser, Tm:LuAG laser, and Tm:LuYAG laser and the physical properties and spectra of Tm:YAG, Tm:LuAG, and Tm:LuYAG are analyzed. The Tm:LuYAG laser is pumped by 785-nm and 788-nm pulses separately, and is compared with Tm:YAG laser. Different output energy values and output wavelengths of Tm:LuAYG lasers pumped by LDs with different wavelengths are obtained and compared with each other. When the repetition frequency is 100 Hz, the pulsed Tm:YAG laser has single pulse energy of 15.9 mJ, pulse width of 126.7 ns, and the center wavelength of 2013.36 nm, and the pulsed Tm:LuAG laser possesses single pulse energy of 11.8 mJ, pulse width of 252.4 ns, and the center wavelength of 2023.65 nm, and the pulsed Tm:LuYAG laser output energy values are 12.32 mJ and 12.25 mJ with the slope efficiencies of 12.5% and 11.85%, the center wavelengths of 2017.89 nm and 2027.11 nm, respectively, while the pump sources are 785-nm and 788-nm pulsed LDs, respectively.

Nonlinear spectroscopy of three-photon excitation of cesium Rydberg atoms in vapor cell

Jiabei Fan(樊佳蓓), Yunhui He(何云辉), Yuechun Jiao(焦月春), Liping Hao(郝丽萍), Jianming Zhao(赵建明), and Suotang Jia(贾锁堂)

Chin. Phys. B, 2021, 30 (3): 034207. DOI: 10.1088/1674-1056/abca25

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We present nonlinear spectra of four-level ladder cesium atoms employing 6S_1/2 $\rightarrow$ 6P_3/2$\rightarrow$ 7S_1/2 $\rightarrow$ 30P_3/2 scheme of a room temperature vapor cell. A coupling laser drives Rydberg transition, a dressing laser couples two intermediate levels, and a probe laser optically probes the nonlinear spectra via electromagnetically induced transparency (EIT). Nonlinear spectra are detected as a function of coupling laser frequency. The observed spectra exhibit an enhanced absorption (EA) signal at coupling laser resonance to Rydberg transition and enhanced transmission (ET) signals at detunings to the transition. We define the enhanced absorption (transmission) strength, H_EA (H_ET), and distance between two ET peaks, γ_ET, to describe the spectral feature of the four-level atoms. The enhanced absorption signal H_EA is found to have a maximum value when we vary the dressing laser Rabi frequency $\varOmega_\rm d$, corresponding Rabi frequency is defined as a separatrix point, $\varOmega_\rm d_\rm Se$. The values of $\varOmega_\rm d_\rm Se$ and further $\eta=\varOmega_\rm d_\rm Se/\varOmega_\rm c$ are found to depend on the probe and coupling Rabi frequency but not the atomic density. Based on $\varOmega_\rm d_\rm Se$, the spectra can be separated into two regimes, weak and strong dressing ranges, $\varOmega_\rm d$ $\lesssim$ $\varOmega_\rm d_\rm Se$ and $\varOmega_\rm d$ $\gtrsim$ $\varOmega_\rm d_\rm Se$, respectively. The spectroscopies display different features at these two regimes. A four-level theoretical model is developed that agrees well with the experimental results in terms of the probe-beam absorption behavior of Rabi frequency-dependent dressed states.

Polarization manipulation of bright-dark vector bisolitons Suggested by editors

Yan Zhou(周延), Xiaoyan Lin(林晓艳), Meisong Liao(廖梅松), Guoying Zhao(赵国营), and Yongzheng Fang(房永征)

Chin. Phys. B, 2021, 30 (3): 034208. DOI: 10.1088/1674-1056/abd76d

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We simulate the polarization manipulation of bright-dark vector bisolitons at 1-μ m wavelength regime. Through changing the pulse parameters, different kinds of pulse shapes and optical spectra are generated in output orthogonal polarization directions. When the input vector bisoliton is polarization-locked with 1064 nm central wavelength, "1+1" fundamental dark-dark and "2+1" pseudo-high-order bright-dark group-velocity-locked vector solitons can be achieved through changing the projection angle. When the input vector bisoliton is group-velocity-locked with 1063 nm and 1065 nm central wavelengths, "2+1" and "2+2" pseudo-high-order bright-dark group-velocity-locked vector solitons, bright-dark group-velocity-locked vector solitons with chirp-like temporal oscillations are generated. Our simulation results can provide beneficial conduct for polarization manipulation of vector multi-solitons, and have promising applications in quantum information register, optical communications, nanophotonics, and all-optical switching.

Controlling multiple optomechanically induced transparency in the distant cavity-optomechanical system

Rui-Jie Xiao(肖瑞杰), Gui-Xia Pan(潘桂侠), and Xiao-Ming Xiu(修晓明)

Chin. Phys. B, 2021, 30 (3): 034209. DOI: 10.1088/1674-1056/abc7a4

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We theoretically investigate a two-cavity optomechanical system in which each optical cavity couples to a mechanical resonator via radiation pressure force, and the two optical cavities couple to each other via a distant waveguide. Our study shows that the multiple optomechanically induced transparency can be observed from the output field at the probe frequency. The number and width of the transparent windows can be tuned by the classical driving power P_l. We also analyze the distance of the two outermost transparency windows, which shows a linear relation with the parameters P_l and Λ. Our approach is feasible for controlling multipartite induced transparency, which represents a valuable step towards quantum networks with photonic and phononic circuits.

Design and fabrication of GeAsSeS chalcogenide waveguides with thermal annealing

Limeng Zhang(张李萌), Jinbo Chen(陈锦波), Jierong Gu(顾杰荣), Yixiao Gao(高一骁), Xiang Shen(沈祥), Yimin Chen(陈益敏), and Tiefeng Xu(徐铁峰)

Chin. Phys. B, 2021, 30 (3): 034210. DOI: 10.1088/1674-1056/abd757

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We reported a chalcogenide glass-based rib waveguide fabricated using photolithography and dry etching method. A commercial software (COMSOL Multiphysics) was used to optimize the waveguide structure and the distribution of the fundamental modes in the waveguide based on the complete vector finite component. We further employed thermal annealing to optimize the surface and sidewalls of the rib waveguides. It was found that the optimal annealing temperature for GeAsSeS films is 220 ^°C, and the roughness of the films could be significantly reduced by annealing. The zero-dispersion wavelength (ZDW) could be shifted to a short wavelength around ∼ 2.1 μ m via waveguide structural optimization, which promotes supercontinuum generation with a short wavelength pump laser source. The insertion loss of the waveguides with cross-sectional areas of 4.0 μ m× 3.5 μ m and 6.0 μ m× 3.5 μ m was measured using lens fiber and the cut-back method. The propagation loss of the 220 ^°C annealed waveguides could be as low as 1.9 dB/cm at 1550 nm.

Beam steering characteristics in high-power quantum-cascade lasers emitting at ∼4.6 μ m Suggested by editors

Yong-Qiang Sun(孙永强), Jin-Chuan Zhang(张锦川), Feng-Min Cheng(程凤敏), Chao Ning(宁超), Ning Zhuo(卓宁), Shen-Qiang Zhai(翟慎强), Feng-Qi Liu(刘峰奇), Jun-Qi Liu(刘俊岐), Shu-Man Liu(刘舒曼), and Zhan-Guo Wang(王占国)

Chin. Phys. B, 2021, 30 (3): 034211. DOI: 10.1088/1674-1056/abd6fe

Abstract ( 438 )

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A beam steering effect of high-power quantum cascade (QC) lasers emitting at ∼ 4.6 μ m was investigated. The continuous wave (CW) output power of an uncoated, 6-mm-long, 7.5-μ m-wide buried-heterostructure QC laser at 25 ^°C was as high as 854.2 mW. The maximum beam steering angle was offset by 14.2^° from the facet normal (0^°) in pulsed mode. The phenomenon was judged explicitly by combining the diffraction limit theory and Fourier transform of the spectra. It was also verified by finite element method software simulation and the calculation of two-dimensional (2D) effective-index model. The observed steering is consistent with a theory for coherence between the two lowest order lateral modes. Therefore, we have established an intrinsic linkage between the spectral instabilities and the beam steering by using the Fourier transform of the spectra, and further presented an extremely valid method to judge the beam steering. The content of this method includes both three equidistant peak positions in the Fourier transform of the spectra and the beam quality located between once the diffraction limit (DL) and twice the DL.

First-principles analysis of phonon thermal transport properties of two-dimensional WS₂/WSe₂ heterostructures

Zheng Chang(常征), Kunpeng Yuan(苑昆鹏), Zhehao Sun(孙哲浩), Xiaoliang Zhang(张晓亮), Yufei Gao(高宇飞), Xiaojing Gong(弓晓晶), and Dawei Tang(唐大伟)

Chin. Phys. B, 2021, 30 (3): 034401. DOI: 10.1088/1674-1056/abd2a6

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The van der Waals (vdW) heterostructures of bilayer transition metal dichalcogenide obtained by vertically stacking have drawn increasing attention for their enormous potential applications in semiconductors and insulators. Here, by using the first-principles calculations and the phonon Boltzmann transport equation (BTE), we studied the phonon transport properties of WS₂/WSe₂ bilayer heterostructures (WS₂/WSe₂-BHs). The lattice thermal conductivity of the ideal WS₂/WSe₂-BHs crystals at room temperature (RT) was 62.98 W/mK, which was clearly lower than the average lattice thermal conductivity of WS₂ and WSe₂ single layers. Another interesting finding is that the optical branches below 4.73 THz and acoustic branches have powerful coupling, mainly dominating the lattice thermal conductivity. Further, we also noticed that the phonon mean free path (MFP) of the WS₂/WSe₂-BHs (233 nm) was remarkably attenuated by the free-standing monolayer WS₂ (526 nm) and WSe₂ (1720 nm), leading to a small significant size effect of the WS₂/WSe₂-BHs. Our results systematically demonstrate the low optical and acoustic phonon modes-dominated phonon thermal transport in heterostructures and give a few important guidelines for the synthesis of van der Waals heterostructures with excellent phonon transport properties.

Modeling and analysis of car-following behavior considering backward-looking effect

Dongfang Ma(马东方), Yueyi Han(韩月一), Fengzhong Qu(瞿逢重), and Sheng Jin(金盛)

Chin. Phys. B, 2021, 30 (3): 034501. DOI: 10.1088/1674-1056/abc3b3

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The car-following behavior can be influenced by its driver's backward-looking effect. Especially in traffic congestion, if vehicles adjust the headway by considering backward-looking effect, the stability of traffic flow can be enhanced. A model of car-following behavior considering backward-looking effect was built using visual information as a stimulus. The critical stability conditions were derived by linear and nonlinear stability analyses. The results of parameter sensitivity analysis indicate that the stability of traffic flow was enhanced by considering the backward-looking effect. The spatiotemporal evolution of traffic flow of different truck ratios and varying degrees of backward-looking effect was determined by numerical simulation. This study lays a foundation for exploring the complex feature of car-following behavior and making the intelligent network vehicles control rules more consistent with human driver habits.

Leakage of an eagle flight feather and its influence on the aerodynamics

Di Tang (唐迪), Dawei Liu(刘大伟), Yin Yang(杨茵), Yang Li(李阳), Xipeng Huang(黄喜鹏), and Kai Liu(刘凯)

Chin. Phys. B, 2021, 30 (3): 034701. DOI: 10.1088/1674-1056/abc3b6

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We investigate how the barb of bird feathers is changed along both the rachis and barb. To investigate the microstructures and the mechanical behaviors of barbs, a series of barbs are manually cut from an eagle's primary feather to observe the cross sections. A Λ -like cross section with a tiny hook is observed at the right feet at each section. Afterwards, a measurement of the setup system is developed to evaluate the leakage ratio of a feather followed by a numerical predicting approach based on the CFD method. It is found that the air leakage increases linearly against the pressure, and the predicted results coincide well with the experimental results. Finally, the influences of leakage of the flight feather on both steady and unsteady aerodynamics are studied.

Flow separation control over an airfoil using continuous alternating current plasma actuator

Jian-Guo Zheng(郑建国)

Chin. Phys. B, 2021, 30 (3): 034702. DOI: 10.1088/1674-1056/abd466

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The flow separation control over an NACA 0015 airfoil using continuous alternating current (AC) dielectric barrier discharge (DBD) plasma actuator is investigated experimentally and numerically. This work is intended to report some observations made from our experiment, to which little attention is paid in the previous studies, but which is thought to be important to the understanding of control of complex flow separation with AC DBD. To this end, the response of separated flow to AC plasma actuation is visualized through the time-resolved particle image velocimetry (PIV) measurement, whereas numerical simulation is carried out to complement the experiment. The flow control process at chord-based Reynolds number (Re) of 3.31 × 10⁵ is investigated. It is found that the response of external flow to plasma forcing is delayed for up to tens of milliseconds and the delay time increases with angle of attack increasing. Also observed is that at the intermediate angle of attack near stall, the forced flow features a well re-organized flow pattern. However, for airfoil at high post-stall angle of attack, the already well suppressed flow field can recover to the massively separated flow state and then reattach to airfoil surface with the flow pattern fluctuating between the two states in an irregular manner. This is contrary to one's first thought that the forced flow at any angles of attack will become well organized and regular, and reflects the complexity of flow separation control.

Influence of uniform momentum zones on frictional drag within the turbulent boundary layer Suggested by editors

Kangjun Wang(王康俊) and Nan Jiang(姜楠)

Chin. Phys. B, 2021, 30 (3): 034703. DOI: 10.1088/1674-1056/abc7a6

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Based on a set of experimental databases of turbulent boundary layers obtained from particle image velocimetry in the streamwise-wall-normal plane at friction-velocity-based Reynolds number Re_τ=612, the influence of uniform momentum zones (UMZs) on the skin-friction drag is investigated. The skin-friction drag is measured by the single-pixel ensemble correlation method. The results show that the velocity fields with the number of UMZs larger than the mean value have a relatively low skin-friction drag, while the velocity fields with the number of UMZs less than the mean value have a relatively high skin-friction drag. By analyzing the statistical characteristics of UMZs, the dynamic correlation between the UMZs and skin-friction drag is explored. The velocity fields with a low number of UMZs present a sweep event. These sweep motions intensify the small-scale Reynolds shear stress in the near-wall region by modulation effects. The enhancement of small-scale Reynolds shear stress is the direct reason for the high skin-friction drag. Increasing the proportion of velocity fields with high UMZs amount may be a direction to reduce the skin-friction drag within the TBL.

Particle-in-cell simulation of ion-acoustic solitary waves in a bounded plasma Suggested by editors

Lin Wei(位琳), Bo Liu(刘博), Fang-Ping Wang(王芳平), Heng Zhang(张恒), and Wen-Shan Duan(段文山)

Chin. Phys. B, 2021, 30 (3): 035201. DOI: 10.1088/1674-1056/abccb1

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We study some nonlinear waves in a viscous plasma which is confined in a finite cylinder. By averaging the physical quantities on the radial direction in some cases, we reduce this system to a simple one-dimensional model. It seems that the effects of the bounded geometry (the radius of the cylinder in this case) can be included in the damping coefficient. We notice that the amplitudes of both Korteweg-de Vries (KdV) solitary waves and dark envelope solitary waves decrease exponentially as time increases from the particle-in-cell (PIC) simulation. The dependence of damping coefficient on the cylinder radius and the viscosity coefficient is also obtained numerically and analytically. Both are in good agreement. By using a definition, we give a condition whether a solitary wave exists in a bounded plasma. Moreover, some of potential applications in laboratory experiments are suggested.

Measurement of electronegativity during the E to H mode transition in a radio frequency inductively coupled Ar/O₂ plasma Suggested by editors

Peng-Cheng Du(杜鹏程), Fei Gao(高飞, Xiao-Kun Wang(王晓坤), Yong-Xin Liu(刘永新), and You-Nian Wang(王友年)

Chin. Phys. B, 2021, 30 (3): 035202. DOI: 10.1088/1674-1056/abccb0

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This paper presents the evolution of the electronegativity with the applied power during the E to H mode transition in a radio frequency (rf) inductively coupled plasma (ICP) in a mixture of Ar and O₂. The densities of the negative ion and the electron, as well as their ratio, i.e., the electronegativity, are measured as a function of the applied power by laser photo-detachment combined with a microwave resonance probe, under different pressures and O₂ contents. Meanwhile, the optical emission intensities at Ar 750.4 nm and O 844.6 nm are monitored via a spectrograph. It was found that by increasing the applied power, the electron density and the optical emission intensity show a similar trench, i.e., they increase abruptly at a threshold power, suggesting that the E to H mode transition occurs. With the increase of the pressure, the negative ion density presents opposite trends in the E-mode and the H-mode, which is related to the difference of the electron density and energy for the two modes. The emission intensities of Ar 750.4 nm and O 844.6 nm monotonously decrease with increasing the pressure or the O₂ content, indicating that the density of high-energy electrons, which can excite atoms, is monotonically decreased. This leads to an increase of the negative ion density in the H-mode with increasing the pressure. Besides, as the applied power is increased, the electronegativity shows an abrupt drop during the E-to H-mode transition.

Influence of sub-bandgap illumination on space charge distribution in CdZnTe detector

Rongrong Guo(郭榕榕, Jinhai Lin(林金海), Lili Liu(刘莉莉), Shiwei Li(李世韦), Chen Wang(王尘), Feibin Xiong(熊飞兵), and Haijun Lin(林海军)

Chin. Phys. B, 2021, 30 (3): 036101. DOI: 10.1088/1674-1056/abc67e

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\baselineskip=12.5pt plus.2pt minus.2pt The space charge accumulation in CdZnTe crystals seriously affects the performance of high-flux pulse detectors. The influence of sub-bandgap illumination on the space charge distribution and device performance in CdZnTe crystals were studied theoretically by Silvaco TCAD software simulation. The sub-bandgap illumination with a wavelength of 890 nm and intensity of 8× 10^-8 W/cm² were used in the simulation to explore the space charge distribution and internal electric field distribution in CdZnTe crystals. The simulation results show that the deep level occupation faction is manipulated by the sub-bandgap illumination, thus space charge concentration can be reduced under the bias voltage of 500 V. A flat electric field distribution is obtained, which significantly improves the charge collection efficiency of the CdZnTe detector. Meanwhile, premised on the high resistivity of CdZnTe crystal, the space charge concentration in the crystal can be further reduced with the wavelength of 850 nm and intensity of 1× 10^-7 W/cm² illumination. The electric field distribution is flatter and the carrier collection efficiency of the device can be improved more effectively.

Comparison of helium bubble formation in F82H, ODS, SIMP and T91 steels irradiated by Fe and He ions simultaneously

Bingsheng Li(李炳生), Zhen Yang(杨振), Shuai Xu(徐帅), Kongfang Wei (魏孔芳), Zhiguang Wang(王志光), Tielong Shen(申铁龙), Tongmin Zhang(张桐民), and Qing Liao(廖庆)

Chin. Phys. B, 2021, 30 (3): 036102. DOI: 10.1088/1674-1056/abc2b4

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Ferritic-martensitic steels and ODS steels are attractive candidates for structural materials in advanced nuclear-power systems due to their good swelling resistance. Four kinds of steels, F82H, 15Cr-ODS, SIMP and T91, are investigated in this study. We take 6.4 MeV Fe³⁺ ions and energy-degraded 1.0 MeV He⁺ ions in the irradiation of these materials to 5 dpa and 60 appm He/dpa, 200 appm He/dpa and 600 appm He/dpa at 300 ^°C and 450 ^°C, respectively. The bubble formation and distribution are investigated by transmission electron microscopy (TEM). Formation and distribution of the bubbles in the four investigated steels are compared. The influence of irradiation temperature and helium injection ratio on bubble formation is discussed. It is found that there appears to be homogenously distributed bubbles at 300 ^°C irradiation while heterogeneously distributed bubbles at 450 ^°C irradiation.

Neutron-induced single event upset simulation in Geant4 for three-dimensional die-stacked SRAM

Li-Hua Mo(莫莉华), Bing Ye(叶兵), Jie Liu(刘杰), Jie Luo(罗捷), You-Mei Sun(孙友梅), Chang Cai(蔡畅), Dong-Qing Li(李东青), Pei-Xiong Zhao(赵培雄), and Ze He(贺泽)

Chin. Phys. B, 2021, 30 (3): 036103. DOI: 10.1088/1674-1056/abccb3

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Three-dimensional integrated circuits (3D ICs) have entered into the mainstream due to their high performance, high integration, and low power consumption. When used in atmospheric environments, 3D ICs are irradiated inevitably by neutrons. In this paper, a 3D die-stacked SRAM device is constructed based on a real planar SRAM device. Then, the single event upsets (SEUs) caused by neutrons with different energies are studied by the Monte Carlo method. The SEU cross-sections for each die and for the whole three-layer die-stacked SRAM device is obtained for neutrons with energy ranging from 1 MeV to 1000 MeV. The results indicate that the variation trend of the SEU cross-section for every single die and for the entire die-stacked device is consistent, but the specific values are different. The SEU cross-section is shown to be dependent on the threshold of linear energy transfer ($\mathrmLET_\rm th$) and thickness of the sensitive volume ($\mathrmT_\rm sv$). The secondary particle distribution and energy deposition are analyzed, and the internal mechanism that is responsible for this difference is illustrated. Besides, the ratio and patterns of multiple bit upset (MBU) caused by neutrons with different energies are also presented. This work is helpful for the aerospace IC designers to understand the SEU mechanism of 3D ICs caused by neutrons irradiation.

Glassy dynamics of model colloidal polymers: Effect of controlled chain stiffness Suggested by editors

Jian Li(李健), Bo-kai Zhang(张博凯), and Yu-Shan Li(李玉山)

Chin. Phys. B, 2021, 30 (3): 036104. DOI: 10.1088/1674-1056/abd6f8

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Colloidal polymers with tunable chain stiffness have been successfully assembled in experiments recently. Similar to molecular polymers, chain stiffness is an important feature which can distinctly affect the dynamical behaviors of colloidal polymers. Hence, we model colloidal polymers with controlled chain stiffness and study the effect of chain stiffness on glassy behaviors. For stiff chains, there are long-ranged periodic intrachain correlations besides two incompatible local length scales, i.e., monomer size and bond length. The mean square displacement of monomers exhibits sub-diffusion at intermediate time/length scale and the sub-diffusive exponent increases with chain stiffness. The data of localization length of stiff polymers versus rescaled volume fraction for different monomer sizes can gather close to an exponential curve and decay slower than those of flexible polymers. The increase of chain stiffness linearly increases the activation energy of the colloidal-polymer system and thus makes the colloidal polymers vitrify at lower volume fraction. Static and dynamic equivalences between stiff colloidal polymers of different monomer sizes have been checked.

Enhanced hyperthermia performance in hard-soft magnetic mixed Zn_0.5Co_xFe_2.5-xO₄/SiO₂ composite magnetic nanoparticles

Xiang Yu(俞翔, Li-Chen Wang(王利晨, Zheng-Rui Li(李峥睿, Yan Mi(米岩), Di-An Wu(吴迪安), and Shu-Li He(贺淑莉)

Chin. Phys. B, 2021, 30 (3): 036201. DOI: 10.1088/1674-1056/abc67c

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High quality Zn_0.5Co_xFe_2.5-xO₄ (x = 0, 0.05, 0.1, 0.15) serial magnetic nanoparticles with single cubic structures were prepared by the modified thermal decomposition method, and Zn_0.5Co_xFe_2.5-xO₄/SiO₂ composite magnetic nanoparticles were prepared by surface modification of SiO₂. The magnetic anisotropy of the sample increases with the increase of the doping amount of Co²⁺. When the doping amount is 0.1, the sample shows the transition from superparamagnetism to ferrimagnetism at room temperature. In the Zn_0.5Co_xFe_2.5-xO₄/SiO₂ serial samples, the maximum value of specific loss power (SLP) with 1974 W/g_metal can also be found at doping amount of x = 0.1. The composite nanoparticles are expected to be an excellent candidate for clinical magnetic hyperthermia.

Structural, mechanical, electronic properties, and Debye temperature of quaternary carbide Ti₃NiAl₂C ceramics under high pressure: A first-principles study

Diyou Jiang(姜迪友), Wenbo Xiao(肖文波), and Sanqiu Liu(刘三秋)

Chin. Phys. B, 2021, 30 (3): 036202. DOI: 10.1088/1674-1056/abca20

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Quaternary carbide Ti₃NiAl₂C ceramics has been investigated as a potential nuclear fusion structural material, and it has advantages in certain aspects compared with Ti₂AlC, Ti₃AlC₂, and Ti₃SiC₂ structural materials. In this paper, quaternary carbide Ti₃NiAl₂C ceramics is pressurized to investigate its structural, mechanical, electronic properties, and Debye temperature. Quaternary carbide Ti₃NiAl₂C ceramics still maintains a cubic structure under pressure (0-110 GPa). At zero pressure, quaternary carbide Ti₃NiAl₂C ceramics only has three bonds: Ti-Al, Ni-Al, and Ti-C. However, at pressures of 20 GPa, 30 GPa, 40 GPa, 60 GPa, and 70 GPa, new Ti-Ni, Ti-Ti, Al-Al, Ti-Al, and Ti-Ti bonds form. When the pressure reaches 20 GPa, the covalent bonds change to metallic bonds. The volume of quaternary carbide Ti₃NiAl₂C ceramics can be compressed to 72% of its original volume at most. Pressurization can improve the mechanical strength and ductility of quaternary carbide Ti₃NiAl₂C ceramics. At 50-60 GPa, its mechanical strength can be comparable to pure tungsten, and the material changes from brittleness to ductility. However, the degree of anisotropy of quaternary carbide Ti₃NiAl₂C ceramics increases with the increasing pressure. In addition, we also investigated the Debye temperature, density, melting point, hardness, and wear resistance of quaternary carbide Ti₃NiAl₂C ceramics under pressure.

Designing thermal demultiplexer: Splitting phonons by negative mass and genetic algorithm optimization

Yu-Tao Tan(谭宇涛), Lu-Qin Wang(王鲁钦), Zi Wang(王子), Jiebin Peng(彭洁彬), and Jie Ren(任捷)

Chin. Phys. B, 2021, 30 (3): 036301. DOI: 10.1088/1674-1056/abd68b

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We propose the concept of thermal demultiplexer, which can split the heat flux in different frequency ranges into different directions. We demonstrate this device concept in a honeycomb lattice with dangling atoms. From the view of effective negative mass, we give a qualitative explanation of how the dangling atoms change the original transport property. We first design a two-mass configuration thermal demultiplexer, and find that the heat flux can flow into different ports in corresponding frequency ranges roughly. Then, to improve the performance, we choose the suitable masses of dangling atoms and optimize the four-mass configuration with genetic algorithm. Finally, we give out the optimal configuration with a remarkable effect. Our study finds a way to selectively split spectrum-resolved heat to different ports as phonon splitter, which would provide a new means to manipulate phonons and heat, and to guide the design of phononic thermal devices in the future.

Low thermal expansion and broad band photoluminescence of Zr_0.1Al_1.9Mo_2.9V_0.1O₁₂

Jun-Ping Wang(王俊平), Qing-Dong Chen(陈庆东), Li-Gang Chen(陈立刚), Yan-Jun Ji(纪延俊), You-Wen Liu(刘友文), and Er-Jun Liang(梁二军)

Chin. Phys. B, 2021, 30 (3): 036501. DOI: 10.1088/1674-1056/abcf39

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A new material of Zr_0.1Al_1.9Mo_2.9V_0.1O₁₂ is synthesized by the traditional solid state synthesis method. The phase transition, coefficient of thermal expansion, and luminescence properties of Zr_0.1Al_1.9Mo_2.9V_0.1O₁₂ are explored with Raman spectrometer, dilatometer, and x-ray diffraction (XRD) diffractometer. The results show that the Zr_0.1Al_1.9Mo_2.9V_0.1O₁₂ possesses the strong broad-band luminescence characteristics almost in the whole visible region. The sample is crystallized in a monoclinic structure group of P2₁/a (No. 14) crystallized at room temperature (RT). The crystal is changed from monoclinic to orthorhombic structure when the temperature increases to 463 K. The material has very low thermal expansion performance in a wide temperature range. Its excellent low thermal expansion and strong pale green light properties in a wide temperature range suggest its potential applications in light-emitting diode (LED) and other optoelectronic devices.

Preparation of AlN film grown on sputter-deposited and annealed AlN buffer layer via HVPE Suggested by editors

Di-Di Li(李迪迪), Jing-Jing Chen(陈晶晶), Xu-Jun Su(苏旭军), Jun Huang(黄俊), Mu-Tong Niu(牛牧童), Jin-Tong Xu(许金通), and Ke Xu(徐科)

Chin. Phys. B, 2021, 30 (3): 036801. DOI: 10.1088/1674-1056/abd392

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AlN films grown on sputter-deposited and annealed AlN buffer layer by high temperature hydride vapor phase epitaxy (HVPE) have been fabricated and structurally characterized. The crystalline quality and surface morphology of as-grown AlN films with various V/III ratios were studied and compared. The XRD results showed that the crystalline quality of the AlN film could be optimized when the growth V/III ratio was 150. At the same time, the full width at half-maximum (FWHM) values of (0002)-and (10$\bar1$2)-plane were 64 arcsec and 648 arcsec, respectively. As revealed by AFM, the AlN films grown with higher V/III ratios of 150 and 300 exhibited apparent hillock-like surface structure due to the low density of screw threading dislocation (TD). The defects microstructure and strain field around the HVPE-AlN/sputtered-AlN/sapphire interfaces have been investigated by transmission electron microscopy (TEM) technique combined with geometric phase analysis (GPA). It was found that the screw TDs within AlN films intend to turn into loops or half-loops after originating from the AlN/sapphire interface, while the edge ones would bend first and then reacted with others within a region of 400 nm above the interface. Consequently, part of the edge TDs propagated to the surface vertically. The GPA analysis indicated that the voids extending from sapphire to HVPE-AlN layer were beneficial to relax the interfacial strain of the best quality AlN film grown with a V/III ratio of 150.

Nonlinear photoncurrent in transition metal dichalcogenide with warping term under illuminating of light

Guo-Bao Zhu(朱国宝), Hui-Min Yang(杨慧敏, and Yun-Hai Zhang(张运海)

Chin. Phys. B, 2021, 30 (3): 037301. DOI: 10.1088/1674-1056/abc53c

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We investigate the photoconductivities of injection current and the shift current in transition metal dichalcogenide with warping term in the presence of sublattice potential and spin orbit coupling. The system shows the valley photoconductivities of injection current and the photoconductivities of shift current. It is found that the warping term and the geometric tensor play a critical role in the system, which are responsible for the photoconductivities. Due to the interplay between the sublattice potential and the spin orbit coupling, the photoconductivities can be tuned. Furthermore, the effect of warping term on geometric tensor and the amplitude of the photoconductivities are also discussed.

Controlling the entropic uncertainty and quantum discord in two two-level systems by an ancilla in dissipative environments

Rong-Yu Wu(伍容玉) and Mao-Fa Fang(方卯发)

Chin. Phys. B, 2021, 30 (3): 037302. DOI: 10.1088/1674-1056/abc54d

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The uncertainty principle is a crucial aspect of quantum mechanics. It has been shown that the uncertainty principle can be tightened by quantum discord and classical correlation in the presence of quantum memory. We investigate the control of the entropic uncertainty and quantum discord in two two-level systems by an ancilla in dissipative environment. Our results show that the entropic uncertainty of an observed system can be reduced and the quantum discord between the observed system and the quantum memory system can be enhanced in the steady state of the system by adding an dissipative ancilla. Particularly, via preparing the state of the system to the highest excited state with hight fidelity, the entropic uncertainty can be reduced markedly and the quantum discord can be enhanced obviously. We explain these results using the definition of state fidelity. Furthermore, we present an effective strategy to further reduce the the entropic uncertainty and to enhance the the quantum discord via quantum-jump-based feedback control. Therefore, our results may be of importance in the context of quantum information technologies.

High-performing silicon-based germanium Schottky photodetector with ITO transparent electrode Suggested by editors

Zhiwei Huang(黄志伟), Shaoying Ke(柯少颖), Jinrong Zhou(周锦荣), Yimo Zhao(赵一默), Wei Huang(黄巍), Songyan Chen(陈松岩), and Cheng Li(李成)

Chin. Phys. B, 2021, 30 (3): 037303. DOI: 10.1088/1674-1056/abd46b

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A near-infrared germanium (Ge) Schottky photodetector (PD) with an ultrathin silicon (Si) barrier enhancement layer between the indium-doped tin oxide (ITO) electrode and Ge epilayer on Si or silicon-on-insulator (SOI) is proposed and fabricated. The well-behaved ITO/Si cap/Ge Schottky junctions without intentional doping process for the Ge epilayer are formed on the Si and SOI substrates. The Si-and SOI-based ITO/Si cap/Ge Schottky PDs exhibit low dark current densities of 33 mA/cm² and 44 mA/cm², respectively. Benefited from the high transmissivity of ITO electrode and the reflectivity of SOI substrate, an optical responsivity of 0.19 A/W at 1550 nm wavelength is obtained for the SOI-based ITO/Si cap/Ge Schottky PD. These complementary metal-oxide-semiconductor (CMOS) compatible Si (or SOI)-based ITO/Si cap/Ge Schottky PDs are quite useful for detecting near-infrared wavelengths with high efficiency.

Enhanced thermoelectric properties in two-dimensional monolayer Si₂BN by adsorbing halogen atoms

Cheng-Wei Wu(吴成伟), Changqing Xiang(向长青), Hengyu Yang(杨恒玉), Wu-Xing Zhou(周五星), Guofeng Xie(谢国锋), Baoli Ou(欧宝立), and Dan Wu(伍丹)

Chin. Phys. B, 2021, 30 (3): 037304. DOI: 10.1088/1674-1056/abd163

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Using the first principles calculation and Boltzmann transport theory, we study the thermoelectric properties of Si₂BN adsorbing halogen atoms (Si₂BN-4X, $X=\textF$, Cl, Br, and I). The results show that the adsorption of halogen atoms can significantly regulate the energy band structure and lattice thermal conductivity of Si₂BN. Among them, Si₂BN-4I has the best thermoelectric performance, the figure of merit can reach 0.50 K at 300 K, which is about 16 times greater than that of Si₂BN. This is because the adsorption of iodine atoms not only significantly increases the Seebeck coefficient due to band degeneracy, but also rapidly reduces the phonon thermal conductivity by enhancing phonon scattering. Our work proves the application potential of Si₂BN-based crystals in the field of thermoelectricity and the effective method for metal crystals to open bandgaps by adsorbing halogens.

Critical behavior and effect of Sr substitution in double perovskite Ca₂CrSbO₆

Yuan-Yuan Jiao(焦媛媛), Jian-Ping Sun(孙建平), and Qi Cui(崔琦)

Chin. Phys. B, 2021, 30 (3): 037501. DOI: 10.1088/1674-1056/abc67b

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The double perovskite Ca₂CrSbO₆ exhibits a ferromagnetic long-range order below T_c = 13 K and a saturation magnetization of 2.35 μ _B at 2 K. In this study, the polycrystalline Ca₂CrSbO₆ is synthesized under high pressure and high temperature, and the critical behavior of the ferromagnetic material as well as the effects of the magnetic behavior due to the isovalent substitution of Sr^{2 +} for Ca^{2 +} is investigated. Also studied are the ferromagnetic criticality of the double perovskite Ca₂CrSbO₆ at the ferromagnetic transition temperature T_c ≈ 12.6 K from the isotherms of magnetization M(H) via an iteration process and the Kouvel-Fisher method. The critical exponents associated with the transition are determined as follows: β = 0.322, γ = 1.241, and δ = 4.84. The magnetization data in the vicinity of T_c can be scaled into two universal curves in the plot of $M/\vert \varepsilon \vert ^\beta $ versus $H/\vert \varepsilon \vert ^\beta + \gamma $, where ε =T/T_c-1. The obtained β and γ values are consistent with the predicted values from a three-dimensional Ising model. The effects of Sr substitution on the double perovskite Ca₂CrSbO₆ are taken into consideration. As the Sr content increases, the (Ca_{2 -x}Sr_x)CrSbO₆ polycrystal shows a continuous switch from ferromagnetic to antiferromagnetic behavior.

Angular control of multi-mode resonance frequencies in obliquely deposited CoZr thin films with rotatable stripe domains

Chao-Zhong Li(李超众), Chang-Jun Jiang(蒋长军), and Guo-Zhi Chai(柴国志)

Chin. Phys. B, 2021, 30 (3): 037502. DOI: 10.1088/1674-1056/abccb4

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We investigate the angular-dependent multi-mode resonance frequencies in CoZr magnetic thin films with a rotatable stripe domain structure. A variable range of multi-mode resonance frequencies from 1.86 GHz to 4.80 GHz is achieved by pre-magnetizing the CoZr films along different azimuth directions, which can be ascribed to the competition between the uniaxial anisotropy caused by the oblique deposition and the rotatable anisotropy induced by the rotatable stripe domain. Furthermore, the regulating range of resonance frequency for the CoZr film can be adjusted by changing the oblique deposition angle. Our results might be beneficial for the applications of magnetic thin films in microwave devices.

Enhanced spin-orbit torque efficiency in Pt_100-xNi_x alloy based magnetic bilayer ^Hot!

Congli He(何聪丽), Qingqiang Chen(陈庆强), Shipeng Shen(申世鹏), Jinwu Wei(魏晋武), Hongjun Xu(许洪军), Yunchi Zhao(赵云驰), Guoqiang Yu(于国强), and Shouguo Wang(王守国)

Chin. Phys. B, 2021, 30 (3): 037503. DOI: 10.1088/1674-1056/abe3f4

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The binary alloy/ferromagnetic metal heterostructure has drawn extensive attention in the research field of spin-orbit torque (SOT) due to the potential enhancement of SOT efficiency via composition engineering. In this work, the magnetic properties and SOT efficiency in the Pt_100-xNi_x/Ni₇₈Fe₂₂ bilayers were investigated via the spin-torque ferromagnetic resonance (ST-FMR) technique. The effective magnetic anisotropy field and effective damping constant extracted by analyzing the ST-FMR spectra show a weak dependence on the Ni concentration. The effective spin-mixing conductance of $8.40\times 10^14 \Omega ^-1\cdot\rm m^-2$ and the interfacial spin transparency T_in of 0.59 were obtained for the sample of Pt₇₀Ni₃₀/NiFe bilayer. More interestingly, the SOT efficiency that is carefully extracted from the angular dependence of ST-FMR spectra shows a nonmonotonic dependence on the Ni concentration, which reaches the maximum at x = 18. The enhancement of the SOT efficiency by alloying the Ni with Pt shows potential in lowering the critical switching current. Moreover, alloying relatively cheaper Ni with Pt may promote to reduce the cost of SOT devices.

Determination of charge-compensated C_3v (II) centers for Er³⁺ ions in CdF₂ and CaF₂ crystals

Rui-Peng Chai(柴瑞鹏), Dan-Hui Hao(郝丹辉), Dang-Li Gao(高当丽), and Qing Pang(庞庆)

Chin. Phys. B, 2021, 30 (3): 037601. DOI: 10.1088/1674-1056/abc3b0

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A unified theoretical method is established to determine the charge-compensated C_3v (II) centers of Er³⁺ ions in CdF₂ and CaF₂ crystals by simulating the electron paramagnetic resonance (EPR) parameters and Stark energy levels. The potential (Er³⁺-F^--$\mathrm{O}_\mathrm4^\mathrm2-$) and (Er³⁺-$\mathrm{F}_\mathrm7^\mathrm-$-O^2-) structures for the C_3v (II) centers of Er³⁺ ions in CdF₂ and CaF₂ crystals are checked by diagonalizing 364×364 complete energy matrices in the scheme of superposition model. Our studies indicate that the C_3v (II) centers of Er³⁺ ions in CdF₂ and CaF₂ may be ascribed to the local (Er³⁺-F^--$\mathrm{O}_\mathrm4^\mathrm2-$) structure, where the upper ligand ion F^- undergoes an off-center displacement by ∆ Z≈ 0.3 Å for CdF₂ and ∆ Z≈ 0.29 Å for the CaF₂ along the C₃ axis. Meanwhile, a local compressed distortion of the (ErFO₄)^6- cluster is expected to be ∆ R≈ 0.07 Å for CdF₂:Er³⁺ and ∆ R≈ 0.079 Å for CaF₂:Er³⁺. The considerable g-factor anisotropy for Er³⁺ ions in each of both crystals is explained reasonably by the obtained local parameters. Furthermore, our studies show that a stronger covalent effect exists in the C_3v (II) center for Er³⁺ in CaF₂ or CaF₂, which may be due to the stronger electrostatic interaction and closer distance between the central Er³⁺ ion and ligand O^2- with the (Er³⁺-F^--$\mathrm{O}_\mathrm4^\mathrm2-$) structure.

Plasmonic properties of graphene on uniaxially anisotropic substrates ^Hot!

Shengchuan Wang(汪圣川), Bin You(游斌), Rui Zhang(张锐), Kui Han(韩奎), Xiaopeng Shen(沈晓鹏, and Weihua Wang(王伟华)

Chin. Phys. B, 2021, 30 (3): 037801. DOI: 10.1088/1674-1056/abd168

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Most of the current graphene plasmonic researches are based on the substrates with isotropic dielectric constant such as silicon. In this work, we investigate optical properties of graphene nanoribbon arrays placed on a uniaxially anisotropic substrate, where the anisotropy provides an additional freedom to tune the behaviors of graphene plasmons, and its effect can be described by a simple effective formula. In practice, the substrates of semi-infinite and finite thickness are discussed by using both the formula and full wave simulations. Particularly, the dielectric constants $\varepsilon_ \parallel $ and $\varepsilon_ \bot $ approaching zero are intensively studied, which show different impacts on the transverse magnetic (TM) surface modes. In reality, the hexagonal boron nitride (hBN) can be chosen as the anisotropic substrate, which is also a hyperbolic material in nature.

Vertical GaN Shottky barrier diode with thermally stable TiN anode

Da-Ping Liu(刘大平), Xiao-Bo Li(李小波), Tao-Fei Pu(蒲涛飞), Liu-An Li(李柳暗), Shao-Heng Cheng(成绍恒), and Qi-Liang Wang(王启亮)

Chin. Phys. B, 2021, 30 (3): 038101. DOI: 10.1088/1674-1056/abc547

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Vertical GaN Schottky barrier diodes with TiN anodes were fabricated to investigate the electrical performance. The turn-on voltage and specific on-resistance of diodes are deduced to be approximately 0.41 V and 0.98 mΩ cm², respectively. The current-voltage curves show rectifying characteristics under different temperatures from 25 ^°C to 200 ^°C, implying a good thermal stability of TiN/GaN contact. The low-frequency noise follows a 1/f behavior due to the multiple traps and/or barrier inhomogeneous at TiN/GaN interface. The trapping/de-trapping between traps and Fermi level causes the slight capacitance dispersion under reverse voltage.

Stability and optoelectronic property of low-dimensional organic tin bromide perovskites

J H Lei(雷军辉), Q Tang(汤琼), J He(何军), and M Q Cai(蔡孟秋)

Chin. Phys. B, 2021, 30 (3): 038102. DOI: 10.1088/1674-1056/abc545

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The toxicity and degradation of hybrid lead-halide perovskites hinder their extensive applications. It is thus of great importance to explore non-toxic alternative materials with excellent stability and optoelectronic property. We investigate the atomic structures and optoelectronic properties of non-toxic organic tin bromide perovskites (OTBP) with one/zero-dimensional (1D/0D) structures by first-principles calculations. The calculated atomic structures show that the 1D/0D OTBPs are stable and the structure of inorganic octahedra in 0D is higher order than that in 1D. Moreover, the origination of exceptional purity emitting light in experiments is explained based on the calculated electronic structure.

Effects of Nb and Mo additions on thermal behavior, microstructure and magnetic property of FeCoZrBGe alloy

Yaming Sun(孙亚明), Zhiqun Wang(王志群), Shi-Chong Xu(徐仕翀), and Zhong Hua(华中)

Chin. Phys. B, 2021, 30 (3): 038103. DOI: 10.1088/1674-1056/abc7a8

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Both Nb and Mo additions play a vital role in FeCo-based alloys and it is crucial to understand their roles and contents on thermal behavior, microstructural feature and magnetic property of alloys. Nanocrystalline alloy ribbons Fe₄₀Co₄₀Zr_9-yM_yB₁₀Ge₁ (y=0-4; M= Nb, Mo) were prepared by crystallizing the as-quenched amorphous alloys. The effects of Nb and Mo additions on structures and properties of the Fe₄₀Co₄₀Zr₉B₁₀Ge₁ alloy are investigated systemically and compared. With increasing Nb or Mo content, the primary crystallization temperature, grain size of α -Fe(Co) phase and coercivity H_c all decrease. Moreover, the effect of Mo addition on thermal behavior, microstructure and magnetic properties of the FeCoZrBGe alloy is greater compared to Nb addition. The gap between primary and secondary crystallization peaks of Mo-containing alloys is wider than that of Nb-containing alloys. Both grain size and H_c of Mo-containing alloys are smaller than those of Nb-containing alloys. For Fe₄₀Co₄₀Zr₉B₁₀Ge₁ alloy, high Mo addition proportion is better compared to high Nb addition proportion.

Weakening effect of plastic yielding inception in thin hard coating systems

Xiao Huang(黄啸), Shujun Zhou(周述军), and Tianmin Shao(邵天敏)

Chin. Phys. B, 2021, 30 (3): 038104. DOI: 10.1088/1674-1056/abc544

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Hard coatings have been widely applied to enhance tribological performance of mechanical components. However, it was predicted that thin hard coatings may have a weakening effect which could reduce the coating/substrate system's resistance to plastic yielding compared with the uncoated substrate material. In this paper, analytical simulation is utilized to investigate the origin of weakening effect. The functions of material mechanical properties and coating thickness on the weakening effect are theoretically investigated. Partial-unloading spherical nanoindentation tests are performed on tungsten coated single crystalline silicon and copper to acquire the stress-strain curves and compared with the uncoated cases. The experimental results are in consistence with the analytical solutions, demonstrating the presence of weakening effect.

Properties of B₄C-TiB₂ ceramics prepared by spark plasma sintering Suggested by editors

Jingzhe Fan(范静哲), Weixia Shen(沈维霞), Zhuangfei Zhang(张壮飞, Chao Fang(房超), Yuewen Zhang(张跃文), Liangchao Chen(陈良超), Qianqian Wang(王倩倩), Biao Wan(万彪), and Xiaopeng Jia(贾晓鹏)

Chin. Phys. B, 2021, 30 (3): 038105. DOI: 10.1088/1674-1056/abd7d8

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By doping titanium hydride (TiH₂) into boron carbide (B₄C), a series of B₄C+x wt% TiH₂ (x = 0, 5, 10, 15, and 20) composite ceramics were obtained through spark plasma sintering (SPS). The effects of the sintering temperature and the amount of TiH₂ additive on the microstructure, mechanical and electrical properties of the sintered B₄C-TiB₂ composite ceramics were investigated. Powder mixtures of B₄C with 0-20 wt% TiH₂ were heated from 1400 ^°C to 1800 ^°C for 20 min under 50 MPa. The results indicated that higher sintering temperatures contributed to greater ceramic density. With increasing TiH₂ content, titanium diboride (TiB₂) formed between the TiH₂ and B₄C matrix. This effectively improved Young's modulus and fracture toughness of the composite ceramics, significantly improving their electrical properties: the electrical conductivity reached 114.9 Scm^-1 at 1800 ^°C when x = 20. Optimum mechanical properties were obtained for the B₄C ceramics sintered with 20 wt% TiH₂, which had a relative density of 99.9 0.1%, Vickers hardness of 31.8 GPa, and fracture toughness of 8.5 MPa m^{1 / 2}. The results indicated that the doping of fine Ti particles into the B₄C matrix increased the conductivity and the fracture toughness of B₄C.

Multi-layer structures including zigzag sculptured thin films for corrosion protection of AISI 304 stainless steel

Fateme Abdi

Chin. Phys. B, 2021, 30 (3): 038106. DOI: 10.1088/1674-1056/abd398

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\baselineskip=12pt plus.2pt minus.2pt To increase corrosion resistance of the sample, its electrical impedance must be increased. Due to the fact that electrical impedance depends on elements such as electrical resistance, capacitance, and inductance, by increasing the electrical resistance, reducing the capacitance and inductance, electrical impedance and corrosion resistance can be increased. Based on the fact that these elements depend on the type of material and the geometry of the material, multilayer structures with different geometries are proposed. For this purpose, conventional multilayer thin films, multilayer thin film including zigzag structure (zigzag 1) and multilayer thin film including double zigzag structure (zigzag 2) of manganese nitride are considered to protect AISI 304 stainless steel against corrosion in salt solution. These multilayer coatings including zigzag structures are prepared by alternately using the conventional deposition of thin film and glancing angle deposition method. After deposition, the samples are placed in a furnace under nitrogen flux for nitriding. The cross sections of the structures are observed by field emission scanning electron microscopy (FESEM). Atomic force microscope (AFM) is used to make surface analyses of the samples. The results show that the multilayer thin films including zigzag structures have smaller grains than conventional multilayer thin films, and the zigzag 2 structure has the smaller grain than the other two samples, which is attributed to the effect of shadowing and porosity on the oblique angle deposition method. Crystallography structures of the samples are studied by using x-ray diffraction (XRD) pattern and the results show that nitride phase formation in zigzag 2 structure is better than that in zigzag 1 structure and conventional multilayer thin film. To investigate the corrosion resistances of the structures, electrochemical impedance spectroscopy (EIS) and potentiodynamic polarization tests are performed. The results reveal that the multilayer thin films with zigzag structures have better corrosion protection than the conventional multilayer thin films, and the zigzag structure 2 has the smallest corrosion current and the highest corrosion resistance. The electrical impedances of the samples are investigated by simulating equivalent circuits. The high corrosion resistance of zigzag 2 structure as compared with conventional multilayer structure and zigzag 1 structure, is attributed to the high electrical impedance of the structure due to its small capacitance and high electrical resistance. Finally, the surfaces of corroded samples are observed by scanning electron microscope (SEM).

Adsorption of propylene carbonate on the LiMn₂O₄ (100) surface investigated by DFT + U calculations Suggested by editors

Wei Hu(胡伟), Wenwei Luo(罗文崴), Hewen Wang(王鹤文), and Chuying Ouyang(欧阳楚英)

Chin. Phys. B, 2021, 30 (3): 038202. DOI: 10.1088/1674-1056/abd77e

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Understanding the mechanism of the interfacial reaction between the cathode material and the electrolyte is a significant work because the interfacial reaction is an important factor affecting the stability, capacity, and cycling performance of Li-ion batteries. In this work, spin-polarized density functional theory calculations with on-site Coulomb energy have been employed to study the adsorption of electrolyte components propylene carbonate (PC) on the LiMn₂O₄ (100) surface. The findings show that the PC molecule prefers to interact with the Mn atom on the LiMn₂O₄ (100) surface via the carbonyl oxygen (O_c), with the adsorption energy of -1.16 eV, which is an exothermic reaction. As the adsorption of organic molecule PC increases the Mn atoms coordination with O atoms on the (100) surface, the Mn^{3 +} ions on the surface lose charge and the reactivity is substantially decreased, which improves the stability of the surface and benefits the cycling performance.

DFT study of solvation of Li⁺/Na⁺ in fluoroethylene carbonate/vinylene carbonate/ethylene sulfite solvents for lithium/sodium-based battery Suggested by editors

Qi Liu(刘琦, Guoqiang Tan(谭国强), Feng Wu(吴锋), Daobin Mu(穆道斌), and Borong Wu(吴伯荣)

Chin. Phys. B, 2021, 30 (3): 038203. DOI: 10.1088/1674-1056/abd763

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Choosing suitable solvent is the key technology for the electrochemical performance of energy storage device. Among them, vinylene carbonate (VC), fluoroethylene carbonate (FEC), and ethylene sulfite (ES) are the potential organic electrolyte solvents for lithium/sodium battery. However, the quantitative relation and the specific mechanism of these solvents are currently unclear. In this work, density functional theory (DFT) method is employed to study the lithium/sodium ion solvation in solvents of VC, ES, and FEC. We first find that 4VC-Li⁺, 4VC-Na⁺, 4ES-Li⁺, 4ES-Na⁺, 4FEC-Li⁺, and 4FEC-Na⁺ are the maximum thermodynamic stable solvation complexes. Besides, it is indicated that the innermost solvation shells are consisted of 5VC-Li⁺/Na⁺, 5ES-Li⁺/Na⁺, and 5FEC-Li⁺/Na⁺. It is also indicated that the Li⁺ solvation complexes are more stable than Na⁺ complexes. Moreover, infrared and Raman spectrum analysis indicates that the stretching vibration of O=\,C peak evidently shifts to high frequency with the Li⁺/Na⁺ concentration reducing in nVC-Li⁺/Na⁺ and nFEC-Li⁺/Na⁺ solvation complexes, and the O=\,C vibration peak frequency in Na⁺ solvation complexes is higher than that of Li⁺ complexes. The S=\,O stretching vibration in nES-Li⁺/Na⁺ solvation complexes moves to high frequency with the decrease of the Li⁺/Na⁺ concentration, the S=\,O vibration in nES-Na⁺ is higher than that in nES-Li⁺. The study is meaningful for the design of new-type Li/Na battery electrolytes.

New DDSCR structure with high holding voltage for robust ESD applications

Zi-Jie Zhou(周子杰), Xiang-Liang Jin(金湘亮), Yang Wang(汪洋), and Peng Dong(董鹏)

Chin. Phys. B, 2021, 30 (3): 038501. DOI: 10.1088/1674-1056/abd38f

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A novel dual direction silicon-controlled rectifier (DDSCR) with an additional P-type doping and gate (APGDDSCR) is proposed and demonstrated. Compared with the conventional low-voltage trigger DDSCR (LVTDDSCR) that has positive and negative holding voltages of 13.371 V and 14.038 V, respectively, the new DDSCR has high positive and negative holding voltages of 18.781 V and 18.912 V in a single finger device, respectively, and it exhibits suitable enough positive and negative holding voltages of 14.60 V and 14.319 V in a four-finger device for 12-V application. The failure current of APGDDSCR is almost the same as that of LVT-DDSCR in the single finger device, and the four-finger APGDDSCR can achieve positive and negative human-body model (HBM) protection capabilities of 22.281 kV and 23.45 kV, respectively, under 40-V voltage of core circuit failure, benefitting from the additional structure. The new structure can generate a snapback voltage on gate A to increase the current gain of the parasitic PNP in holding voltage. Thus, a sufficiently high holding voltage increased by the structure can ensure that a multi-finger device can also reach a sufficient holding voltage, it is equivalent to solving the non-uniform triggering problem of multi-finger device. The operating mechanism and the gate voltage are both discussed and verified in two-dimensional (2D) simulation and experiemnt.

Graphene/SrTiO₃ interface-based UV photodetectors with high responsivity

Heng Yue(岳恒), Anqi Hu(胡安琪), Qiaoli Liu(刘巧莉), Huijun Tian(田慧军), Chengri Hu(胡成日), Xiansong Ren(任显松), Nianyu Chen(陈年域), Chen Ge(葛琛), Kuijuan Jin(金奎娟), and Xia Guo(郭霞)

Chin. Phys. B, 2021, 30 (3): 038502. DOI: 10.1088/1674-1056/abda2e

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Strontium titanate (SrTiO₃), which is a crucial perovskite oxide with a direct energy band gap of 3.2 eV, holds great promise for ultraviolet (UV) photodetection. However, the response performance of the conventional SrTiO₃-based photodetectors is limited by the large relative dielectric constant of the material, which reduces the internal electric field for electron-hole pair separation to form a current collected by electrodes. Recently, graphene/semiconductor hybrid photodetectors by van-der-Waals heteroepitaxy method demonstrate ultrahigh sensitivity, which is benefit from the interface junction architecture and then prolonged lifetime of photoexcited carriers. Here, a graphene/SrTiO₃ interface-based photodetector is demonstrated with an ultrahigh responsivity of 1.2× 10⁶ A/W at the wavelength of 325 nm and ∼ 2.4× 10⁴ A/W at 261 nm. The corresponding response time is in the order of ∼ ms. Compared with graphene/GaN interface junction-based hybrid photodetectors, ∼ 2 orders of magnitude improvement of the ultrahigh responsivity originates from a gain mechanism which correlates with the large work function difference induced long photo-carrier lifetime as well as the low background carrier density. The performance of high responsivity and fast response speed facilitates SrTiO₃ material for further efforts seeking practical applications.

Multi-scale molecular dynamics simulations and applications on mechanosensitive proteins of integrins

Shouqin Lü(吕守芹), Qihan Ding(丁奇寒), Mingkun Zhang(张明焜), and Mian Long(龙勉)

Chin. Phys. B, 2021, 30 (3): 038701. DOI: 10.1088/1674-1056/abc540

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Molecular dynamics simulation (MDS) is a powerful technology for investigating evolution dynamics of target proteins, and it is used widely in various fields from materials to biology. This mini-review introduced the principles, main preforming procedures, and advances of MDS, as well as its applications on the studies of conformational and allosteric dynamics of proteins especially on that of the mechanosensitive integrins. Future perspectives were also proposed. This review could provide clues in understanding the potentiality of MD simulations in structure-function relationship investigation of biological proteins.

Estimation of biophysical properties of cell exposed to electric field

Hui Zhang(张辉), Liyang Wang(王李阳), Peijie Zhang(张培杰), Xiaodi Zhang(张小娣), and Jun Ma(马军)

Chin. Phys. B, 2021, 30 (3): 038702. DOI: 10.1088/1674-1056/abc543

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Excitable media, such as cells, can be polarized and magnetized in the presence of an external electromagnetic field. In fact, distinct geometric deformation can be induced by the external electromagnetic field, and also the capacitance of the membrane of cell can be changed to pump the field energy. Furthermore, the distribution of ion concentration inside and outside the cell can also be greatly adjusted. Based on the theory of bio-electromagnetism, the distribution of field energy and intracellular and extracellular ion concentrations in a single shell cell can be estimated in the case with or without external electric field. Also, the dependence of shape of cell on the applied electronic field is calculated. From the viewpoint of physics, the involvement of external electric field will change the gradient distribution of field energy blocked by the membrane. And the intracellular and extracellular ion concentration show a certain difference in generating time-varying membrane potential in the presence of electric field. When a constant electric field is applied to the cell, distinct geometric deformation is induced, and the cell triggers a transition from prolate to spherical and then to oblate ellipsoid shape. It is found that the critical frequency in the applied electric field for triggering the distinct transition from prolate to oblate ellipsoid shape obtains smaller value when larger dielectric constant of the cell membrane and intracellular medium, and smaller conductivity for the intracellular medium are used. Furthermore, the effect of cell deformation is estimated by analyzing the capacitance per unit area, the density of field energy, and the change of ion concentration on one side of cell membrane. The intensity of external applied electric field is further increased to detect the change of ion concentration. And the biophysical effect in the cell is discussed. So the deformation effect of cells in electric field should be considered when regulating and preventing harm to normal neural activities occurs in a nervous system.

Effective suppression of beta oscillation in Parkinsonian state via a noisy direct delayed feedback control scheme

Hai-Tao Yu(于海涛), Zi-Han Meng(孟紫寒), Chen Liu(刘晨), Jiang Wang(王江), and Jing Liu(刘静)

Chin. Phys. B, 2021, 30 (3): 038703. DOI: 10.1088/1674-1056/abd395

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This work explores the function of the noisy direct delayed feedback (NDDF) control strategy in suppressing the pathological oscillations in the basal ganglia (BG) with Parkinson's disease (PD). Deep brain stimulation (DBS) alleviates the PD state fantastically. However, due to its unclear mechanism and open-loop characteristic, it is challenging to further improve its effects with lower energy expenditure. The noise stimulus performs competitively in alleviating the PD state theoretically, but it cannot adapt to the neural condition timely and automatically due to its open-loop control scheme. The direct delayed feedback (DDF) control strategy is able to disturb excessive synchronous effectively. Therefore, the NDDF control strategy is proposed and researched based on a BG computational model, which can reflect the intrinsic properties of the BG neurons and their connections with thalamic neurons. Simulation results show that the NDDF control strategy with optimal parameters is effective in removing the pathological beta oscillations. By comparison, we find the NDDF control strategy performs more excellent than DDF in alleviating PD state. Additionally, we define the multiple-NDDF control strategy and find that the multiple-NDDF with appropriate parameters performs better than NDDF. The obtained results contribute to the cure for PD symptoms by optimizing the noise-induced improvement of the BG dysfunction.

Improved efficiency and stability of perovskite solar cells with molecular ameliorating of ZnO nanorod/perovskite interface and Mg-doping ZnO Suggested by editors

Zhenyun Zhang(张振雲), Lei Xu(许磊), and Junjie Qi(齐俊杰)

Chin. Phys. B, 2021, 30 (3): 038801. DOI: 10.1088/1674-1056/abd748

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Despite the advanced efficiency of perovskite solar cells (PSCs), electron transportation is still a pending issue. Here the polymer polyvinylpyrrolidone (PVP) is used to enhance the electron injection, which is thanks to the passivation of the defects at the interface between the ZnO electron transporting layer (ETL) and the perovskite. The application of the PVP layer inhibits the device degradation, and 80% of the primary efficiency is kept after 30 d storage in air condition. Additionally, the efficiency of the device is further enhanced by improving the conductivity and crystallinity of the ZnO ETL via Magnesium (Mg) doping in the ZnO nanorods (ZnO NRs). Moreover, the preparation parameters of the ZnO NRs are optimized. By employing the high-crystallinity ZnO ETL and the PVP layer, the power conversion efficiency (PCE) of the champion device is increased from 16.29% to 19.63%. These results demonstrate the advantages of combining mesoscale manipulation with interface modification and doping together.

Constructing refined null models for statistical analysis of signed networks

Ai-Wen Li(李艾纹), Jing Xiao(肖婧, and Xiao-Ke Xu(许小可)

Chin. Phys. B, 2021, 30 (3): 038901. DOI: 10.1088/1674-1056/abc2c4

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The establishment of effective null models can provide reference networks to accurately describe statistical properties of real-life signed networks. At present, two classical null models of signed networks (i.e., sign and full-edge randomized models) shuffle both positive and negative topologies at the same time, so it is difficult to distinguish the effect on network topology of positive edges, negative edges, and the correlation between them. In this study, we construct three refined edge-randomized null models by only randomizing link relationships without changing positive and negative degree distributions. The results of nontrivial statistical indicators of signed networks, such as average degree connectivity and clustering coefficient, show that the position of positive edges has a stronger effect on positive-edge topology, while the signs of negative edges have a greater influence on negative-edge topology. For some specific statistics (e.g., embeddedness), the results indicate that the proposed null models can more accurately describe real-life networks compared with the two existing ones, which can be selected to facilitate a better understanding of complex structures, functions, and dynamical behaviors on signed networks.

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