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15 February 2025, Volume 34 Issue 2 Previous issue    Next issue

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TOPICAL REVIEW — Moiré physics in two-dimensional materials

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Moiré physics in two-dimensional materials: Novel quantum phases and electronic properties Zi-Yi Tian(田子弈), Si-Yu Li(李思宇), Hai-Tao Zhou(周海涛), Yu-Hang Jiang(姜宇航), and Jin-Hai Mao(毛金海) Chin. Phys. B, 2025, 34 (2):  027301.  DOI: 10.1088/1674-1056/ad9e96 Abstract ( 166 )   HTML ( 7 )   PDF (1715KB) ( 129 )   Moiré superlattices have revolutionized the study of two-dimensional materials, enabling unprecedented control over their electronic, magnetic, optical, and mechanical properties. This review provides a comprehensive analysis of the latest advancements in moiré physics, focusing on the formation of moiré superlattices due to rotational misalignment or lattice mismatch in two-dimensional materials. These superlattices induce flat band structures and strong correlation effects, leading to the emergence of exotic quantum phases, such as unconventional superconductivity, correlated insulating states, and fractional quantum anomalous Hall effects. The review also explores the underlying mechanisms of these phenomena and discusses the potential technological applications of moiré physics, offering insights into future research directions in this rapidly evolving field.

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Orbital XY models in moiré superlattices Yanqi Li(李彦琪), Yi-Jie Wang(王一杰), and Zhi-Da Song(宋志达) Chin. Phys. B, 2025, 34 (2):  027303.  DOI: 10.1088/1674-1056/ad9ffc Abstract ( 168 )   HTML ( 3 )   PDF (1036KB) ( 184 )   Moiré superlattices provide a new platform to engineer various many-body problems. In this work, we consider arrays of quantum dots (QD) realized on semiconductor moiré superlattices with a deep moiré potential. We diagonalize single QD with multiple electrons, and find degenerate ground states serving as local degrees of freedom (qudits) in the superlattice. With a deep moiré potential, the hopping and exchange interaction between nearby QDs become irrelevant, and the direct Coulomb interaction of the density-density type dominates. Therefore, nearby QDs must arrange the spatial densities to optimize the Coulomb energy. When the local Hilbert space has a two-fold orbital degeneracy, we find that a square superlattice realizes an anisotropic $XY$ model, while a triangular superlattice realizes a generalized $XY$ model with geometric frustration.

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Correlated physics, charge and magnetic orders in moiré kagomé systems Zhaochen Liu(刘兆晨) and Jing Wang(王靖) Chin. Phys. B, 2025, 34 (2):  027304.  DOI: 10.1088/1674-1056/ad9ffa Abstract ( 189 )   HTML ( 2 )   PDF (1747KB) ( 121 )   Moiré systems have emerged as an ideal platform for exploring interaction effects and correlated states. However, most of the experimental systems are based on either triangular or honeycomb lattices. In this study, based on the self-consistent Hartree-Fock calculation, we investigate the phase diagram of the kagomé lattice in a recently discovered system with two degenerate $\Gamma$ valley orbitals and strong spin-orbit coupling. By focusing on the filling factors of $1/2$, $1/3$ and $2/3$, we identify various symmetry-breaking states by adjusting the screening length and dielectric constant. At the half filling, we discover that the spin-orbit coupling induces Dzyaloshinskii-Moriya interaction and stabilizes a classical magnetic state with ${120}^{\circ }$ ordering. Additionally, we observe a transition to a ferromagnetic state with out-of-plane ordering. In the case of $1/3$ filling, the system is ferromagnetically ordered due to the lattice frustration. Furthermore, for $2/3$ filling, the system exhibits a pinned droplet state and a ${120}^{\circ }$ magnetic ordered state at weak and immediate coupling strengths, respectively. For the strong coupling case, when dealing with non-integer filling, the system is always charge ordered with sublattice polarization. Our study serves as a starting point for exploring the effects of correlation in moiré kagomé systems.

SPECIAL TOPIC — Quantum communication and quantum network

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Effect of pseudo-random number on the security of quantum key distribution protocol Xiao-Liang Yang(杨晓亮), Yu-Qing Li(李毓擎), and Hong-Wei Li(李宏伟) Chin. Phys. B, 2025, 34 (2):  020301.  DOI: 10.1088/1674-1056/ad99c9 Abstract ( 225 )   HTML ( 2 )   PDF (479KB) ( 85 )   In the process of quantum key distribution (QKD), the communicating parties need to randomly determine quantum states and measurement bases. To ensure the security of key distribution, we aim to use true random sequences generated by true random number generators as the source of randomness. In practical systems, due to the difficulty of obtaining true random numbers, pseudo-random number generators are used instead. Although the random numbers generated by pseudo-random number generators are statistically random, meeting the requirements of uniform distribution and independence, they rely on an initial seed to generate corresponding pseudo-random sequences. Attackers may predict future elements from the initial elements of the random sequence, posing a security risk to quantum key distribution. This paper analyzes the problems existing in current pseudo-random number generators and proposes corresponding attack methods and applicable scenarios based on the vulnerabilities in the pseudo-random sequence generation process. Under certain conditions, it is possible to obtain the keys of the communicating parties with very low error rates, thus effectively attacking the quantum key system. This paper presents new requirements for the use of random numbers in quantum key systems, which can effectively guide the security evaluation of quantum key distribution protocols.

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Improved reference-frame-independent quantum key distribution with intensity fluctuations Zi-Qi Chen(陈子骐), Hao-Bing Sun(孙昊冰), Ming-Shuo Sun(孙铭烁), and Qin Wang(王琴) Chin. Phys. B, 2025, 34 (2):  020302.  DOI: 10.1088/1674-1056/ad99cb Abstract ( 172 )   HTML ( 0 )   PDF (671KB) ( 67 )   Reference-frame-independent quantum key distribution (RFI-QKD) can avoid real-time calibration operation of reference frames and improve the efficiency of the communication process. However, due to imperfections of optical devices, there will inevitably exist intensity fluctuations in the source side of the QKD system, which will affect the final secure key rate. To reduce the influence of intensity fluctuations, an improved 3-intensity RFI-QKD scheme is proposed in this paper. After considering statistical fluctuations and implementing global parameter optimization, we conduct corresponding simulation analysis. The results show that our present work can present both higher key rate and a farther transmission distance than the standard method.

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Quantum-enhanced interferometry with unbalanced entangled coherent states Jun Tang(汤俊), Zi-Hang Du(堵子航), Wei Zhong(钟伟), Lan Zhou(周澜), and Yu-Bo Sheng(盛宇波) Chin. Phys. B, 2025, 34 (2):  020303.  DOI: 10.1088/1674-1056/ad99ca Abstract ( 198 )   HTML ( 0 )   PDF (924KB) ( 94 )   We propose a quantum-enhanced metrological scheme utilizing unbalanced entangled coherent states (ECSs) generated by passing a coherent state and a coherent state superposition through an unbalanced beam splitter (BS). We identify the optimal phase sensitivity of this scheme by maximizing the quantum Fisher information (QFI) with respect to the BS transmission ratio. Our scheme outperforms the conventional scheme with a balanced BS, particularly in the presence of single-mode photon loss. Notably, our scheme retains quantum advantage in phase sensitivity in the limit of high photon intensity, where the balanced scheme offers no advantage over the classical strategy.

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Mask-coding-assisted continuous-variable quantum direct communication with orbital angular momentum multiplexing Zhengwen Cao(曹正文), Yujie Wang(王禹杰), Geng Chai(柴庚), Xinlei Chen(陈欣蕾), and Yuan Lu(卢缘) Chin. Phys. B, 2025, 34 (2):  020308.  DOI: 10.1088/1674-1056/ad9ff7 Abstract ( 160 )   HTML ( 0 )   PDF (1123KB) ( 81 )   Quantum secure direct communication (QSDC) is a communication method based on quantum mechanics and it is used to transmit secret messages. Unlike quantum key distribution, secret messages can be transmitted directly on a quantum channel with QSDC. Higher channel capacity and noise suppression capabilities are key to achieving long-distance quantum communication. Here, we report a continuous-variable QSDC scheme based on mask-coding and orbital angular momentum, in which the mask-coding is employed to protect the security of the transmitting messages and to suppress the influence of excess noise. The combination of orbital angular momentum and information block transmission effectively improves the secrecy capacity. In the $800$ information blocks $\times 1310$ bits length 10-km experiment, the results show a statistical average bit error rate of 0.38%, a system excess noise value of 0.0184 SNU, and a final secrecy capacity of 6.319$\times {10}^6$ bps. Therefore, this scheme reduces error bits while increasing secrecy capacity, providing a solution for long-distance large-scale quantum communication, which is capable of transmitting text, images and other information of reasonable size.

SPECIAL TOPIC — Structures and properties of materials under high pressure

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Novel high-temperature-resistant material SbLaO3 with superior hardness under high pressure Haoqi Chen(陈浩琦), Haowen Jiang(姜皓文), Xuehui Jiang(姜雪辉), Jialin Wang(王佳琳), Chengyao Zhang(张铖瑶), Defang Duan(段德芳), Jing Dong(董晶), and Yanbin Ma(马艳斌) Chin. Phys. B, 2025, 34 (2):  026201.  DOI: 10.1088/1674-1056/ad989e Abstract ( 188 )   HTML ( 1 )   PDF (1696KB) ( 69 )   Perovskites have garnered significant attention in recent years. However, the presence of La atoms at the $B$-site in $AB{X}_3$ structures has not yet been observed. Under high pressure, perovskites exhibit unexpected phase transitions. In this study, we report the discovery of SbLaO${}_3$ under ambient pressure, with a space group of $R3m$. Mechanical property calculations indicate that it is a brittle material, and it possesses a band gap of 4.0266 eV, classifying it as an insulator. We also investigate the phase at 300 GPa, where the space group shifts to $P{2}_1/m$. Additionally, the $P{2}_1/m$ phase of LaInO${}_3$ under 300 GPa is explored. Ab initio molecular dynamics calculations reveal that the melting point of SbLaO${}_3$ is exceptionally high. The inclusion of Sb alters the electronic structure compared with LaInO${}_3$, and the Vickers hardness ($H_{\mathrm{v}}$) is estimated to reach 20.97 GPa. This research provides insights into the phase transitions of perovskites under high pressure.

INSTRUMENTATION AND MEASUREMENT

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Grating pitch comparison measurement based on Cr atomic transition frequency and Si lattice constant Jingtong Feng(冯婧桐), Rao Xu(徐娆), Ziruo Wu(吴子若), Lihua Lei(雷李华), Yingfan Xiong(熊英凡), Zhaohui Tang(唐朝辉), Guangxu Xiao(肖光旭), Yuying Xie(解钰莹), Dongbai Xue(薛栋柏), Xiao Deng(邓晓), Xinbin Cheng(程鑫彬), and Tongbao Li(李同保) Chin. Phys. B, 2025, 34 (2):  020601.  DOI: 10.1088/1674-1056/ad9e9a Abstract ( 173 )   HTML ( 0 )   PDF (2974KB) ( 107 )   Traceability is the fundamental premise of all metrological activities. The establishment of a traceability chain characterized by a shortened structure, while simultaneously enabling on-site traceability, represents a key trend in the advancement of metrology. This study explores the periodic accuracy and overall uniformity of self-traceable gratings, employing multilayer film gratings with a nominal period of 25.00 nm as the medium. We present a comparative analysis of measurement capabilities in a self-traceable grating calibration system characterized by a 'top-down' calibration approach and a Si lattice constant calibration system characterized by a 'bottom-up' calibration approach. The results indicate that the values obtained for the multilayer film grating periods, calibrated using the self-traceable grating system, are 24.40 nm with a standard deviation of 0.11 nm. By comparing with the values derived from the Si lattice constant, which yield 24.34 nm with a standard deviation of 0.14 nm, the validity and feasibility of the self-traceable calibration system are confirmed. This system extends and complements existing metrological frameworks, offering a precise pathway for traceability in precision engineering and nanotechnology research.

RAPID COMMUNICATION

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Elastic properties of Cu-6wt% Ag alloy wires for pulsed magnets investigated by ultrasonic techniques Hot! Ziyu Li(李滋雨), Tianyi Gu(顾天逸), Wenqi Wei(魏文琦), Yang Yuan(袁洋), Zhuo Wang(王卓), Kangjian Luo(罗康健), Yupeng Pan(潘宇鹏), Jianfeng Xie(谢剑峰), Shaozhe Zhang(张绍哲), Tao Peng(彭涛), Lin Liu(柳林), Qi Chen(谌祺), Xiaotao Han(韩小涛), Yongkang Luo(罗永康), and Liang Li(李亮) Chin. Phys. B, 2025, 34 (2):  020701.  DOI: 10.1088/1674-1056/ada1c8 Abstract ( 502 )   HTML ( 16 )   PDF (795KB) ( 354 )   Conductor materials with good mechanical performance as well as high electrical and thermal conductivities are particularly important to break through the current bottle-neck limit ($\sim 100$ T) of pulsed magnets. Here, we perform systematic studies on the elastic properties of the Cu-6wt% Ag alloy wire, which is a promising candidate material for the new-generation pulsed magnets, by employing two independent ultrasonic techniques, i.e., resonant ultrasound spectroscopy (RUS) and ultrasound pulse-echo experiments. Our RUS measurements manifest that the elastic properties of the Cu-6wt% Ag alloy wires can be improved by an electroplastic drawing procedure as compared with the conventional cold drawing. We also take this opportunity to test the availability of our newly-built ultrasound pulse-echo facility at the Wuhan National High Magnetic Field Center (WHMFC, China), and the results suggest that the elastic performance of the electroplastically-drawn Cu-6wt% Ag alloy wire remains excellent without anomalous softening under extreme conditions, e.g., in ultra-high magnetic field up to 50 T and nitrogen or helium cryogenic liquids.

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Evolution from the Kondo phase to the RKKY phase in the small impurity spacing regime of the two-impurity Anderson model Hot! Hou-Min Du(杜厚旻) and Yu-Liang Liu(刘玉良) Chin. Phys. B, 2025, 34 (2):  027102.  DOI: 10.1088/1674-1056/ada54f Abstract ( 303 )   HTML ( 8 )   PDF (1118KB) ( 265 )   Understanding the quantum critical phenomena is one of the most important and challenging tasks in condensed matter physics and the two-impurity Anderson model (TIAM) is a good starting point for this exploration. To this end, we employ the algebraic equation of motion approach to calculate the TIAM and analytically obtain the explicit single-particle impurity Green function under the soft cut-off approximation (SCA). This approach effectively incorporates the impurity spacing as an intrinsic parameter. By solving the pole equations of the Green function, we have, for the first time, qualitatively calculated the spectral weight functions of the corresponding low-energy excitations. We find that when the impurity spacing is less than one lattice distance, the dynamic Rudermann-Kittel-Kasuya-Yosida (RKKY) interaction effectively enters, resulting in a rapid increase in the spectral weights of the RKKY phase, which ultimately surpass those of the Kondo phase; while the spectral weights of the Kondo phase are strongly suppressed. From the perspective of spectral weights, we further confirm the existence of a crossover from the Kondo phase to the RKKY phase in the TIAM. Based on these results, the reasons for the phenomenon of the Kondo resonance splitting are also discussed.

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Possible coexistence of superconductivity and topological electronic states in 1T-RhSeTe Hot! Tengdong Zhang(张腾东), Rui Fan(樊睿), Yan Gao(高炎), Yanling Wu(吴艳玲), Xiaodan Xu(徐晓丹), Dao-Xin Yao(姚道新), and Jun Li(李军) Chin. Phys. B, 2025, 34 (2):  027403.  DOI: 10.1088/1674-1056/ada432 Abstract ( 225 )   HTML ( 0 )   PDF (1824KB) ( 173 )   Transition metal dichalcogenides (TMDs), exhibit a range of crystal structures and topological quantum states. The 1T phase, in particular, shows promise for superconductivity driven by electron-phonon coupling (EPC), strain, pressure, and chemical doping. In this theoretical investigation, we explore 1T-RhSeTe as a novel type of TMD superconductor with topological electronic states. The optimal doping structure and atomic arrangement of 1T-RhSeTe are constructed. Phonon spectrum calculations validate the integrity of the constructed doping structure. The analysis of the electron-phonon coupling using the electron-phonon Wannier (EPW) method has confirmed the existence of a robust electron-phonon interaction in 1T-RhSeTe, resulting in total EPC constant $\lambda =2.02$, the logarithmic average frequency ${\omega }_{\mathrm{l}\mathrm{o}\mathrm{g}}=3.15$ meV and $T_{\mathrm{c}}=4.61$ K, consistent with experimental measurements and indicative of its classification as a BCS superconductor. The band structure analysis revealed the presence of Dirac-like band crossing points. The topological non-trivial electronic structures of the 1T-RhSeTe are confirmed via the evolution of Wannier charge centers (WCCs) and time-reversal symmetry-protected topological surface states (TSSs). These distinctive properties underscore 1T-RhSeTe as a possible candidate for a topological superconductor, warranting further investigation into its potential implications and applications.

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Auxiliary-field Monte Carlo method for frustrated spin systems Hot! Ning Cai(蔡凝), Yuan Gao(高源), Wei Li(李伟), and Yang Qi(戚扬) Chin. Phys. B, 2025, 34 (2):  027504.  DOI: 10.1088/1674-1056/ada758 Abstract ( 209 )   HTML ( 3 )   PDF (588KB) ( 158 )   We extend a semiclassical numerical method, bosonic auxiliary-field Monte Carlo, to quantum spin systems. This method breaks the lattice into clusters, solves each cluster precisely and couples them with classical auxiliary fields through classical Monte Carlo simulation. We test the method with antiferromagnetic spin models in one-dimensional chains, square lattices and triangular lattices, and obtain reasonable results at finite temperatures. This algorithm builds a bridge between classical Monte Carlo method and quantum methods. The algorithm can be improved with either progress in classical Monte Carlo sampling or the development of quantum solvers, and can also be further applied to systems with different lattices or interactions.

GENERAL

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Enhancing entanglement and steering in a hybrid atom-optomechanical system via Duffing nonlinearity Ling-Hui Dong(董凌晖), Xiao-Jie Wu(武晓捷), Cheng-Hua Bai(白成华), and Shao-Xiong Wu(武少雄) Chin. Phys. B, 2025, 34 (2):  020304.  DOI: 10.1088/1674-1056/ad9ba2 Abstract ( 163 )   HTML ( 0 )   PDF (801KB) ( 92 )   We introduce a novel scheme for achieving quantum entanglement and Einstein-Podolsky-Rosen (EPR) steering between an atomic ensemble and a mechanical oscillator within a hybrid atom-optomechanical system. The system comprises an optical cavity, a two-level atomic ensemble and a mechanical resonator that possesses Duffing nonlinearity. The interaction between these components is mediated by the cavity mode, which is driven by an external laser. Our findings indicate that optimizing the coupling strengths between photons and phonons, as well as between atoms and the cavity, leads to maximal entanglement and EPR steering. The amplitude of the driving laser plays a pivotal role in enhancing the coupling between photons and phonons, and the system maintains robust entanglement and EPR steering even under high dissipation, thereby mitigating the constraints on initial conditions and parameter precision. Remarkably, the Duffing nonlinearity enhances the system's resistance to thermal noise, ensuring its stability and entanglement protection. Our analysis of EPR steering conditions reveals that the party with lower dissipation exhibits superior stability and a propensity to steer the party with higher dissipation. These discoveries offer novel perspectives for advancing quantum information processing and communication technologies.

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Sudden change of interferometric power for X-shape states Dian Zhu(朱典), Fu-Lin Zhang(张福林), and Jing-Ling Chen(陈景灵) Chin. Phys. B, 2025, 34 (2):  020305.  DOI: 10.1088/1674-1056/ad9732 Abstract ( 106 )   HTML ( 0 )   PDF (535KB) ( 9 )   Quantum interferometric power (IP), a discordlike measure, plays an important role in quantum metrology. We study the dynamics of IP for two-qubit X-shape states under different noisy environments. Our study shows that IP exhibits sudden change, and one side quantum channel is enough for the occurrence of a sudden change of IP. In particular, we show that the initial state having no sudden change of quantum discord exhibits a sudden change of IP under the dynamics of amplitude noise, but the converse is not true. Besides, we also investigate the dynamics of IP under two different kinds of composite noises. Our results also confirm that sudden change of IP occurs under such composite noises.

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Entanglement and energy transportation in central-spin quantum battery Fan Liu(刘帆), Hui-Yu Yang(杨慧宇), Shuai-Li Wang(王帅立), Jun-Zhong Wang(王俊钟), Kun Zhang(张堃), and Xiao-Hui Wang(王晓辉) Chin. Phys. B, 2025, 34 (2):  020306.  DOI: 10.1088/1674-1056/ad9a9d Abstract ( 115 )   HTML ( 0 )   PDF (664KB) ( 14 )   Quantum battery exploits the principle of quantum mechanics to transport and store energy. We study the energy transportation of the central-spin quantum battery, which is composed of $N_{\mathrm{b}}$ spins serving as the battery cells, and surrounded by $N_{\mathrm{c}}$ spins serving as the charger cells. We apply the invariant subspace method to solve the dynamics of the central-spin battery with a large number of spins. We establish a universal inverse relationship between the battery capacity and the battery-charger entanglement, which persists in any size of the battery and charger cells. Moreover, we find that when $N_{\mathrm{b}}=N_{\mathrm{c}}$, the central-spin battery has the optimal energy transportation, corresponding to the minimal battery-charger entanglement. Surprisingly, the central-spin battery has a uniform energy transportation behaviors in certain battery-charger scales. Our results reveal a nonmonotonic relationship between the battery-charger size and the energy transportation efficiency, which may provide more insights on designing other types of quantum batteries.

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Quantum manipulation of asymmetric Einstein-Podolsky-Rosen steering in controllable dynamical Casimir arrays Ruinian Li(李瑞年), Yumei Long(龙玉梅), and Xue Zhang(张雪) Chin. Phys. B, 2025, 34 (2):  020307.  DOI: 10.1088/1674-1056/ad9a99 Abstract ( 123 )   HTML ( 0 )   PDF (2562KB) ( 15 )   We design dynamical Casimir arrays (DCA) consisting of giant atoms and coupled resonator waveguides (CRWs) to investigate the Einstein-Podolsky-Rosen (EPR) steering at finite temperatures. Our designed system exhibits an asymmetry in its structure, which is caused by the differences in the sizes and the coupling positions of the giant atoms. The system achieves different types of EPR steering and the reversal of one-way EPR steering by modulating parameters. Furthermore, the symmetry and asymmetry of the system structure, in their responses to parameter modulation, both reveal the asymmetry of EPR steering. In this process, we discover that with the increase in temperature, different types of steering can be transferred from Casimir photons to giant atoms. We also achieve the monogamy of the multipartite system. These results provide important assistance for secure quantum communication, and further intuitively validating the asymmetry of EPR steering from multiple perspectives.

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Quantum decoder design for subsystem surface code based on multi-head graph attention and edge weighting Nai-Hua Ji(纪乃华), Hui-Qian Sun(孙汇倩), Bo Xiao(肖博), Ping-Li Song(宋平俐), and Hong-Yang Ma(马鸿洋) Chin. Phys. B, 2025, 34 (2):  020309.  DOI: 10.1088/1674-1056/ada1c7 Abstract ( 108 )   HTML ( 1 )   PDF (4735KB) ( 58 )   Quantum error-correcting codes are essential for fault-tolerant quantum computing, as they effectively detect and correct noise-induced errors by distributing information across multiple physical qubits. The subsystem surface code with three-qubit check operators demonstrates significant application potential due to its simplified measurement operations and low logical error rates. However, the existing minimum-weight perfect matching (MWPM) algorithm exhibits high computational complexity and lacks flexibility in large-scale systems. Therefore, this paper proposes a decoder based on a graph attention network (GAT), representing error syndromes as undirected graphs with edge weights, and employing a multi-head attention mechanism to efficiently aggregate node features and enable parallel computation. Compared to MWPM, the GAT decoder exhibits linear growth in computational complexity, adapts to different quantum code structures, and demonstrates stronger robustness under high physical error rates. The experimental results demonstrate that the proposed decoder achieves an overall accuracy of 89.95% under various small code lattice sizes $(L=2,3,4,5)$, with the logical error rate threshold increasing to 0.0078, representing an improvement of approximately 13.04% compared to the MWPM decoder. This result significantly outperforms traditional methods, showcasing superior performance under small code lattice sizes and providing a more efficient decoding solution for large-scale quantum error correction.

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Hawking radiation and Page curve of regular black holes Chen-Yang Dong(董晨阳) and Li-Jun Tian(田立君) Chin. Phys. B, 2025, 34 (2):  020401.  DOI: 10.1088/1674-1056/ad989b Abstract ( 98 )   HTML ( 0 )   PDF (611KB) ( 17 )   We discuss the information paradox and its implications for regular black holes. Our primary focus is on Page curve using the island treatment and analyzing relevant parameters like Page time and scrambling time. Calculations without considering the island show that the entanglement entropy increases linearly and continues to infinity. When we consider the generalized entropy, we find that the island extends just beyond the horizon, leading to a constant entanglement entropy. Specifically, we find that in the early stages, the island never forms, regardless of the charge and mass configuration of the black hole.

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Probing the shape of the primordial curvature power spectrum and the energy scale of reheating with pulsar timing arrays Lele Fan(范乐乐), Jie Zheng(郑捷), Fengge Zhang(张丰阁), and Zhi-Qiang You(尤志强) Chin. Phys. B, 2025, 34 (2):  020402.  DOI: 10.1088/1674-1056/ad9a98 Abstract ( 97 )   HTML ( 0 )   PDF (752KB) ( 10 )   Recent observations by pulsar timing array collaborations have detected a stochastic common-spectrum signal, which may originate from scalar-induced gravitational waves generated by primordial curvature perturbations during inflation. Using the NANOGrav 15-year data set, we explore this hypothesis by constraining the primordial curvature power spectrum and reheating energy scale. We model the primordial power spectrum with a lognormal form and consider reheating with the equation of state parameter $w=1/6$. Our Bayesian analysis reveals a narrow peak in the primordial power spectrum (the width of the spectrum $\mathrm{\Delta }<0.05$ at the $95$ confidence level) and constrains the reheating temperature to be $0.03\mathrm{G}\mathrm{e}\mathrm{V}\lesssim T_{\mathrm{r}\mathrm{h}}\lesssim 7.2$ GeV. The best-fit SIGW spectrum shows a characteristic turning point near $f\sim {10}^{-8.1}$ Hz, marking the transition from reheating to radiation domination, providing a unique probe of the properties of the early Universe.

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Excitation threshold of solitons in anharmonic chains Yi Ming(明燚) Chin. Phys. B, 2025, 34 (2):  020501.  DOI: 10.1088/1674-1056/ad9ff6 Abstract ( 116 )   HTML ( 0 )   PDF (727KB) ( 55 )   This study numerically estimates the momentum threshold required to excite solitons in anharmonic chains. For both Fermi-Pasta-Ulam-Tsingou (FPUT)-$\alpha \beta$ and FPUT-$\beta$ chains, regardless of whether the interatomic interaction potential is symmetric, the required excitation momentum converges to the momentum of the soliton center (i.e., the peak momentum of the soliton) as the number of initially excited atoms increases. As the amplitude of the soliton approaches zero, the momentum threshold decreases to nearly zero, allowing soliton being excited with infinitesimal initial excitation momentum. These findings enhance the understanding of soliton dynamics and offer insights for optimizing soliton excitation methods, with potential applications in straintronics and nonlinear wave control technologies.

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The N-periodic wave solutions to the N =1 supersymmetric Sawada-Kotera-Ramani equation Pengcheng Xin(辛鹏程), Zhonglong Zhao(赵忠龙), and Yu Wang(王宇) Chin. Phys. B, 2025, 34 (2):  020502.  DOI: 10.1088/1674-1056/ad9912 Abstract ( 148 )   HTML ( 0 )   PDF (1179KB) ( 43 )   The $N$-periodic wave solvability problem for the $\mathcal{N}=1$ supersymmetric Sawada-Kotera-Ramani equation is considered by combining the Hirota's bilinear method and the super Riemann theta function. The constraint equations and unknown parameters are redefined, and the numerical calculation process of the $N$-periodic wave solutions is derived. It has been verified that under certain conditions, the asymptotic relations between $N$-periodic wave solutions and $N$-soliton solutions can be established. Some numerical solutions of three-periodic wave are presented. Under the influence of the Grassmann variable, the three-periodic wave solutions will generate an influence band in the middle region, and the amplitude becomes bigger as the distance from the influence band increases.

ATOMIC AND MOLECULAR PHYSICS

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A new search for the variation of fundamental constants using the rovibrational levels and isotope effects of the magnesium fluoride molecule Di Wu(吴迪), Jin Wei(魏晋), Taojing Dong(董涛晶), Chenyu Zu(祖晨宇), Yong Xia(夏勇), and Jianping Yin(印建平) Chin. Phys. B, 2025, 34 (2):  023101.  DOI: 10.1088/1674-1056/ad990e Abstract ( 231 )   HTML ( 0 )   PDF (758KB) ( 73 )   The recently demonstrated methods for cooling and trapping diatomic molecules offer new possibilities for precision searches in fundamental physical theories. Here, we propose to study the variations of the fine-structure constant ($\alpha =e^2/(\hslash c)$) and the proton-to-electron mass ratio ($\mu =m_{\mathrm{p}}/m_{\mathrm{e}}$) with time by taking advantage of the nearly degenerate rovibrational levels in the electronic states of the magnesium fluoride (MgF) molecule. Specifically, due to the cancellation between the fine-structure splitting and the rovibrational intervals in the different MgF natural isotopes, a degeneracy occurs for A${}^2{\mathrm{\Pi }}_{3/2}$ $(v^{\prime }=0,J^{\prime }=18.5,-)$ and A${}^2{\mathrm{\Pi }}_{1/2}$ $(v^{″}=0,J^{″}=20.5,-)$. We find that using the nearly degenerate energy level of such states can be 10${}^4$ times more sensitive than using a pure rotational transition to measure the variations of $\alpha$ and $\mu$. To quantify the small gap between A${}^2{\mathrm{\Pi }}_{3/2}$ $(v^{\prime }=0,J^{\prime }=18.5,-)$ and A${}^2{\mathrm{\Pi }}_{1/2}$ $(v^{″}=0,J^{″}=20.5,-)$, special transitions of choice are feasible: X${}^2{\mathrm{\Sigma }}_{1/2}^{+}$ $(v=0,J=19.5,+)$ to A${}^2{\mathrm{\Pi }}_{3/2}$ $(v^{\prime }=0,J^{\prime }=18.5,-)$ and X${}^2{\mathrm{\Sigma }}_{1/2}^{+}$ $(v=0,J=19.5,+)$ to A${}^2{\mathrm{\Pi }}_{1/2}$ $(v^{″}=0,J^{″}=20.5,-)$. In addition, we estimate the frequency uncertainties caused by the narrow linewidth, Zeeman shift, Stark shift, Doppler broadening and blackbody radiation.

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Nondestructive detection of atom counts in laser-trapped 171Yb atoms Congcong Tian(田聪聪), Qiang Zhu(朱强), Bing Wang(王兵), Dezhi Xiong(熊德智), Zhuanxian Xiong(熊转贤), Lingxiang He(贺凌翔), and Baolong Lyu(吕宝龙) Chin. Phys. B, 2025, 34 (2):  023201.  DOI: 10.1088/1674-1056/ad9e9d Abstract ( 168 )   HTML ( 1 )   PDF (1479KB) ( 59 )   We present the experimental demonstration of nondestructive detection of ${}^{171}$Yb atoms in a magneto-optical trap (MOT) based on phase shift measurement induced by the atoms on a weak off-resonant laser beam. After loading a green MOT of ${}^{171}$Yb atoms, the phase shift is obtained with a two-color Mach-Zehnder interferometer by means of $\pm 45$ MHz detuning with respect to the ${}^1$S${}_0$-${}^1$P${}_1$ transition. We measured a phase shift of about 100 mrad corresponding to an atom count of around $5\times {10}^5$. This demonstrates that it is possible to obtain the number of atoms without direct destructive measurement compared with the absorption imaging method. This scheme could be an important approach towards a high-precision lattice clock for clock operation through suppression of the impact of the Dick effect.

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Relativistic hyperpolarizabilities of atomic H, Li, and Be+ systems Shan-Shan Lu(卢闪闪), Hong-Yuan Zheng(郑弘远), Zong-Chao Yan(严宗朝), James F. Babb, and Li-Yan Tang(唐丽艳) Chin. Phys. B, 2025, 34 (2):  023202.  DOI: 10.1088/1674-1056/ad9911 Abstract ( 199 )   HTML ( 0 )   PDF (570KB) ( 49 )   For atoms in external electric fields, the hyperpolarizabilities are the coefficients describing the nonlinear interactions contributing to the induced energies at the fourth power of the applied electric fields. Accurate evaluations of these coefficients for various systems are crucial for improving precision in advanced atom-based optical lattice clocks and for estimating field-induced effects in atoms for quantum information applications. However, there is a notable scarcity of research on atomic hyperpolarizabilities, especially in the relativistic realm. Our work addresses this gap by establishing a novel set of alternative formulas for the hyperpolarizability based on the fourth-order perturbation theory. These formulas offer a more reasonable regrouping of scalar and tensor components compared to previous formulas, thereby enhancing their correctness and applicability. To validate our formulas, we perform the calculations for the ground and low-lying excited pure states of few-electron atoms H, Li, and Be${}^{+}$. The highly accurate results obtained for the H atom could serve as benchmarks for further development of other theoretical methods.

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Design and photophysical characterization of quasi-intrinsic fluorescent probes utilized in DNA sequencing Yaning Zhang(张雅宁), Yongkang Lyu(吕永康), Zhizheng Cao(曹智正), Xiaolin Chen(陈晓琳), Qingtian Meng(孟庆田), and Changzhe Zhang(张常哲) Chin. Phys. B, 2025, 34 (2):  023203.  DOI: 10.1088/1674-1056/ad9a9a Abstract ( 152 )   HTML ( 0 )   PDF (3002KB) ( 4 )   To understand the gene-based biological processes in-depth, the single-molecule real-time sequencing has drawn increasing attention with promoted by the Human Genome Project. Herein, a set of newly designed canonical fluorescent bases (A${}_{\mathrm{y}}$, tC, G${}_{\mathrm{b}}$, T${}_{\mathrm{p}}$) are proposed for four-color DNA sequencing. These quasi-intrinsic probes are derived from the fluorophore replacement and ring expansion on natural bases, which still keep the pyrimidine or purine underlying skeleton and Watson-Crick hydrogen bonding face to allow minimal perturbation to the native DNA duplex. More importantly, these nucleobase analogues possess red-shifted absorption and efficient photoluminescence due to the enhanced $\pi$-conjugation in character. Meanwhile, the four analogues could generate distinct emission wavelength ($\mathrm{\Delta }\lambda \sim 50$ nm) for real-time sequencing. To assess the biological employment of the proposed biosensors, the effects of base pairing and linking deoxyribose are also considered.

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Characterization of nonlinear spectral linewidth and light shift in diffuse laser-cooled atoms Yiran Yin(殷怡然), An-Ning Xu(许安宁), Jin Peng(彭瑾), and Bei Liu(刘贝) Chin. Phys. B, 2025, 34 (2):  023401.  DOI: 10.1088/1674-1056/ad990f Abstract ( 182 )   HTML ( 0 )   PDF (1933KB) ( 63 )   We demonstrate an integrating sphere to cool ${}^{87}\mathrm{R}\mathrm{b}$ atoms and measure the recoil-induced resonance and electromagnetically induced absorption spectrum. We measure the relationship between their linewidth and light shift with variation of the detuning and power of the cooling laser and study the performance of the diffuse laser cooling mechanism by the absorption linewidth radio $\mathrm{\Delta }{\nu }_{\mathrm{E}}/\mathrm{\Delta }{\nu }_{\mathrm{R}}$ and light shift $|{\Delta }_{\mathrm{R}}-{\Delta }_{\mathrm{E}}|$ using nonlinear spectroscopy. Specifically, when $\mathrm{\Delta }{\nu }_{\mathrm{E}}/\mathrm{\Delta }{\nu }_{\mathrm{R}}$ reaches a value of 1.57, the temperature and number of cold atoms achieve the optimal cooling effect. This characterization of absorption linewidth and light shift will provide a method to estimate whether diffuse light cooling achieves the best cooling effect, contributing to the future development of isotropic laser cooling for application in quantum sensing.

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Observation of momentum-induced broadening of width in narrow Feshbach resonances of ultracold 133Cs atoms Zhennan Liu(刘震南), Hongxing Zhao(赵宏星), Yunfei Wang(王云飞), Yuqing Li(李玉清), Jizhou Wu(武寄洲), Wenliang Liu(刘文良), Peng Li(李鹏), Yongming Fu(付永明), Liantuan Xiao(肖连团), Jie Ma(马杰), and Suotang Jia(贾锁堂) Chin. Phys. B, 2025, 34 (2):  023701.  DOI: 10.1088/1674-1056/ad92fc Abstract ( 208 )   HTML ( 0 )   PDF (772KB) ( 77 )   Interactions between atoms in ultracold quantum gases play an important role in the study of the quantum simulation of many-body physics. Feshbach resonance is a versatile tool to control atomic interactions, where the atom-loss spectra are widely used to characterize Feshbach resonances of various atomic species. Here, we report the experimental observation of momentum-induced broadening of widths in atom-loss spectra of narrow ${}^{133}$Cs Feshbach resonances. We drive Bragg excitation to kick the Bose-Einstein condensate of Cs atoms in a cigar-shaped optical trap, and measure the atom-loss spectra of narrow Feshbach resonances of moving ultracold atoms near the magnetic fields 19.84 G and 47.97 G. We show that the widths of the atom-loss spectra are broadened for the atoms with the momenta of 2$\hslash k$ and 4$\hslash k$, and even observe splitting in the Feshbach resonance of the atoms with momentum 4$\hslash k$. Our work may open the way for exploring the interesting physical phenomena arising from the collective velocity of colliding atoms that have been ignored in general.

ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS

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Improved particle tracking velocimetry based on level set segmentation for measuring the velocity field of granular flow Jing-Yi Gao(高靖宜), Quan Chen(陈泉), Ran Li(李然), Ge Sun(孙歌), Tong-Tong Mu(牟彤彤), and Hui Yang(杨晖) Chin. Phys. B, 2025, 34 (2):  024201.  DOI: 10.1088/1674-1056/ad989a Abstract ( 202 )   HTML ( 0 )   PDF (4408KB) ( 39 )   Using traditional particle tracking velocimetry based on optical flow for measuring areas with large velocity gradient changes may cause oversmoothing, resulting in significant measurement errors. To address this problem, the traditional particle tracking velocimetry method based on an optical flow was improved. The level set segmentation algorithm was used to obtain the boundary contour of the region with large velocity gradient changes, and the non-uniform flow field was divided into regions according to the boundary contour to obtain sub-regions with uniform velocity distribution. The particle tracking velocimetry method based on optical flow was used to measure the granular flow velocity in each sub-region, thus avoiding the problem of granular flow distribution. The simulation results show that the measurement accuracy of this method is approximately 10% higher than that of traditional methods. The method was applied to a velocity measurement experiment on dense granular flow in silos, and the velocity distribution of the granular flow was obtained, verifying the practicality of the method in granular flow fields.

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Modulation of Bessel-like vector vortex beam using the resonant magneto-optical effect in rubidium vapor Yan Ma(马燕), Xin Yang(杨欣), Hong Chang(常虹), Ming-Tao Cao(曹明涛), Xiao-Fei Zhang(张晓斐), Rui-Fang Dong(董瑞芳), and Shou-Gang Zhang(张首刚) Chin. Phys. B, 2025, 34 (2):  024202.  DOI: 10.1088/1674-1056/ad9c43 Abstract ( 177 )   HTML ( 0 )   PDF (1609KB) ( 73 )   The Bessel-like vector vortex beam (BlVVB) has gained increasing significance across numerous applications. However, its practical application is restricted by manufacturing difficulties and polarization manipulation. Thus, the ability to manipulate its degrees of freedom is highly desirable. In this paper, the full-domain polarization modulation of BlVVB within a hot atomic ensemble has been investigated. We begin with the theoretical analysis of the resonant magneto-optical effect of atoms with a horizontal linear-polarized beam and experimentally demonstrate precise manipulation of the polarization state across the entire domain of the BlVVB, achieving an error margin of less than $3^{\circ }$ at various cross-sectional points. Our study provides a novel approach for the modulation of BlVVB based on atomic media, which holds potential applications in sensitive vector magnetometers, optical communications, and signal processing.

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Quantum-state engineering using enhanced tripartite interactions in atom-photon-phonon hybrid systems Yaowu Guo(郭耀武), Jiaqiang Zhao(赵加强), Lianzhen Cao(曹连振), Yingde Li(李英德), and Hong-Yan Lu(路红艳) Chin. Phys. B, 2025, 34 (2):  024203.  DOI: 10.1088/1674-1056/ad9a5d Abstract ( 156 )   HTML ( 0 )   PDF (1740KB) ( 40 )   We introduce a hybrid cavity optomechanical model capable of generating significant genuine tripartite interactions and entanglement among coherent degrees of freedom. However, realizing and controlling such tripartite interactions and their entanglement pose crucial challenges that remain largely unexplored. In this work, we predict a tripartite coupling mechanism within a hybrid quantum system consisting of a vibrating mechanical oscillator, a two-level atom and a single-frequency cavity field. We specifically propose a mechanism for tripartite and cross-Kerr nonlinear coupling through displacement and squeezing transformations. By adjusting the optical amplitude of the pump light, we can effectively enhance these nonlinear couplings, facilitating the manipulation of entangled and squeezed states. The resulting tripartite genuine entanglement exhibits distinct evolutionary characteristics. Notably, when the pump light amplitude is large, the tripartite entanglement persists for longer time. Additionally, the phonon displays characteristics of both cooling and squeezing. Our study presents a pathway for exploring and exploiting controllable multipartite entanglement, as well as achieving phonon cooling and squeezing with the assistance of a mesoscopic harmonic oscillator. This work underscores the innovative potential of our model in advancing the field of optomechanics and quantum entanglement.

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Planar structure of organic photodetector for low dark current Mohammad Nofil, Amirul Ashraf Md Sabri, Fadlan Arif Natashah, Tahani M Bawazeer, Mohammad S Alsoufi, Nur Adilah Roslan, and Azzuliani Supangat Chin. Phys. B, 2025, 34 (2):  024204.  DOI: 10.1088/1674-1056/ad9731 Abstract ( 147 )   HTML ( 0 )   PDF (2430KB) ( 6 )   The focus of this study is on investigating the vanadyl 2,9,16,23-tetraphenoxy-29H, 31H-phthalocyanine (VOPcPhO) and its blend with o-xylenyl C60 bis-adduct (OXCBA), for use as a lateral ultraviolet organic photodetector. The research focuses on improving dark current reduction, which is a challenge in lateral organic photodetector. By integrating the OXCBA, low dark current values of 4.83 $\mathrm{n}\mathrm{A}\cdot {\mathrm{c}\mathrm{m}}^{-2}$ ($D_{\mathrm{s}\mathrm{h}\mathrm{o}\mathrm{t}}^{\ast }=1.414\times {10}^{11}\mathrm{J}\mathrm{o}\mathrm{n}\mathrm{e}\mathrm{s}$) have been achieved as compared to the stand-alone VoPcPhO device of 14.06 $\mathrm{n}\mathrm{A}\cdot {\mathrm{c}\mathrm{m}}^{-2}$. The major contributing factors to dark current reduction are due to the efficient charge transfer at the photoactive-electrode interface, the deep highest occupied molecular orbital (HOMO) level of OXCBA, which leads to favorable energy level alignments hindering hole injection, and the occurrence of bulk heterojunction vertical phase segregation between VOPcPhO and OXCBA. These findings shed light on the relationship between the organic photoconductor's material composition, morphology, and performance metrics and open new avenues for metal phthalocyanine-based lateral ultraviolet organic photodetectors with low dark current and enhanced performance.

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Acoustic wave propagation in a porous medium saturated with two fluids and a solid Lin Liu(刘琳), Xiu-Mei Zhang(张秀梅), and Xiu-Ming Wang(王秀明) Chin. Phys. B, 2025, 34 (2):  024301.  DOI: 10.1088/1674-1056/ad9d17 Abstract ( 189 )   HTML ( 2 )   PDF (975KB) ( 19 )   Wave propagation in multi-phase porous media is a significant research topic. There are a series of studies about porous media saturated with a single fluid, a solid and a fluid, two fluids, and three fluids. Some gas hydrate-bearing sediments are typical multiphase porous media saturated with a solid (gas hydrates) and two fluids (water and gas). Based on existing theories of porous media, we develop a theory and give a comprehensive analysis of wave propagation in a poroelastic medium saturated with two fluids and a solid. Initially, we establish the constitutive relations and equations of motion. Based on Biot's approach for describing the equations of motion in fluid-saturated porous media at the macroscale, the kinetic energy density, potential energy density, and dissipative energy density are derived. After deriving the equations of motion, a plane wave analysis predicts the existence of four compressional waves, denoted P1, P2, P3, and P4 waves, and two shear waves, denoted S1 and S2 waves. Numerical examples are presented to demonstrate how velocities and attenuations of various waves behave with gas saturation, gas hydrate saturation, and frequency. A model degradation to porous media saturated with a single fluid supports the validity of the theory, which enriches the theory of multiphase porous media and provides a foundation for the evaluation of gas hydrate-bearing sediments.

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Topological rainbow trapping of sound waves in synthesized three-dimensional space for square lattice Jie-Yu Lu(卢杰煜), Shi-Feng Li(李石峰), Xin Li(李鑫), Xin-Ye Zou(邹欣晔), and Jian-Chun Cheng(程建春) Chin. Phys. B, 2025, 34 (2):  024302.  DOI: 10.1088/1674-1056/ada1c5 Abstract ( 41 )   HTML ( 0 )   PDF (2646KB) ( 51 )   The three-dimensional (3D) synthetic space offers a platform for exploring the valley Hall insulator, which is usually constructed in graphene lattice. Here, based on the valley transports in the square lattice, we construct a synthetic space by treating the rotation angle as the third dimension and observe the emergent Weyl points in this synthetic space. Since the construction of synthetic Weyl points results in the formation of edge states between the phononic crystal (PC) and the hard boundary, and the factors of rotation angle and the distance from the PC to the hard boundary affect the frequency of these edge states, we can construct topological rainbow concentrator based on the above principles. We conduct a comprehensive numerical and experimental study to explore the characteristics of topological rainbow concentrators. This work may play a driving role in the development of topological rainbow devices.

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Neural network analysis for prediction of heat transfer of aqueous hybrid nanofluid flow in a variable porous space with varying film thickness over a stretched surface Abeer S Alnahdi and Taza Gul Chin. Phys. B, 2025, 34 (2):  024701.  DOI: 10.1088/1674-1056/ad989c Abstract ( 149 )   HTML ( 0 )   PDF (7781KB) ( 4 )   The high thermal conductivity of the nanoparticles in hybrid nanofluids results in enhanced thermal conductivity associated with their base fluids. Enhanced heat transfer is a result of this high thermal conductivity, which has significant applications in heat exchangers and engineering devices. To optimize heat transfer, a liquid film of Cu and TiO${}_2$ hybrid nanofluid behind a stretching sheet in a variable porous medium is being considered due to its importance. The nature of the fluid is considered time-dependent and the thickness of the liquid film is measured variable adjustable with the variable porous space and favorable for the uniform flow of the liquid film. The solution of the problem is acquired using the homotopy analysis method HAM, and the artificial neural network ANN is applied to obtain detailed information in the form of error estimation and validations using the fitting curve analysis. HAM data is utilized to train the ANN in this study, which uses Cu and TiO${}_2$ hybrid nanofluids in a variable porous space for unsteady thin film flow, and it is used to train the ANN. The results indicate that Cu and TiO${}_2$ play a greater role in boosting the rate.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

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Experimental study on performance of 100-kW low temperature superconducting steady-state magnetoplasmadynamic thruster Cheng Zhou(周成), Peng Wu(吴鹏), Yun-Tao Song(宋云涛), Jin-Xing Zheng(郑金星), Yong Li(李永), Ge Wang(王戈), and Hai-Yang Liu(刘海洋) Chin. Phys. B, 2025, 34 (2):  025201.  DOI: 10.1088/1674-1056/ad9910 Abstract ( 127 )   HTML ( 0 )   PDF (1722KB) ( 93 )   Applied field magnetoplasmadynamic thrusters (AF-MPDTs), with their high specific impulse and considerable thrust, are increasingly favored for large-scale space missions. This paper presents the composition, functionality, and testing methods of a high-power electric propulsion performance testing system, along with the vacuum ignition test results of a 100 kW superconducting MPD thruster. The relationships between thruster efficiency, magnetic field strength, current, and mass flow rate are analyzed. For each combination of current and flow rate in an AF-MPDT, there is an optimal magnetic field strength where the thruster efficiency reaches its peak. Under conditions of 320 A current and 60 mg/s flow rate, the optimal magnetic field strength is 0.5 T, yielding the highest thruster efficiency of 71%.

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Temporal variation characteristics of cathode temperature in a magnetoplasmadynamic thruster Cheng Zhou(周成), Peng Wu(吴鹏), Yun-Tao Song(宋云涛), Jin-Xing Zheng(郑金星), Yong Li(李永), Ge Wang(王戈), and Hai-Yang Liu(刘海洋) Chin. Phys. B, 2025, 34 (2):  025202.  DOI: 10.1088/1674-1056/ad9e9b Abstract ( 90 )   HTML ( 0 )   PDF (1912KB) ( 49 )   The magnetoplasmadynamic thruster (MPDT) is characterized by its high specific impulse and substantial thrust density, making it a promising propulsion system for deep space exploration missions. In both laboratory experiments and practical applications, cathode ablation has emerged as a critical concern. An optical diagnostic approach based on monochromatic radiation temperature measurement, utilizing plume emission spectra and the selection of an appropriate test band, has been successfully employed. This method provides an accurate temperature distribution across the cathode surface, offering a novel testing technique for the optimization and evaluation of magnetic plasma thruster designs.

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An experimental study on the magnetic field permeability of an inductive-pulsed plasma thruster Bi-Xuan Che(车碧轩), Jian-Jun Wu(吴建军), Mou-Sen Cheng(程谋森), Xiao-Kang Li(李小康), Yu Zhang(张宇), and Da-Wei Guo(郭大伟) Chin. Phys. B, 2025, 34 (2):  025203.  DOI: 10.1088/1674-1056/ad9e95 Abstract ( 91 )   HTML ( 0 )   PDF (2833KB) ( 11 )   Inductive-pulsed plasma thruster is an in-space propulsion device that generates thrust by ionizing and accelerating plasma through pulsed electromagnetic field. In this paper, the correlation between plasma structure evolution and magnetic field permeability is studied using a B-dot probe array system, combing with high-speed camera and electrical parameter measurement. Further discussions explained the mechanism how the magnetic permeation characteristics affect the energy deposition between circuit and plasma.

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Three-dimensional simulations of RF wave propagation and power coupling in cold magnetized plasma near an ICRF antenna Lei-Yu Zhang(张雷宇), Yi-Xuan Li(李屹轩), and Quan-Zhi Zhang(张权治) Chin. Phys. B, 2025, 34 (2):  025204.  DOI: 10.1088/1674-1056/ad9a9c Abstract ( 88 )   HTML ( 0 )   PDF (2993KB) ( 35 )   The electromagnetic wave propagations and their coupling characteristics in magnetized plasma near the antenna of ion cyclotron range of frequencies (ICRF) is studied based on self-developed 3DFEM-IA code. This code effectively resolves the three-dimensional (3D) geometry and the electromagnetic field using the finite element method. Our findings reveal that the distributions of electromagnetic fields and energy flow density significantly depend on the antenna phases, surface current density on the antenna straps, and background plasma density. Notably, the non-uniform surface current density on the antenna straps, resulting from the presence of induced currents, contributes to a reduction in coupling power within the edge plasma. Furthermore, the calculated coupling impedance increases with plasma density, corroborating well with experimental measurements.

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Turbulent drag reduction by sector-shaped counter-flow dielectric barrier discharge plasma actuator Borui Zheng(郑博睿), Shaojie Qi(齐少杰), Minghao Yu(喻明浩), Jianbo Zhang(张剑波), Linwu Wang(王林武), and Dongliang Bian(卞栋梁) Chin. Phys. B, 2025, 34 (2):  025205.  DOI: 10.1088/1674-1056/ada1c6 Abstract ( 80 )   HTML ( 0 )   PDF (2065KB) ( 13 )   The primary objective in aircraft transportation is to minimize turbulent drag, thereby conserving energy and reducing emissions. We propose a sector-shaped counter-flow dielectric barrier discharge plasma actuator, which leverages jet synthesis for drag reduction. A drag control experiment was conducted in a low-speed wind tunnel with a controlled flow velocity of 9.6 m/s ($Re=1.445\times {10}^4$). This study investigated the effects of varying pulse frequencies and actuation voltages on the turbulent boundary layer. Using a hot-wire measurement system, we analyzed the pulsating and time-averaged velocity distributions within the boundary layer to evaluate the streamwise turbulent drag reduction. The results show that the local TDR decreases as the pulse frequency increases, reaching a maximum reduction of approximately 20.97% at a pulse frequency of 50 Hz. In addition, as the actuation voltage increases, the friction coefficient decreases, increasing the drag reduction rate. The maximum drag reduction of approximately 33.34% is achieved at an actuation voltage of 10 kV.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

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Stokes-Einstein-Debye relation in TIP5P water Gan Ren(任淦) Chin. Phys. B, 2025, 34 (2):  026101.  DOI: 10.1088/1674-1056/ad94e3 Abstract ( 175 )   HTML ( 0 )   PDF (1026KB) ( 22 )   The Stokes-Einstein-Debye (SED) relation in TIP5P water is tested with the original formula and its variants within the temperature range 240-390 K. The results indicate that although the variants explicitly break down, the original SED relation is almost valid. Compared with the Stokes-Einstein relation, no explicit decoupling is observed in translational and rotational motion. Variation of the effective hydrodynamic radius is critical to testing the validity of the SED relation.

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High-burn-up structure evolution in polycrystalline UO2: Phase-field modeling investigation Dan Sun(孙丹), Yanbo Jiang(姜彦博), Chuanbao Tang(唐传宝), Yong Xin(辛勇), Zhipeng Sun(孙志鹏), Wenbo Liu(柳文波), and Yuanming Li(李垣明) Chin. Phys. B, 2025, 34 (2):  026102.  DOI: 10.1088/1674-1056/ad9c42 Abstract ( 103 )   HTML ( 0 )   PDF (1780KB) ( 11 )   Understanding the evolution of microstructures in nuclear fuels under high-burn-up conditions is critical for extending fuel refueling cycles and enhancing nuclear reactor safety. In this study, a phase-field model is proposed to examine the evolution of high-burn-up structures in polycrystalline UO${}_2$. The formation and growth of recrystallized grains were initially investigated. It was demonstrated that recrystallization kinetics adhere to the Kolmogorov-Johnson-Mehl-Avrami (KJMA) equation, and that recrystallization represents a process of free-energy reduction. Subsequently, the microstructural evolution in UO${}_2$ was analyzed as the burn up increased. Gas bubbles acted as additional nucleation sites, thereby augmenting the recrystallization kinetics, whereas the presence of recrystallized grains accelerated bubble growth by increasing the number of grain boundaries. The observed variations in the recrystallization kinetics and porosity with burn-up closely align with experimental findings. Furthermore, the influence of grain size on microstructure evolution was investigated. Larger grain sizes were found to decrease porosity and the occurrence of high-burn-up structures.

CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES

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Optical signature of flat bands in topological hourglass semimetal Nb3SiTe6 Shize Cao(曹仕泽), Cuiwei Zhang(张翠伟), Yueshan Xu(徐越山), Jianzhou Zhao(赵建洲), Youguo Shi(石友国), Yun-Ze Long(龙云泽), Jianlin Luo(雒建林), and Zhi-Guo Chen(谌志国) Chin. Phys. B, 2025, 34 (2):  027101.  DOI: 10.1088/1674-1056/ad9e9c Abstract ( 200 )   HTML ( 0 )   PDF (1554KB) ( 67 )   Flat electronic bands in condensed matter provide a rich avenue for exploring novel quantum phenomena. Here, we report an optical spectroscopy study of a topological hourglass semimetal Nb${}_3$SiTe${}_6$ with the electric field of the incident light parallel to its crystalline $ab$-plane. The $ab$-plane optical conductivity spectra of Nb${}_3$SiTe${}_6$ single crystals exhibit a remarkable peak-like feature around 1.20 eV, which is mainly contributed by the direct optical transitions between the two ab-initio-calculation-derived flat bands along the momentum direction $Z$-$U$. Our results pave the way for investigating exotic quantum phenomena based on the flat bands in topological hourglass semimetals.

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Highly responsive photodetectors based on NiPS3/WS2 van der Waals type-II heterostructures Zhiteng Li(李志腾), Yian Wang(王易安), Zhenming Qiu(邱振铭), Lin Wang(王琳), Xiaofeng Liu(刘小峰), Zhengwei Chen(陈政委), and Xiao Zhang(张晓) Chin. Phys. B, 2025, 34 (2):  027201.  DOI: 10.1088/1674-1056/ad9e97 Abstract ( 138 )   HTML ( 0 )   PDF (1254KB) ( 55 )   A heterostructure photodetector composed of few-layer NiPS${}_3$/WS${}_2$ is made by using mechanical exfoliation and micro-nano fabrication techniques. The photodetector exhibits a broad-band response wavelengths of ranging of 405 nm and 800 nm. Under the light illumination of 405-nm wavelength and a bias voltage of $-2$ V, the photoresponsivity is 62.6 mA/W and the specific detectivity is 8.59$\times {10}^{10}$ Jones. In addition, the device demonstrates a relatively fast response with rise and fall times of 70 ms and 120 ms. Theoretical calculation suggest that this excellent performance can be ascribed to the type-II band alignment at the NiPS${}_3$/WS${}_2$ heterostructure interface.

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Disentangling electronic and phononic thermal transport across two-dimensional interfaces Linxin Zhai(翟麟鑫) and Zhiping Xu(徐志平) Chin. Phys. B, 2025, 34 (2):  027202.  DOI: 10.1088/1674-1056/ad9ffd Abstract ( 131 )   HTML ( 1 )   PDF (8337KB) ( 55 )   Electrical and thermal transport at two-dimensional (2D) interfaces is critical for semiconductor technology, yet their interplay remains unclear. We report a theoretical proposal to separate electronic and phononic contributions to thermal conductance at 2D interfaces with graphene, which is validated by non-equilibrium Green's function calculations and molecular dynamics simulations for graphene-gold contacts. Our results reveal that while metal-graphene interfaces are transparent for both electrons and phonons, non-covalent graphene interfaces block electronic tunneling beyond two layers but not phonon transport. This suggests that the Wiedemann-Franz law can be experimentally tested by measuring transport across interfaces with varying graphene layers.

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High-throughput screening and evaluation of double-linker metal-organic frameworks for CO2/H2 adsorption and separation Ji-Long Huang(黄纪龙), Xiu-Ying Liu(刘秀英), Hao Chen(陈浩), Xiao-Dong Li(李晓东), and Jing-Xin Yu(于景新) Chin. Phys. B, 2025, 34 (2):  027302.  DOI: 10.1088/1674-1056/ad925a Abstract ( 148 )   HTML ( 0 )   PDF (3999KB) ( 57 )   The capture of CO${}_2$ from CO${}_2$/H${}_2$ gas mixtures in syngas is a crucial issue for hydrogen production from steam methane reforming in industry, as the presence of CO${}_2$ directly affects the purity of H${}_2$. A combination of a high-throughput screening method and grand canonical Monte Carlo simulation was utilized to evaluate and screen 1725 metal-organic frameworks (MOFs) in detail as a means of determining their adsorption performance for CO${}_2$/H${}_2$ gas mixtures. The adsorption and separation performance of double-linker MOFs was comprehensively evaluated using eight evaluation indicators, namely, the largest cavity diameter, accessible surface area, pore occupied accessible volume, porosity, adsorption selectivity, working capacity, adsorbent performance score and percent regeneration. Six optimal performance frameworks were screened to further study their single-component adsorption and binary competitive adsorption of CO${}_2$/H${}_2$ respectively. The CO${}_2$ adsorption selectivity at different CO${}_2$/H${}_2$ feed ratios was also evaluated, which indicated their excellent adsorption and separation performance. The microscopic adsorption mechanisms for CO${}_2$ and H${}_2$ at the molecular level were investigated by analyzing the radial distribution function and density distribution. This study may provide directional guidance and reference for subsequent experiments on the adsorption and separation of CO${}_2$/H${}_2$.

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Phonon-mediated superconductivity in orthorhombic XS (X = Nb, Ta or W) Guo-Hua Liu(刘国华), Kai-Yue Jiang(江恺悦), Yi Wan(万一), Shu-Xiang Qiao(乔树祥), Jin-Han Tan(谭锦函), Na Jiao(焦娜), Ping Zhang(张平), and Hong-Yan Lu(路洪艳) Chin. Phys. B, 2025, 34 (2):  027401.  DOI: 10.1088/1674-1056/ad9733 Abstract ( 161 )   HTML ( 0 )   PDF (7402KB) ( 96 )   The unique three-dimensional orthorhombic NbS (o-NbS) compound synthesized in 1969 has recently been experimentally confirmed to be a superconductor [Phys. Rev. B 108 174517 (2023)]. However, there is currently no theoretical research on its superconducting mechanism. In this work, we investigate the superconducting properties of o-NbS from first-principles calculations. Based on the Eliashberg equation, it is found that the superconductivity mainly originates from the coupling between the electrons of Nb-4d orbitals and the vibrations of Nb atoms in the low-frequency region and those of S atoms in the high-frequency region. A superconducting transition temperature ($T_{\mathrm{c}}$) of 10.7 K is obtained, which is close to the experimental value and higher than most transition metal chalcogenides (TMCs). The calculated thermodynamic properties in the superconducting state, such as specific heat, energy gap, isotope coefficient, etc., also indicate that o-NbS is a conventional phonon-mediated superconductor. These results are consistent with recent experimental reports and provide a good understanding of the superconducting mechanism of o-NbS. Furthermore, the TMCs of o-TaS and o-WS are also investigated; these belong to the same and neighboring groups of Nb, and we find that o-TaS and o-WS are also phonon-mediated superconductors with $T_{\mathrm{c}}$ of 8.9 K and 7.2 K, respectively.

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Realization of robust Ohmic contact for semiconducting black arsenic by coupling with graphene Xinjuan Cheng(程新娟) and Xuechao Zhai(翟学超) Chin. Phys. B, 2025, 34 (2):  027402.  DOI: 10.1088/1674-1056/ada0b3 Abstract ( 160 )   HTML ( 0 )   PDF (1770KB) ( 61 )   Ohmic contacts are fundamental components in semiconductor technology, facilitating efficient electrical connection and excellent device performance. We employ first-principles calculations to show that semimetallic graphene is a natural Ohmic contact partner of monolayer semiconducting black arsenic (BAs), for which the top of the valence band is below the Fermi energy of the order of 10${}^2$ meV. The Ohmic contact arises from the giant Stark effect induced by van der Waals electron transfer from BAs to graphene, which does not destroy their respective band features. Remarkably, we show that this intrinsic Ohmic contact remains robust across a wide range of interlayer distances (adjustable by strain) or vertical electric fields, whereas the weak spin splitting of the order of 1 meV induced by symmetry breaking plays little part in Ohmic contact. These findings reveal the potential applications of graphene-BAs in ultralow dissipation transistors.

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Strain-manipulated dispersion characteristics of magnonic crystals with Dzyaloshinskii-Moriya interaction and applications on spin-wave devices Chuhan Zhou(周楚涵), Xiaotian Jiao(焦晓天), Jiaxi Xu(徐佳熙), Zhaonian Jin(金兆年), Lin Chen(陈琳), and Zhikuo Tao(陶志阔) Chin. Phys. B, 2025, 34 (2):  027501.  DOI: 10.1088/1674-1056/ad9892 Abstract ( 137 )   HTML ( 0 )   PDF (1231KB) ( 40 )   Dispersion characteristics of magnonic crystals have attracted considerable attention because of the potential applications for spin-wave devices. In this work, we investigated the strain-manipulated dispersion characteristics of magnonic crystals with Dzyaloshinskii-Moriya interaction (DMI) and discussed the potential applications in spin-wave devices. Here, the ground states and stabilities of the magnonic crystals were investigated. Then, the strain-manipulated dispersion characteristics of the magnonic crystals based on domains and skyrmions were studied. The simulation results indicated that, the applied strain could manipulate the band widths and the positions of the allowed frequency bands. Finally, the realization of magnonic crystal heterojunctions and potential applications in spin-wave devices, such as filters, diodes, and transistors based on strain-manipulated magnonic crystals were proposed. Our research provides a theoretical foundation for designing tunable spin-wave devices based on strain-manipulated magnonic crystals with DMI.

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Effect of Co substitution for Fe on microstructure and magnetic properties of FeNiSiBCuNb alloy ribbons Wen-Feng Liu(刘文峰), Ya-Ting Yuan(袁雅婷), Chang-Jiang Yu(于长江), Shu-Jie Kang(康树杰), Qian-Ke Zhu(朱乾科), Zhe Chen(陈哲), Ke-Wei Zhang(张克维), and Min-Gang Zhang(张敏刚) Chin. Phys. B, 2025, 34 (2):  027502.  DOI: 10.1088/1674-1056/ad9e98 Abstract ( 105 )   HTML ( 0 )   PDF (2006KB) ( 17 )   This work investigated the microstructure, magnetic properties, and crystallization kinetics of the as-spun and annealed alloy ribbons of (Fe${}_{40-x}$Co${}_x$Ni${}_{40}$Si${}_{6.33}$B${}_{12.66}$Cu${}_1$) ${}_{0.97}$Nb${}_{0.03}$, where $x=0$, 6, 7, 8, 9, prepared using the melt-spinning method. The results show that adding a moderate amount of Co can improve the glass forming ability (GFA), the first peak crystallization temperature, and thermal stability of the as-spun alloy ribbons. With $x=7$, the two-stage crystallization temperature interval $\mathrm{\Delta }{T}_x=90$ exhibits optimal thermal stability, and the alloy annealed at 673 K for 10 minutes shows the favorable combined magnetic properties, with $H_{\mathrm{c}}=0.12$ A/m, $M_{\mathrm{s}}=88.7$ A$\cdot$m${}^2$/kg, and ${\mu }_{\mathrm{e}}=13800$. The magnetic domain results show that annealing removes numerous pinning points in the magnetic domains of the alloy ribbons, making the domain walls smoother and effectively reducing the pinning effect.

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Thickness-dependent magnetic property of FeNi thin film grown on flexible graphene substrate Suixin Zhan(詹遂鑫), Shaokang Yuan(袁少康), Yuming Bai(白宇明), Fu Liu(刘福), Bohan Zhang(张博涵), Weijia Han(韩卫家), Tao Wang(王韬), Shengxiang Wang(汪胜祥), and Cai Zhou(周偲) Chin. Phys. B, 2025, 34 (2):  027503.  DOI: 10.1088/1674-1056/ad92fd Abstract ( 171 )   HTML ( 1 )   PDF (5444KB) ( 44 )   Electronics over flexible substrates offer advantages of flexibility, portability and low cost, and promising applications in the areas of energy, information, defense science and medical service. In recent years, tremendous progress has been witnessed in the development of flexible wearable devices that can be potentially massively deployed. Of particular interest are intelligent wearable devices, such as sensors and storage cells, which can be integrated by flexible magnetoelectronic devices based on magnetic thin films. To examine this further, the magnetic properties of FeNi thin films with different thicknesses grown on flexible graphene substrate are investigated at room temperature. The coercivity increases with increasing thicknesses of FeNi thin film, which can be attributed to the increase of grain size and decrease of surface roughness. Moreover, the thickness modulated magnetic property shows a magnetic anisotropy shift increase with varying thicknesses of FeNi thin film by using measurements based on ferromagnetic resonance, which further enhances the resonance frequency. In addition, the resonance peak is quite stable after bending it for ten cycles. The result is promising for the future design of flexible magnetoelectronic devices.

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Understanding thermal hysteresis of ferroelectric phase transitions in BaTiO3 with combined first-principle-based approach and phase-field model Cancan Shao(邵灿灿) and Houbing Huang(黄厚兵) Chin. Phys. B, 2025, 34 (2):  027701.  DOI: 10.1088/1674-1056/ad9e94 Abstract ( 137 )   HTML ( 1 )   PDF (1681KB) ( 69 )   Based on the principles of thermodynamics, we elucidate the fundamental reasons behind the hysteresis of spontaneous polarization in ferroelectric materials during heating and cooling processes. By utilizing the effective Hamiltonian method in conjuction with the phase-field model, we have successfully reproduced the thermal hysteresis observed in ferroelectric materials during phase transitions. The computational results regarding the electrocaloric effect from these two different computational scales closely align with experimental measurements. Furthermore, we analyze how the first-order ferroelectric phase transition gradually diminishes with an increasing applied electric field, exhibiting characteristics of second-order-like phase transition. By employing the characteristic parameters of thermal hysteresis, we have established a pathway for calculations across different computational scales, thereby providing theoretical support for further investigations into the properties of ferroelectric materials through concurrent multiscale simulations.

INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

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Significant increase in thermal conductivity of cathode material LiFePO4 by Na substitution: A machine learning interatomic potential-assisted investigation Shi-Yi Li(李诗怡), Qian Liu(刘骞), Yu-Jia Zeng(曾育佳), Guofeng Xie(谢国锋), and Wu-Xing Zhou(周五星) Chin. Phys. B, 2025, 34 (2):  028201.  DOI: 10.1088/1674-1056/ad9e99 Abstract ( 163 )   HTML ( 0 )   PDF (2155KB) ( 68 )   LiFePO${}_4$ is a cathode material with good thermal stability, but low thermal conductivity is a critical problem. In this study, we employ a machine learning potential approach based on first-principles methods combined with the Boltzmann transport theory to investigate the influence of Na substitution on the thermal conductivity of LiFePO${}_4$ and the impact of Li-ion de-embedding on the thermal conductivity of Li${}_{3/4}$Na${}_{1/4}$FePO${}_4$, with the aim of enhancing heat dissipation in Li-ion batteries. The results show a significant increase in thermal conductivity due to an increase in phonon group velocity and a decrease in phonon anharmonic scattering by Na substitution. In addition, the thermal conductivity increases significantly with decreasing Li-ion concentration due to the increase in phonon lifetime. Our work guides the improvement of the thermal conductivity of LiFePO${}_4$, emphasizing the crucial roles of both substitution and Li-ion detachment/intercalation for the thermal management of electrochemical energy storage devices.

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Triadic percolation in computer virus spreading dynamics Jie Gao(高杰), Jianfeng Luo(罗建锋), Xing Li(李星), Yihong Li(李毅红), Zunguang Guo(郭尊光), and Xiaofeng Luo(罗晓峰) Chin. Phys. B, 2025, 34 (2):  028701.  DOI: 10.1088/1674-1056/ad9ff8 Abstract ( 151 )   HTML ( 0 )   PDF (975KB) ( 77 )   In recent years, the threats posed by computer viruses have become increasingly diverse and complex. While classic percolation theory provides a novel perspective for analyzing epidemics and information dissemination, it fails to capture the temporal dynamics of these systems and the effects of virus invasion and governmental regulation. Triadic percolation theory, a recent advancement, addresses these limitations. In this paper, we apply this new percolation mechanism to model the diffusion of computer viruses, deriving a precise mathematical formulation of the triadic percolation model and providing an analytical solution of the triadic percolation threshold. Additionally, we investigate the impact of nonlinear transmission probability characteristics on virus propagation. Numerical simulations demonstrate that reducing the network's average degree (or the positive regulation) or increasing regulatory interventions raises the outbreak threshold for computer viruses while decreasing their final size. Moreover, the study reveals that nonlinear transmission probabilities result in an increased number of solutions for the final size of the computer viruses. Our findings contribute new insights into controlling the spread of computer viruses.

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Cross-correlations between signal's components Quankun Zhao(赵全坤), Sen Li(李森), Changgui Gu(顾长贵), Haiying Wang(王海英), and Huijie Yang(杨会杰) Chin. Phys. B, 2025, 34 (2):  028702.  DOI: 10.1088/1674-1056/ad9ffb Abstract ( 154 )   HTML ( 0 )   PDF (2943KB) ( 61 )   Detecting coupling pattern between elements in a complex system is a basic task in data-driven analysis. The trajectory for each specific element is a cooperative result of its intrinsic dynamic, its couplings with other elements, and the environment. It is subsequently composed of many components, only some of which take part in the couplings. In this paper we present a framework to detect the component correlation pattern. Firstly, the interested trajectories are decomposed into components by using decomposing methods such as the Fourier expansion and the Wavelet transformation. Secondly, the cross-correlations between the components are calculated, resulting into a component cross-correlation matrix (network). Finally, the dominant structure in the network is identified to characterize the coupling pattern in the system. Several deterministic dynamical models turn out to be characterized with rich structures such as the clustering of the components. The pattern of correlation between respiratory (RESP) and ECG signals is composed of five sub-clusters that are mainly formed by the components in ECG signal. Interestingly, only $7$ components from RESP (scattered in four sub-clusters) take part in the realization of coupling between the two signals.

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Node ranking based on graph curvature and PageRank Hongbo Qu(曲鸿博), Yu-Rong Song(宋玉蓉), Ruqi Li(李汝琦), Min Li(李敏), and Guo-Ping Jiang(蒋国平) Chin. Phys. B, 2025, 34 (2):  028901.  DOI: 10.1088/1674-1056/ad9a9b Abstract ( 163 )   HTML ( 0 )   PDF (1007KB) ( 79 )   Identifying key nodes in complex networks is crucial for understanding and controlling their dynamics. Traditional centrality measures often fall short in capturing the multifaceted roles of nodes within these networks. The PageRank algorithm, widely recognized for ranking web pages, offers a more nuanced approach by considering the importance of connected nodes. However, existing methods generally overlook the geometric properties of networks, which can provide additional insights into their structure and functionality. In this paper, we propose a novel method named Curv-PageRank (C-PR), which integrates network curvature and PageRank to identify influential nodes in complex networks. By leveraging the geometric insights provided by curvature alongside structural properties, C-PR offers a more comprehensive measure of a node's influence. Our approach is particularly effective in networks with community structures, where it excels at pinpointing bridge nodes critical for maintaining connectivity and facilitating information flow. We validate the effectiveness of C-PR through extensive experiments. The results demonstrate that C-PR outperforms traditional centrality-based and PageRank methods in identifying critical nodes. Our findings offer fresh insights into the structural importance of nodes across diverse network configurations, highlighting the potential of incorporating geometric properties into network analysis.

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Critical station identification of metro networks based on the integrated topological-functional algorithm: A case study of Chengdu Zi-Qiang Zeng(曾自强), Sheng-Jie He(何圣洁), and Wang Tian(田旺) Chin. Phys. B, 2025, 34 (2):  028902.  DOI: 10.1088/1674-1056/ad9734 Abstract ( 171 )   HTML ( 0 )   PDF (2086KB) ( 64 )   As a key mode of transportation, urban metro networks have significantly enhanced urban traffic environments and travel efficiency, making the identification of critical stations within these networks increasingly essential. This study presents a novel integrated topological-functional (ITF) algorithm for identifying critical nodes, combining topological metrics such as K-shell decomposition, node information entropy, and neighbor overlapping interaction with the functional attributes of passenger flow operations, while also considering the coupling effects between metro and bus networks. Using the Chengdu metro network as a case study, the effectiveness of the algorithm under different conditions is validated. The results indicate significant differences in passenger flow patterns between working and non-working days, leading to varying sets of critical nodes across these scenarios. Moreover, the ITF algorithm demonstrates a marked improvement in the accuracy of critical node identification compared to existing methods. This conclusion is supported by the analysis of changes in the overall network structure and relative global operational efficiency following targeted attacks on the identified critical nodes. The findings provide valuable insight into urban transportation planning, offering theoretical and practical guidance for improving metro network safety and resilience.