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15 March 2025, Volume 34 Issue 3 Previous issue    Next issue

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TOPICAL REVIEW — Moiré physics in two-dimensional materials

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Higher-order topology in twisted multilayer systems: A review Chunbo Hua(花春波) and Dong-Hui Xu(许东辉) Chin. Phys. B, 2025, 34 (3):  037301.  DOI: 10.1088/1674-1056/ada885 Abstract ( 39 )   HTML ( 0 )   PDF (1959KB) ( 9 )   In recent years, there has been a surge of interest in higher-order topological phases (HOTPs) across various disciplines within the field of physics. These unique phases are characterized by their ability to harbor topological protected boundary states at lower-dimensional boundaries, a distinguishing feature that sets them apart from conventional topological phases and is attributed to the higher-order bulk-boundary correspondence. Two-dimensional (2D) twisted systems offer an optimal platform for investigating HOTPs, owing to their strong controllability and experimental feasibility. Here, we provide a comprehensive overview of the latest research advancements on HOTPs in 2D twisted multilayer systems. We will mainly review the HOTPs in electronic, magnonic, acoustic, photonic and mechanical twisted systems, and finally provide a perspective of this topic.

SPECIAL TOPIC — Moiré physics in two-dimensional materials

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Emergence of metal-semiconductor phase transition in MX2(M = Ni, Pd, Pt; X = S, Se, Te) moiré superlattices Jie Li(李杰), Rui-Zi Zhang(张瑞梓), Jinbo Pan(潘金波), Ping Chen(陈平), and Shixuan Du(杜世萱) Chin. Phys. B, 2025, 34 (3):  037302.  DOI: 10.1088/1674-1056/ada7d9 Abstract ( 33 )   HTML ( 1 )   PDF (1334KB) ( 36 )   Two-dimensional (2D) moiré superlattices with a small twist in orientation exhibit a broad range of physical properties due to the complicated intralayer and interlayer interactions modulated by the twist angle. Here, we report a metal-semiconductor phase transition in homojunction moiré superlattices of NiS${}_2$ and PtTe${}_2$ with large twist angles based on high-throughput screening of 2D materials $M{X}_2$ ($M=\mathrm{N}\mathrm{i}$, Pd, Pt; $X=\mathrm{S}$, Se, Te) via density functional theory (DFT) calculations. Firstly, the calculations for different stacking configurations (AA, AB and AC) reveal that AA stacking ones are stable for all the bilayer $M{X}_2$. The metallic or semiconducting properties of these 2D materials remain invariable for different stacking without twisting except for NiS${}_2$ and PtTe${}_2$. For the twisted configurations, NiS${}_2$ transfers from metal to semiconductor when the twist angles are 21.79${}^{\circ }$, 27.79${}^{\circ }$, 32.20${}^{\circ }$ and 60${}^{\circ }$. PtTe${}_2$ exhibits a similar transition at 60${}^{\circ }$. The phase transition is due to the weakened d-p orbital hybridization around the Fermi level as the interlayer distance increases in the twisted configurations. Further calculations of untwisted bilayers with increasing interlayer distance demonstrate that all the materials undergo metal-semiconductor phase transition with the increased interlayer distance because of the weakened d-p orbital hybridization. These findings provide fundamental insights into tuning the electronic properties of moiré superlattices with large twist angles.

SPECIAL TOPIC — Computational programs in complex systems

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GPIC: A GPU-based parallel independent cascade algorithm in complex networks Chang Su(苏畅), Xu Na(那旭), Fang Zhou(周方), and Linyuan Lü(吕琳媛) Chin. Phys. B, 2025, 34 (3):  030204.  DOI: 10.1088/1674-1056/adb67c Abstract ( 77 )   HTML ( 0 )   PDF (1756KB) ( 4 )   Independent cascade (IC) models, by simulating how one node can activate another, are important tools for studying the dynamics of information spreading in complex networks. However, traditional algorithms for the IC model implementation face significant efficiency bottlenecks when dealing with large-scale networks and multi-round simulations. To settle this problem, this study introduces a GPU-based parallel independent cascade (GPIC) algorithm, featuring an optimized representation of the network data structure and parallel task scheduling strategies. Specifically, for this GPIC algorithm, we propose a network data structure tailored for GPU processing, thereby enhancing the computational efficiency and the scalability of the IC model. In addition, we design a parallel framework that utilizes the full potential of GPU's parallel processing capabilities, thereby augmenting the computational efficiency. The results from our simulation experiments demonstrate that GPIC not only preserves accuracy but also significantly boosts efficiency, achieving a speedup factor of 129 when compared to the baseline IC method. Our experiments also reveal that when using GPIC for the independent cascade simulation, 100-200 simulation rounds are sufficient for higher-cost studies, while high precision studies benefit from 500 rounds to ensure reliable results, providing empirical guidance for applying this new algorithm to practical research.

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Impact of message fatigue and individual behavioral responses on epidemiological spread in temporal simplicial networks Xiao-Nan Fan(樊晓楠) and Xuemei You(由雪梅) Chin. Phys. B, 2025, 34 (3):  038703.  DOI: 10.1088/1674-1056/adaade Abstract ( 91 )   HTML ( 0 )   PDF (3062KB) ( 6 )   Health information spreads rapidly, which can effectively control epidemics. However, the swift dissemination of information also has potential negative impacts, which increasingly attracts attention. Message fatigue refers to the psychological response characterized by feelings of boredom and anxiety that occur after receiving an excessive amount of similar information. This phenomenon can alter individual behaviors related to epidemic prevention. Additionally, recent studies indicate that pairwise interactions alone are insufficient to describe complex social transmission processes, and higher-order structures representing group interactions are crucial. To address this, we develop a novel epidemic model that investigates the interactions between information, behavioral responses, and epidemics. Our model incorporates the impact of message fatigue on the entire transmission system. The information layer is modeled using a static simplicial network to capture group interactions, while the disease layer uses a time-varying network based on activity-driven model with attractiveness to represent the self-protection behaviors of susceptible individuals and self-isolation behaviors of infected individuals. We theoretically describe the co-evolution equations using the microscopic Markov chain approach (MMCA) and get the epidemic threshold. Experimental results show that while the negative impact of message fatigue on epidemic transmission is limited, it significantly weakens the group interactions depicted by higher-order structures. Individual behavioral responses strongly inhibit the epidemic. Our simulations using the Monte Carlo (MC) method demonstrate that greater intensity in these responses leads to clustering of susceptible individuals in the disease layer. Finally, we apply the proposed model to real networks to verify its reliability. In summary, our research results enhance the understanding of the information-epidemic coupling dynamics, and we expect to provide valuable guidance for managing future emerging epidemics.

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Vital nodes identification method integrating degree centrality and cycle ratio Yu Zhao(赵玉) and Bo Yang(杨波) Chin. Phys. B, 2025, 34 (3):  038901.  DOI: 10.1088/1674-1056/ada42d Abstract ( 104 )   HTML ( 0 )   PDF (7010KB) ( 13 )   Identifying vital nodes is one of the core issues of network science, and is crucial for epidemic prevention and control, network security maintenance, and biomedical research and development. In this paper, a new vital nodes identification method, named degree and cycle ratio (DC), is proposed by integrating degree centrality (weight $\alpha$) and cycle ratio (weight $1-\alpha$). The results show that the dynamic observations and weight $\alpha$ are nonlinear and non-monotonicity (i.e., there exists an optimal value ${\alpha }^{\ast }$ for $\alpha$), and that DC performs better than a single index in most networks. According to the value of ${\alpha }^{\ast }$, networks are classified into degree-dominant networks (${\alpha }^{\ast }>0.5$) and cycle-dominant networks (${\alpha }^{\ast }<0.5$). Specifically, in most degree-dominant networks (such as Chengdu-BUS, Chongqing-BUS and Beijing-BUS), degree is dominant in the identification of vital nodes, but the identification effect can be improved by adding cycle structure information to the nodes. In most cycle-dominant networks (such as Email, Wiki and Hamsterster), the cycle ratio is dominant in the identification of vital nodes, but the effect can be notably enhanced by additional node degree information. Finally, interestingly, in Lancichinetti-Fortunato-Radicchi (LFR) synthesis networks, the cycle-dominant network is observed.

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SNSAlib: A python library for analyzing signed network Ai-Wen Li(李艾纹), Jun-Lin Lu(陆俊霖), Ying Fan(樊瑛), and Xiao-Ke Xu(许小可) Chin. Phys. B, 2025, 34 (3):  038902.  DOI: 10.1088/1674-1056/ada439 Abstract ( 100 )   HTML ( 0 )   PDF (3095KB) ( 10 )   The unique structure of signed networks, characterized by positive and negative edges, poses significant challenges for analyzing network topology. In recent years, various statistical algorithms have been developed to address this issue. However, there remains a lack of a unified framework to uncover the nontrivial properties inherent in signed network structures. To support developers, researchers, and practitioners in this field, we introduce a Python library named SNSAlib (Signed Network Structure Analysis), specifically designed to meet these analytical requirements. This library encompasses empirical signed network datasets, signed null model algorithms, signed statistics algorithms, and evaluation indicators. The primary objective of SNSAlib is to facilitate the systematic analysis of micro- and meso-structure features within signed networks, including node popularity, clustering, assortativity, embeddedness, and community structure by employing more accurate signed null models. Ultimately, it provides a robust paradigm for structure analysis of signed networks that enhances our understanding and application of signed networks.

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Algorithm for computing time correlation functions in non-stationary complex dynamic systems Jiu Zhang(张鹫), Lifu Jin(金立孚), Bo Zheng(郑波), Xiongfei Jiang(蒋雄飞), Tingting Chen(陈婷婷), Cong Xu(徐匆), and Yanqing Hu(胡延庆) Chin. Phys. B, 2025, 34 (3):  038904.  DOI: 10.1088/1674-1056/adb8bd Abstract ( 80 )   HTML ( 0 )   PDF (1612KB) ( 21 )   For non-stationary complex dynamic systems, a standardized algorithm is developed to compute time correlation functions, addressing the limitations of traditional methods reliant on the stationary assumption. The proposed algorithm integrates two-point and multi-point time correlation functions into a unified framework. Further, it is verified by a practical application in complex financial systems, demonstrating its potential in various complex dynamic systems.

SPECIAL TOPIC — Quantum communication and quantum network

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Continuous-variable quantum secure direct communication based on N-APSK with Boltzmann-Maxwell distribution Zheng-Wen Cao(曹正文), Yu-Jie Zhang(张昱洁), Geng Chai(柴庚), Zhang-Tao Liang(梁章韬), Xin-Lei Chen(陈欣蕾), Lei Wang(王磊), and Yu-Jie Wang(王禹杰) Chin. Phys. B, 2025, 34 (3):  030303.  DOI: 10.1088/1674-1056/ada549 Abstract ( 98 )   HTML ( 0 )   PDF (1010KB) ( 13 )   Continuous-variable quantum secure direct communication (CVQSDC) with Gaussian modulation (GM) demands a considerable quantity of random numbers during the preparation process and encodes them separately on the quadrature components of the quantum states. Hence, high-speed random number generators are required to satisfy this demand, which is difficult to implement in practical applications. CVQSDC with discrete modulation (DM), correspondingly, employs a finite number of quantum states to achieve encoding, which can circumvent the shortcomings of the GM scheme. Based on the advantages of DM, the issue of attaining the most optimal secrecy capacity and communication distance remains to be resolved. Here, we propose a CVQSDC protocol based on $N$-symbol amplitude phase shift keying ($N$-APSK), which exploits the Boltzmann-Maxwell distribution assisted probability shaping technique. In comparison with the uniform distribution, according to 32-APSK CVQSDC, the proposed scheme extends the communication distance by about 38%, while obtaining a higher secrecy capacity at the same communication distance. Furthermore, increasing the value of $N$ will concurrently increase the quantity of rings in the constellation, thereby facilitating enhancements of communication distance. This work incorporates the modulation approaches prevalently employed in classical communication into the realm of quantum communication, attaining gratifying advancements in communication distance and secrecy capacity, and concurrently facilitating the integrated development of quantum communication and classical communication.

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A pure quantum secret sharing scheme based on GHZ basis measurement and quantum entanglement exchange Bai Liu(刘白), Jun Zhang(张俊), Shupin Qiu(邱书品), and Mingwu Zhang(张明武) Chin. Phys. B, 2025, 34 (3):  030304.  DOI: 10.1088/1674-1056/ada548 Abstract ( 83 )   HTML ( 0 )   PDF (609KB) ( 7 )   At present, most quantum secret sharing (QSS) protocols are more or less designed with the incorporation of classical secret sharing schemes. With the increasing maturity of quantum technology, QSS protocols based on pure quantum mechanics are becoming more important. Classical secret sharing schemes cannot achieve absolute security, and their involvement can compromise the security of QSS protocols. This paper proposes a QSS scheme based on Greenberger-Horn-Zeilinger (GHZ) basis measurement and quantum entanglement exchange. In this protocol, the secret sender stores the secret information using Pauli operations. Participants obtain their shares by measuring the product state sequentially. Finally, participants complete the secret reconstruction through quantum entanglement exchange and other related quantum operations. In addition, the particles held by participants in the protocol do not contain any secret information. Each participant's particles are in a state of maximum entanglement, and no participant can deduce the particle information of other participants through their own particles. At the same time, the protocol is based on pure quantum mechanics and does not involve classical schemes, which avoids the problem of reduced security of the protocol. Security analysis indicates that the protocol is not vulnerable to retransmission interception and collusion attacks. Moreover, it is capable of detecting and terminating the protocol promptly when facing with attacks from dishonest participants.

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Measurement-based entanglement purification for hybrid entangled state Cheng-Chen Luo(罗程晨), Shi-Pu Gu(顾世浦), Xing-Fu Wang(王兴福), Lan Zhou(周澜), and Yu-Bo Sheng(盛宇波) Chin. Phys. B, 2025, 34 (3):  030307.  DOI: 10.1088/1674-1056/adb267 Abstract ( 78 )   HTML ( 0 )   PDF (563KB) ( 5 )   Hybrid entangled states (HESs), which involve different particles with various degrees of freedom, have garnered significant attention and been applied in a wide range of quantum technologies. However, similar to other categories of entanglement, maximally HESs inevitably degrade to mixed states due to the environmental noise and operational imperfections. To address the degradation problem, measurement-based entanglement purification offers a feasible and robust solution alternative to conventional gate-based purification methods. In this paper, we propose a measurement-based hybrid entanglement purification protocol (MB-HEPP) for a certain kind of HES which consists of polarization photons and coherent states. We extend our methodology to several conditions, such as the multi-copy and multi-party scenarios, and the photon-loss condition. Compared with previous HEPPs, this protocol has several advantages. First, it does not depend on post-selection and the purified HESs can be retained for further application. Second, it does not require the Bell state measurement, but only uses the parity check with conventional linear optical elements, which makes it have the higher success probability and more feasible. Our MB-HEPP has potential applications in future heterogeneous quantum networks.

SPECIAL TOPIC — Structures and properties of materials under high pressure

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Pressure-promoted ligand to metal energy transfer for emission enhancement of [Tb2(BDC)3(DMF)2(H2O)2]n metal-organic framework Yunfeng Yang(杨云峰), Kaiyan Yuan(袁开岩), Binhao Yang(杨斌豪), Qing Yang(杨青), Yixuan Wang(王艺璇), and Xinyi Yang(杨新一)§ Chin. Phys. B, 2025, 34 (3):  036101.  DOI: 10.1088/1674-1056/ada755 Abstract ( 31 )   HTML ( 0 )   PDF (1740KB) ( 2 )   Lanthanide metal-organic frameworks (Ln-MOFs) have received extensive attention in the development of photoluminescent (PL) materials due to their stable structures and unique line-like emission spectroscopic properties. However, in order to prepare Ln-MOFs with high PL quantum yield (PLQY), further improving the sensitization efficiency of the "antenna effect" is essential. Herein, remarkably enhanced PL in [Tb${}_2$(BDC)${}_3$(DMF)${}_2$(H${}_2$O)${}_2$]${}_n$ MOF is successfully achieved via high-pressure engineering at room temperature. Notably, the PL intensity continues to increase as the pressure increases, reaching its peak at 12.0 GPa, which is 4.4 times that of the initial state. Detailed experimental and theoretical calculations have demonstrated that pressure engineering significantly narrows the bandgap of [Tb${}_2$(BDC)${}_3$(DMF)${}_2$(H${}_2$O)${}_2$]${}_n$, optimizing both singlet and triplet energy levels. Ultimately, higher antenna effect sensitization efficiency is achieved by promoting intersystem crossing and energy transfer processes. Our work provides a promising strategy for the development of high PLQY Ln-MOFs.

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Structural and transport properties of (Mg,Fe)SiO3 at high temperature and high pressure Shu Huang(黄澍), Zhiyang Xiang(向志洋), Shi He(何适), Luhan Yin(尹路寒), Shihe Zhang(张时赫), Chen Chen(陈晨), Kaihua He(何开华), and Cheng Lu(卢成) Chin. Phys. B, 2025, 34 (3):  036102.  DOI: 10.1088/1674-1056/ada759 Abstract ( 47 )   HTML ( 0 )   PDF (770KB) ( 9 )   (Mg,Fe)SiO${}_3$ is primarily located in the mantle and has a substantial impact on geophysical and geochemical processes. Here, we employ molecular dynamics simulations to investigate the structural and transport properties of (Mg,Fe)SiO${}_3$ with varying iron contents at temperatures up to 5000 K and pressures up to 135 GPa. We thoroughly examine the effects of pressure, temperature, and iron content on the bond lengths, coordination numbers, viscosities, and electrical conductivities of (Mg,Fe)SiO${}_3$. Our calculations indicate that the increase of pressure leads to the shortening of the O-O and Mg-O bond lengths, while the Si-O bond lengths exhibit the initial increase with pressure up to 40 GPa, after which they are almost unchanged. The coordination numbers of Si transition from four-fold to six-fold and eventually reach eight-fold coordination at 135 GPa. The enhanced pressure causes the decrease of the diffusion coefficients and the increase of the viscosities of (Mg,Fe)SiO${}_3$. The increased temperatures slightly decrease the coordination numbers and viscosities, as well as obviously increase the diffusion coefficients and electrical conductivities of (Mg,Fe)SiO${}_3$. Additionally, iron doping facilitates the diffusion of Si and O, reduces the viscosities, and enhances the electrical conductivities of (Mg,Fe)SiO${}_3$. These findings advance fundamental understanding of the structural and transport properties of (Mg,Fe)SiO${}_3$ under high temperature and high pressure, which provide novel insights for unraveling the complexities of geological processes within the Earth's mantle.

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Exploring superconductivity in dynamically stable carbon-boron clathrates trapping molecular hydrogen Akinwumi Akinpelu, Mangladeep Bhullar, Timothy A. Strobel, and Yansun Yao Chin. Phys. B, 2025, 34 (3):  036103.  DOI: 10.1088/1674-1056/ada757 Abstract ( 35 )   HTML ( 0 )   PDF (923KB) ( 4 )   The recent discovery of type-VII boron-carbon clathrates with calculated superconducting transition temperatures approaching $\sim 100$ K has sparked interest in exploring new conventional superconductors that may be stabilized at ambient pressure. The electronic structure of the clathrate is highly tunable based on the ability to substitute different metal atoms within the cages, which may also be large enough to host small molecules. Here we introduce molecular hydrogen (H${}_2$) within the clathrate cages and investigate its impact on electron-phonon coupling interactions and the superconducting transition temperature ($T_{\mathrm{c}}$). Our approach involves combining molecular hydrogen with the new diamond-like covalent framework, resulting in a hydrogen-encapsulated clathrate, (H${}_2$)B${}_3$C${}_3$. A notable characteristic of (H${}_2$)B${}_3$C${}_3$ is the dynamic behavior of the H${}_2$ molecules, which exhibit nearly free rotations within the B-C cages, resulting in a dynamic structure that remains cubic on average. The static structure of (H${}_2$)B${}_3$C${}_3$ (a snapshot in its dynamic trajectory) is calculated to be dynamically stable at ambient and low pressures. Topological analysis of the electron density reveals weak van der Waals interactions between molecular hydrogen and the B-C cages, marginally influencing the electronic structure of the material. The electron count and electronic structure calculations indicate that (H${}_2$)B${}_3$C${}_3$ is a hole conductor, in which H${}_2$ molecules donate a portion of their valence electron density to the metallic cage framework. Electron-phonon coupling calculation using the Migdal-Eliashberg theory predicts that (H${}_2$)B${}_3$C${}_3$ possesses a $T_{\mathrm{c}}$ of 46 K under ambient pressure. These results indicate potential for additional light-element substitutions within the type-VII clathrate framework and suggest the possibility of molecular hydrogen as a new approach to optimizing the electronic structures of this new class of superconducting materials.

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First-principles insights into the high-pressure stability and electronic characteristics of molybdenum nitride Tao Wang(王涛), Ming-Hong Wen(温铭洪), Xin-Xin Zhang(张新欣), Wei-Hua Wang(王伟华), Jia-Mei Liu(刘佳美), Xu-Ying Wang(王旭颖), and Pei-Fang Li(李培芳) Chin. Phys. B, 2025, 34 (3):  036104.  DOI: 10.1088/1674-1056/adab66 Abstract ( 33 )   HTML ( 1 )   PDF (1440KB) ( 6 )   Molybdenum nitride, renowned for its exceptional physical and chemical properties, has garnered extensive attention and research interest. In this study, we employed first-principles calculations and the CALYPSO structure prediction method to conduct a comprehensive analysis of the crystal structures and electronic properties of molybdenum nitride (Mo${}_x$N${}_{1-x}$) under high pressure. We discovered two novel high-pressure phases: Imm2-MoN${}_3$ and Cmmm-MoN${}_4$, and confirmed their stability through the analysis of elastic constants and phonon dispersion curves. Notably, the MoN${}_4$ phase, with its high Vickers hardness of 36.9 GPa, demonstrates potential as a hard material. The results of this study have broadened the range of known high-pressure phases of molybdenum nitride, providing the groundwork for future theoretical and experimental researches.

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Insights to unusual antiferromagnetic behavior and exchange coupling interactions in Mn23C6 Ze-Kun Yu(于泽坤), Chao Zhou(周超), Kuo Bao(包括), Zhao-Qing Wang(王兆卿), En-Xuan Li(李恩萱), Jin-Ming Zhu(朱金铭), Yuan Qin(秦源), Yu-Han Meng(孟钰涵), Pin-Wen Zhu(朱品文), Qiang Tao(陶强), and Tian Cui(崔田) Chin. Phys. B, 2025, 34 (3):  037101.  DOI: 10.1088/1674-1056/adaadd Abstract ( 48 )   HTML ( 0 )   PDF (5113KB) ( 9 )   We report the structural, mechanical and electromagnetic properties of the intermetallic compound Mn${}_{23}$C${}_6$. The bulk Mn${}_{23}$C${}_6$ sample was synthesized using high temperature high pressure quenching method (HTHPQM), and investigated in detail by x-ray diffraction, electron microscope, magnetization and electrical resistivity measurements, etc. First-principles calculation based on density functional theory ab intio simulation was carried out to calculate the bonding and electromagnetic properties of Mn${}_{23}$C${}_6$. Based on our experimental and simulated results, the Mn${}_{23}$C${}_6$ in this work is single phase of a faced-centered cubic structure with space group Fm-3$m$ (No. 225). Determined by SEM and TEM, the bulk sample consists of monocrystal Mn${}_{23}$C${}_6$ crystals with 2-15 μm grain sizes, it is the quick quenching method in the synthesizing process that brings such small crystal grain size. Archimedes method gives its density of 7.14 g/cm${}^3$, 95.74% of its theoretically calculated density 7.458 g/cm${}^3$. Owing to the abundant Mn 3d electrons and a framework of strongly linked Mn atoms in Mn${}_{23}$C${}_6$, the electrical conductivity is up to $8.47\times {10}^{-4}$ $\mathrm{\Omega }\cdot$m, which shows that Mn${}_{23}$C${}_6$ is a good conductor. Our magnetic susceptibility analyses reveal a magnetization peak in the $M$-$T$ curve at 104 K, combined with the $M$-$H$ curve and Curie-Weiss law, this peak usually means the transformation between paramagnetic and antiferromagnetic orders. To gain an insight into the mechanism of the magnetic phase transition, we calculated the magnetic properties, and the results show that different from normal antiferromagnetic order, the magnetic orders in Mn${}_{23}$C${}_6$ consist of three parts, the direct ferromagnetic and antiferromagnetic exchange coupling interactions between Mn atoms, and the indirect antiferromagnetic super-exchange interaction between Mn and C atoms. Therefore, we reveal that the Mn${}_{23}$C${}_6$ is a complex magnetic competition system including different magnetic orders and interactions, instead of the normal long-range antiferromagnetic order.

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Exploring Lifshitz transition and superconductivity in 3R-NbS2 under pressure Kun Chen(陈坤), Xindeng Lv(吕心邓), Simin Li(李思敏), Yanping Huang(黄艳萍), and Tian Cui(崔田) Chin. Phys. B, 2025, 34 (3):  037403.  DOI: 10.1088/1674-1056/adacd2 Abstract ( 40 )   HTML ( 0 )   PDF (1335KB) ( 14 )   The interplay between electronic topological phase transitions and superconductivity in the field of condensed matter physics has consistently captivated researchers. Here we have succeeded in modulating the Lifshitz transition by pressure and realized superconductivity. At 25.7 GPa, superconductivity with a transition temperature of 1.9 K has been observed in 3R-NbS${}_2$. The Hall coefficient changes from negative to positive at 14 GPa, indicating a Lifshitz transition in 3R-NbS${}_2$, and the carrier concentration continues to increase with increasing pressure. X-ray diffraction results indicate that the appearance of superconductivity cannot be attributable to structural transitions. Based on theoretical calculations, the emergence of a new band is attributed to the Lifshitz transition and the new band coincides with the Fermi surface at the pressure of 30 GPa. These findings provide new insights into the relationship between the Lifshitz transition and superconductivity.

COMPUTATIONAL PROGRAMS FOR PHYSICS

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Impurity sputtering model for ICRF edge plasma-surface interactions Quan-Zhi Zhang(张权治), Ze-Xuan Liu(刘泽璇), Fang-Fang Ma(马方方), Lei-Yu Zhang(张雷宇), and Nosir Matyakubov Chin. Phys. B, 2025, 34 (3):  035201.  DOI: 10.1088/1674-1056/ada437 Abstract ( 29 )   HTML ( 0 )   PDF (1276KB) ( 1 )   One of the primary concerns associated with ion cyclotron resonance heating (ICRH) is the enhanced impurity sputtering resulting from radio frequency (RF) sheath formation near plasma-facing components (PFCs), such as limiters. Developing a sputtering model integrated with RF sheath simulations allows for a more comprehensive understanding of the kinetic behavior of incident ions and their interactions with the limiter surface. We accordingly develop an impurity sputtering model "PMSAD", which computes the sputtering yield (amount of impurity) on the limiter surface based on incident ion characteristics and predicts the spatial distribution of impurities. The model provides a robust method for understanding and analyzing the impurity sputtering process from limiter surfaces, which is crucial for preventing ICRH surface erosion and reducing edge and core plasma contamination.

RAPID COMMUNICATION

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Anomalous Hall effect in Bernal tetralayer graphene enhanced by spin-orbit interaction Hot! Zhuangzhuang Qu(曲壮壮), Zhihao Chen(陈志豪), Xiangyan Han(韩香岩), Zhiyu Wang(王知雨), Zhuoxian Li(李卓贤), Qianling Liu(刘倩伶), Wenjun Zhao(赵文俊), Kenji Watanabe, Takashi Taniguchi, Zhi-Gang Cheng(程智刚), Zizhao Gan(甘子钊), and Jianming Lu(路建明) Chin. Phys. B, 2025, 34 (3):  037201.  DOI: 10.1088/1674-1056/adb411 Abstract ( 49 )   HTML ( 2 )   PDF (4650KB) ( 27 )   Spin-orbit interaction (SOI) can be introduced by the proximity effect to modulate the electronic properties of graphene-based heterostructures. In this work, we stack trilayer WSe${}_2$ on Bernal tetralayer graphene to investigate the influence of SOI on the anomalous Hall effect (AHE). In this structurally asymmetric device, by comparing the magnitude of AHE at positive and negative displacement fields, we find that AHE is strongly enhanced by bringing electrons in proximity to the WSe${}_2$ layer. Meanwhile, the enhanced AHE signal persists up to 80 K, providing important routes for topological device applications at high temperatures.

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Electronic structure and carrier mobility of BSb nanotubes Hot! Lantian Xue(薛岚天), Chennan Song(宋晨楠), Miaomiao Jian(见苗苗), Qiang Xu(许强), Yuhao Fu(付钰豪), Pengyue Gao(高朋越), and Yu Xie(谢禹) Chin. Phys. B, 2025, 34 (3):  037304.  DOI: 10.1088/1674-1056/adacd3 Abstract ( 87 )   HTML ( 0 )   PDF (1097KB) ( 45 )   High-mobility semiconductor nanotubes have demonstrated great potential for applications in high-speed transistors, single-charge detection, and memory devices. Here we systematically investigated the electronic properties of single-walled boron antimonide (BSb) nanotubes using first-principles calculations. We observed that rolling the hexagonal boron antimonide monolayer into armchair (ANT) and zigzag (ZNT) nanotubes induces compression and wrinkling effects, significantly modifying the band structures and carrier mobilities through band folding and ${\pi }^{\ast }$-${\sigma }^{\ast }$ hybridization. As the chiral index increases, the band gap and carrier mobility of ANTs decrease monotonically, where electron mobility consistently exceeds hole mobility. In contrast, ZNTs exhibit a more complex trend: the band gap first increases and then decreases, and the carrier mobility displays oscillatory behavior. In particular, both ANTs and ZNTs could exhibit significantly higher carrier mobilities compared to hexagonal monolayer and zinc-blende BSb, reaching ${10}^3$-${10}^7$ cm${}^2\cdot$V${}^{-1}\cdot$s${}^{-1}$. Our findings highlight strong curvature-induced modifications in the electronic properties of single-walled BSb nanotubes, demonstrating the latter as a promising candidate for high-performance electronic devices.

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Manipulation of vortex array via a magnetism-tunable spin-polarized scanning tunnelling microscopy Hot! Bing Xia(夏冰), Hong-Yuan Chen(陈虹源), Jian Zheng(郑健), Bo Yang(杨波), Jie Cai(蔡杰), Yi Zhang(章毅), Yi Yang(杨毅), Hao Yang(杨浩), Dan-Dan Guan(管丹丹), Xiao-Xue Liu(刘晓雪), Liang Liu(刘亮), Yao-Yi Li(李耀义), Shi-Yong Wang(王世勇), Can-Hua Liu(刘灿华), Hao Zheng(郑浩), and Jin-Feng Jia(贾金锋) Chin. Phys. B, 2025, 34 (3):  037402.  DOI: 10.1088/1674-1056/adb38d Abstract ( 43 )   HTML ( 0 )   PDF (1457KB) ( 15 )   Manipulating and braiding Majorana zero modes (MZM) are a critical step toward realizing topological quantum computing. The primary challenge is controlling the vortex, which hosts the MZM, within a superconducting film in a spatially precise manner. To address this, we developed a magnetic force-based vortex control technology using the STM system with a self-designed four-electrode piezo-scanner tube and investigated vortex manipulation on the NbSe${}_2$ superconducting film. We employed ferromagnetic tips to control the movement of vortex array induced by the tip's remanent magnetism. A magnetic core solenoid device was integrated into the STM system and a strong magnetic tip demagnetization technique was developed, providing a viable technical solution for further enabling single vortex manipulation.

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Explosive information spreading in higher-order networks: Effect of social reinforcement Hot! Yu Zhou(周宇), Yingpeng Liu(刘英鹏), Liang Yuan(袁亮), Youhao Zhuo(卓友濠), Kesheng Xu(徐克生), Jiao Wu(吴娇), and Muhua Zheng(郑木华) Chin. Phys. B, 2025, 34 (3):  038704.  DOI: 10.1088/1674-1056/adacc8 Abstract ( 27 )   HTML ( 0 )   PDF (1135KB) ( 16 )   Information spreading has been investigated for many years, but the mechanism of why the information explosively catches on overnight is still under debate. This explosive spreading phenomenon was usually considered driven separately by social reinforcement or higher-order interactions. However, due to the limitations of empirical data and theoretical analysis, how the higher-order network structure affects the explosive information spreading under the role of social reinforcement has not been fully explored. In this work, we propose an information-spreading model by considering the social reinforcement in real and synthetic higher-order networks, describable as hypergraphs. Depending on the average group size (hyperedge cardinality) and node membership (hyperdegree), we observe two different spreading behaviors: (i) The spreading progress is not sensitive to social reinforcement, resulting in the information localized in a small part of nodes; (ii) a strong social reinforcement will promote the large-scale spread of information and induce an explosive transition. Moreover, a large average group size and membership would be beneficial to the appearance of the explosive transition. Further, we display that the heterogeneity of the node membership and group size distributions benefit the information spreading. Finally, we extend the group-based approximate master equations to verify the simulation results. Our findings may help us to comprehend the rapidly information-spreading phenomenon in modern society.

GENERAL

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Dynamical analysis and localized waves of the n-component nonlinear Schrödinger equation with higher-order effects Yu Lou(娄瑜) and Guoan Xu(许国安) Chin. Phys. B, 2025, 34 (3):  030201.  DOI: 10.1088/1674-1056/ada435 Abstract ( 122 )   HTML ( 0 )   PDF (2224KB) ( 31 )   Under investigation is the $n$-component nonlinear Schrödinger equation with higher-order effects, which describes the ultrashort pulses in the birefringent fiber. Based on the Lax pair, the eigenfunction and generalized Darboux transformation are derived. Next, we construct several novel higher-order localized waves and classified them into three categories: (i) higher-order rogue waves interacting with bright/antidark breathers, (ii) higher-order breather fission/fusion, (iii) higher-order breather interacting with soliton. Moreover, we explore the effects of parameters on the structure, collision process and energy distribution of localized waves and these characteristics are significantly different from previous ones. Finally, the dynamical properties of these solutions are discussed in detail.

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Influence of conformity on the evolution of cooperation in games with sampling rules on networks Xianjia Wang(王先甲) and Qiaoyu He(何翘愚) Chin. Phys. B, 2025, 34 (3):  030202.  DOI: 10.1088/1674-1056/ada42e Abstract ( 97 )   HTML ( 0 )   PDF (1508KB) ( 16 )   We study the influence of conformity on the evolution of cooperative behavior in games under the learning method of sampling on networks. A strategy update rule based on sampling is introduced into the stag hunt game, where agents draw samples from their neighbors and then update their strategies based on conformity or inference according to the situation in the sample. Based on these assumptions, we present the state transition equations in the dynamic evolution of population cooperation, conduct simulation analysis on lattice networks and scale-free networks, and discuss how this mechanism affects the evolution of cooperation and how cooperation evolves under different levels of conformity in the network. Our simulation results show that blindly imitating the strategies of neighbors does not necessarily lead to rapid consensus in the population. Instead, rational inference through samples can better promote the evolution of the same strategy among all agents in the population. Moreover, the simulation results also show that a smaller sample size cannot reflect the true situation of the neighbors, which has a large randomness, and the size of the benefits obtained in cooperation determines the direction of the entire population towards cooperation or defection. This work incorporates the conforming behavior of agents into the game, uses the method of sampling for strategy updates and enriches the theory of evolutionary games with a more realistic significance.

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Riemann-Hilbert approach to the higher-order Kaup-Newell equation on the half line Hui Yu(于慧) and Ning Zhang(张宁) Chin. Phys. B, 2025, 34 (3):  030203.  DOI: 10.1088/1674-1056/ada54e Abstract ( 110 )   HTML ( 0 )   PDF (607KB) ( 12 )   The higher-order Kaup-Newell equation is examined by applying the Fokas unified method on the half-line. We demonstrate that the solution can be expressed in relation to the resolution of the Riemann-Hilbert problem. The jump matrix for this problem is derived from the spectral matrix, which is calculated based on both the initial conditions and the boundary conditions. The jump matrix is explicitly dependent and expressed through the spectral functions, which are derived from the initial and boundary information, respectively. These spectral functions are interdependent and adhere to a so-called global relationship.

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Density distribution of ground state of one-dimensional Bose gas with dipole interaction Shuchang Hao(郝舒畅) and Yajiang Hao(郝亚江) Chin. Phys. B, 2025, 34 (3):  030301.  DOI: 10.1088/1674-1056/ada433 Abstract ( 114 )   HTML ( 0 )   PDF (650KB) ( 19 )   Using the Bose-Fermi mapping method, we obtain the exact ground state wavefunction of one-dimensional (1D) Bose gas with the zero-range dipolar interaction in the strongly repulsive contact interaction limit. Its ground state density distributions for both repulsive and attractive dipole interactions are exhibited. It is shown that in the case of the finite dipole interaction the density profiles do not change obviously with the increase of dipole interaction and display the typical shell structure of Tonks-Girardeau gases. As the repulsive dipole interaction is greatly strong, the density decreases at the center of the trap and displays a sunken valley. As the attractive dipole interaction increases, the density displays more oscillations and sharp peaks appear in the strong attraction limit, which mainly originate from the atoms occupying the low single particle levels.

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Coherence-protected operations in hybrid superconducting circuit-magnon system Le-Tian Zhu(朱乐天), Xing-Yu Zhu(朱行宇), Zhu-Cheng Yue(岳祝诚), Tao Tu(涂涛), and Chuan-Feng Li(李传锋) Chin. Phys. B, 2025, 34 (3):  030302.  DOI: 10.1088/1674-1056/ada550 Abstract ( 101 )   HTML ( 0 )   PDF (2946KB) ( 10 )   Hybrid systems consisting of superconducting circuits and magnon systems are a promising platform for quantum technology. However, realizing high-fidelity magnon state preparation and manipulation remains an outstanding challenge due to the complexity of interactions and noise sources in hybrid systems. Here, we propose a coherence-preserving magnon state manipulation scheme. By engineering a superconducting-magnon coupling pulse and combining it with dynamical decoupling pulses, we design a composite pulse sequence. We demonstrate the manipulation and preparation of non-classical states of magnons with a fidelity of up to 98% under realistic conditions. These designs significantly improve the fidelity of manipulation and robustness to noise in hybrid systems compared to existing schemes. These results pave the way for practical applications of quantum magnonics platforms.

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Periodic modulation of adiabatic dynamics in non-reciprocal Landau-Zener systems Rong Chang(常蓉) and Sheng-Chang Li(栗生长) Chin. Phys. B, 2025, 34 (3):  030305.  DOI: 10.1088/1674-1056/adab64 Abstract ( 113 )   HTML ( 0 )   PDF (4280KB) ( 11 )   The control of adiabatic dynamics is essential for quantum manipulation. We investigate the effects of both periodic modulating field and linear sweeping field on adiabatic dynamics based on a non-reciprocal Landau-Zener model with periodic modulation. We obtain adiabatic phase diagrams in the $(\omega ,\delta )$ parameter space, where the adiabatic region is bounded by the modulating frequency $\omega$ greater than a critical value ${\omega }_{\mathrm{c}}$ and the non-reciprocal parameter $\delta$ less than one. The results show that the adiabaticity of the system is not sensitive to the modulating amplitude. We find that the critical modulating frequency can be expressed as a power function of the modulating period number or the sweeping rate. Our findings suggest that one can change the adiabatic region or improve the adiabaticity by adjusting the parameters of both the modulating and the sweeping fields, which provides an effective means to flexibly control the adiabatic dynamics of non-reciprocal systems.

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Global receptive field transformer decoder method on quantum surface code data and syndrome error correction Ao-Qing Li(李熬庆), Ce-Wen Tian(田策文), Xiao-Xuan Xu(徐晓璇), Hong-Yang Ma(马鸿洋), and Jun-Qing Liang(梁俊卿) Chin. Phys. B, 2025, 34 (3):  030306.  DOI: 10.1088/1674-1056/adab63 Abstract ( 80 )   HTML ( 0 )   PDF (1714KB) ( 6 )   Quantum computing has the potential to solve complex problems that are inefficiently handled by classical computation. However, the high sensitivity of qubits to environmental interference and the high error rates in current quantum devices exceed the error correction thresholds required for effective algorithm execution. Therefore, quantum error correction technology is crucial to achieving reliable quantum computing. In this work, we study a topological surface code with a two-dimensional lattice structure that protects quantum information by introducing redundancy across multiple qubits and using syndrome qubits to detect and correct errors. However, errors can occur not only in data qubits but also in syndrome qubits, and different types of errors may generate the same syndromes, complicating the decoding task and creating a need for more efficient decoding methods. To address this challenge, we used a transformer decoder based on an attention mechanism. By mapping the surface code lattice, the decoder performs a self-attention process on all input syndromes, thereby obtaining a global receptive field. The performance of the decoder was evaluated under a phenomenological error model. Numerical results demonstrate that the decoder achieved a decoding accuracy of 93.8%. Additionally, we obtained decoding thresholds of 5% and 6.05% at maximum code distances of 7 and 9, respectively. These results indicate that the decoder used demonstrates a certain capability in correcting noise errors in surface codes.

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Gravitational quasi-normal modes of charged spherically symmetric black holes surrounded by quintessence fluid in Rastall gravity Tongzheng Wang(王同征), Yuhao Cui(崔宇昊), and Kai Lin(林恺) Chin. Phys. B, 2025, 34 (3):  030401.  DOI: 10.1088/1674-1056/ada42c Abstract ( 86 )   HTML ( 0 )   PDF (2278KB) ( 8 )   We apply the WKB approximation method, matrix method, and finite difference method to study the gravitational quasi-normal modes of charged spherically symmetric black holes surrounded by quintessence fluid in Rastall gravity. By comparing the spherically symmetric spacetime metric of charged black holes surrounded by quintessence fluid in Rastall gravity with that of general relativity, we can find that the modifications to general relativity in this modified gravity theory can be described by parameters such as $\lambda$, $Q$, and $C_{\mathrm{a}}$, etc. In four-dimensional spacetime, we investigate the impact of charge $Q$ and parameter $C_{\mathrm{a}}$ on the gravitational quasi-normal modes of charged black holes surrounded by quintessence field in Rastall gravity. The aim is to search for observational evidence of such black holes in astrophysical observations and, consequently, test the validity of Rastall theory. In five-dimensional (5D) spacetime, we study the impact of the parameter $C_{\mathrm{a}}$ on the gravitational quasi-normal modes of Rastall black holes surrounded by quintessence field and summarize the corresponding variation patterns.

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Abundant invariant solutions of (3+1)-dimensional combined pKP-BKP equation Hengchun Hu(胡恒春) and Xu Xu(徐旭) Chin. Phys. B, 2025, 34 (3):  030501.  DOI: 10.1088/1674-1056/ada43b Abstract ( 127 )   HTML ( 0 )   PDF (1583KB) ( 22 )   Lie symmetry analysis is applied to a (3+1)-dimensional combined potential Kadomtsev-Petviashvili equation with B-type Kadomtsev-Petviashvili equation (pKP-BKP equation) and the corresponding similarity reduction equations are obtained with the different infinitesimal generators. Invariant solutions with arbitrary functions and constants for the (3+1)-dimensional pKP-BKP equation, including the lump solution, the periodic-lump solution, the two-kink solution, the breather solution and the lump-two-kink solution, have been studied analytically and graphically.

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A kinetic description of the goods exchange market allowing transfer of agents Rongmei Sun(孙溶镁) and Daixin Wang(汪代薪) Chin. Phys. B, 2025, 34 (3):  030502.  DOI: 10.1088/1674-1056/ada54a Abstract ( 74 )   HTML ( 0 )   PDF (736KB) ( 4 )   In order to avoid the worsening of wealth inequality, it is necessary to explore the influencing factors of wealth distribution and discuss measures to reduce wealth inequality. We investigate the wealth distribution in the goods exchange market by using the kinetic theory of rarefied gas. The trading objects are two kinds of commodities (commodities A and B) and the trading subjects are agents of two groups (dealers and speculators). We deduce the interaction rules according to the principle of utility maximization and consider the transfer of agents in the Boltzmann equation. The steady solution of the Fokker-Planck equation for a special case is obtained and the effects of trading strategy and transfer frequency on the steady distribution are analyzed in numerical experiments. The conclusions illustrate that the transfer of agents is conducive to reducing the inequality of wealth distribution.

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Hybrid image encryption scheme based on hyperchaotic map with spherical attractors Zhitang Han(韩智堂), Yinghong Cao(曹颖鸿), Santo Banerjee, and Jun Mou(牟俊) Chin. Phys. B, 2025, 34 (3):  030503.  DOI: 10.1088/1674-1056/ada7db Abstract ( 96 )   HTML ( 0 )   PDF (9626KB) ( 6 )   Existing chaotic encryption schemes primarily focus on single types of images, making the design of hybrid image encryption schemes more suitable for practical applications. In this paper, a hyperchaotic map with a spherical attractor is proposed, which is constructed using spherical coordinates. Dynamical analyses reveal that the hyperchaotic map exhibits global hyperchaos and high complexity, making it capable of generating more complex chaotic sequences suitable for image encryption. A hybrid encryption scheme based on a hyperchaotic map is proposed for two-dimensional (2D) images, three-dimensional (3D) models, and 3D point clouds. Firstly, the pixels of 2D image and the coordinate data of 3D image are fused into a plaintext cube, which is combined with Hash-512 to obtain the initial value of the hyperchaotic map. Chaotic sequences are utilized for cube space internal confusion and dynamic cross-diffusion. The encrypted images demonstrate high information entropy, and the test results show that the encryption scheme effectively protects the images. The proposed hybrid image encryption scheme provides an efficient solution for securing various types of images.

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Impact of the chaotic semiconductor laser output power on time-delay-signature of chaos and random bit generation Chenpeng Xue(薛琛鹏), Xu Wang(王绪), Likai Zheng(郑利凯), Haoyu Zhang(张昊宇), Yanhua Hong, and Zuxing Zhang(张祖兴) Chin. Phys. B, 2025, 34 (3):  030504.  DOI: 10.1088/1674-1056/ada7dd Abstract ( 96 )   HTML ( 0 )   PDF (929KB) ( 12 )   We experimentally analyze the effect of the optical power on the time delay signature identification and the random bit generation in chaotic semiconductor laser with optical feedback. Due to the inevitable noise during the photoelectric detection and analog-digital conversion, the varying of output optical power would change the signal to noise ratio, then impact time delay signature identification and the random bit generation. Our results show that, when the optical power is less than -14 dBm, with the decreasing of the optical power, the actual identified time delay signature degrades and the entropy of the chaotic signal increases. Moreover, the extracted random bit sequence with lower optical power is more easily pass through the randomness testing.

ATOMIC AND MOLECULAR PHYSICS

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Three-body physics under dissipative spin-orbit coupling Xi Zhao(赵茜) Chin. Phys. B, 2025, 34 (3):  033101.  DOI: 10.1088/1674-1056/ada43e Abstract ( 139 )   HTML ( 0 )   PDF (1650KB) ( 26 )   We study the trimer state in a three-body system, where two of the atoms are subject to Rashba-type spin-orbit coupling and spin-dependent loss while interacting spin-selectively with the third atom. The short-time conditional dynamics of the three-body system is effectively governed by a non-Hermitian Hamiltonian with an imaginary Zeeman field. Remarkably, the interplay of non-Hermitian single particle dispersion and the spin-selective interaction results in a Borromean state and an enlarged trimer phase. The stability of trimer state can be reflected by the imaginary part of trimer energy and the momentum distribution of trimer wave function. We also show the phase diagram of the three-body system under both real and imaginary Zeeman fields. Our results illustrate the interesting consequence of non-Hermitian spectral symmetry on the few-body level, which may be readily observable in current cold-atom experiments.

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Frequency shifts of high-order harmonics from ZnO crystals by chirped laser pulses Yu Zhao(赵宇), Xiao-Jin Liu(刘晓瑾), Shuang Wang(王爽), Xiao-Xin Huo(霍晓鑫), Yun-He Xing(邢云鹤), and Jun Zhang(张军) Chin. Phys. B, 2025, 34 (3):  033201.  DOI: 10.1088/1674-1056/ada9dc Abstract ( 89 )   HTML ( 0 )   PDF (4400KB) ( 11 )   We investigate theoretically the effects of chirped laser pulses on high-order harmonic generation (HHG) from solids. We find that the harmonic spectra display redshifts for the driving laser pulses with negative chirp and blueshifts for those with positive chirp, which is due to the change in the instantaneous frequency of the driving laser for different chirped pulses. The analysis of crystal-momentum-resolved ($\text{bm}k$-resolved) HHG reveals that the frequency shifts are equal for the harmonics generated by different crystal momentum channels. The frequency shifts in the cutoff region are larger than those in the plateau region. With the increase of the absolute value of the chirp parameters, the frequency shifts of HHG become more significant, leading to the shifts from odd- to even-order harmonics. We also demonstrate that the frequency shifts of harmonic spectra are related to the duration of the chirped laser field, but are insensitive to the laser intensity and dephasing time.

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Two-photon dissociation of BeH+ with a middle ultraviolet band laser Qian-Yu Zhang(张乾煜), Wen-Li Bai(白文丽), Zhi-Yuan Ao(敖致远), Wen-Cui Peng(彭文翠), Sheng-Guo He(何胜国), and Xin Tong(童昕) Chin. Phys. B, 2025, 34 (3):  033301.  DOI: 10.1088/1674-1056/ada436 Abstract ( 86 )   HTML ( 0 )   PDF (802KB) ( 11 )   Two-photon dissociation of BeH${}^{+}$ ions is studied by detecting the fluorescence changes of Be${}^{+}$-BeH${}^{+}$ bi-component Coulomb crystal in a linear Paul trap. BeH${}^{+}$ ions generated by an exothermic reaction between electronically excited Be${}^{+}$ ions and residual H${}_2$ in the vacuum chamber are photon-dissociated with two photons scanning over the range of 201 nm to 208 nm. Our experiment provides a novel method to maintain the number of Be${}^{+}$ ions stable in a Coulomb crystal with a middle ultraviolet band dissociation laser. This two-photon dissociation method extends the wavelength range of the dissociation laser for BeH${}^{+}$ compared to the one-photon dissociation, and the method can be utilized to all alkaline earth atomic ions which require suppression of the reaction with residual H${}_2$ gas in vacuum.

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Channel competition in dissociation of ammonia clusters (n ≤ 5) induced by femtosecond laser fields Tao Yang(杨涛), Xinyu Zhang(张馨予), Xing Li(李兴), Wankai Li(李万凯), Menghao Wei(卫孟昊), Dongdong Zhang(张栋栋), Lanhai He(赫兰海), and Dajun Ding(丁大军) Chin. Phys. B, 2025, 34 (3):  033302.  DOI: 10.1088/1674-1056/ada552 Abstract ( 104 )   HTML ( 0 )   PDF (922KB) ( 18 )   We investigated the ionization and dissociation processes of ammonia clusters ranging from dimer to pentamer induced by 800-nm femtosecond laser fields. Time-of-flight (TOF) mass spectra of the ammonia clusters were recorded over a range of laser intensities from 2.1$\times {10}^{12}$ W/${\text{cm}}^2$ to 5.6$\times {10}^{12}$ W/${\text{cm}}^2$. The protonated ion signals dominate the spectra, which is consistent with the stability of the geometric structures. The ionization and dissociation channels of ammonia clusters are discussed. The competition and switching among observed dissociation channels are revealed by analyzing the variations in the relative ionic yields of specific protonated and unprotonated clusters under different laser intensities. These results indicate that the ionization of the neutral multiple-ammonia units, produced through the dissociation of cluster ions, may start to contribute, as well as the additional processes to consume protonated ions and/or produce unprotonated ions induced by the femtosecond laser fields when the laser intensity is above $\sim 4\times {10}^{12}{\text{W/cm}}^2$. These findings provide deeper insights into the ionization and dissociation dynamics in multi-photon ionization experiments involving ammonia clusters.

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Observation of Josephson effect in 23Na spinor Bose-Einstein condensates Yong Qin(秦永), Xin Wang(王鑫), Jun Jian(蹇君), Wenliang Liu(刘文良), Jizhou Wu(武寄洲), Yuqing Li(李玉清), Jie Ma(马杰), Liantuan Xiao(肖连团), and Suotang Jia(贾锁堂) Chin. Phys. B, 2025, 34 (3):  033701.  DOI: 10.1088/1674-1056/ada42f Abstract ( 95 )   HTML ( 0 )   PDF (1243KB) ( 8 )   The Josephson effect, an important quantum supercurrent phenomenon, has been extensively studied in superconductors and superfluids. In this paper, we investigate the rich physics of one-dimensional Josephson junctions in a red-detuned optical lattice with sodium (Na) quantum gas. A one-dimensional Josephson array is formed by setting up an optical lattice using a red-detuned laser. By characterizing the dependence of Josephson oscillations of the lattice depth, we experimentally demonstrate the Josephson current. The lattice depth is controlled by altering the lattice power, and our observations are consistent with theoretical predictions. These findings offer valuable insights into quantum coherent transport and the intricate dynamics inherent to superfluidity.

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

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Influence of surface contamination on electric field distribution of insulators Xingcai Li(李兴财), Yingge Liu(刘滢格), and Juan Wang(王娟) Chin. Phys. B, 2025, 34 (3):  034101.  DOI: 10.1088/1674-1056/ada54d Abstract ( 78 )   HTML ( 0 )   PDF (2987KB) ( 5 )   Atmospheric particle adsorption on insulator surfaces, coupled with humid environments, significantly affects contamination flashover, necessitating a clear understanding of the electric field distribution on insulator surfaces with adsorbed particles. This is crucial for accurately assessing insulator safety and informing critical decision-making. Although previous research has demonstrated that particle arrangement significantly influences the electric field distribution around transmission lines, an in-depth analysis of its effects on insulator surfaces remains lacking. To address this gap, this study establishes a composite insulator model to examine how three types of spherical contamination layers affect the electric field distribution on insulator surfaces under varying environmental conditions. The results reveal that in dry environments, the electric field strength at the apex of single-particle contamination layers increases with the particle size and relative permittivity. For the double-particle contamination layers, the electric field intensity on the insulator surface decreases as the particle spacing increases, and larger particles are more likely to attract smaller charged particles. For triple-particle contamination layers arranged in a triangular pattern, the maximum surface field strength is nearly double that of the chain-arranged particles. Furthermore, within the chain-arranged triple-particle contamination layers, a large-small-large size arrangement has a more pronounced impact on the surface electric field than a small-large-small size arrangement. In humid environments, the surface electric field strength of insulators decreases with increasing contamination levels. These findings are of significant theoretical and practical importance for ensuring the safe operation of power systems.

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An adjustment-free laser resonator based on micron-scale corner cube array Pengyuan Chang(常鹏媛), Xinrong Huang(黄欣荣), Caolei Fu(傅曹雷), Aiping Liu(刘爱萍), Duo Pan(潘多), Zhiyang Wang(王志洋), and Jingbiao Chen(陈景标) Chin. Phys. B, 2025, 34 (3):  034201.  DOI: 10.1088/1674-1056/ada434 Abstract ( 124 )   HTML ( 0 )   PDF (1459KB) ( 9 )   The topic of improving the mechanical stability of external cavity diode lasers (ECDLs) has recently attracted widespread attention and interest. The use of corner-cube-array (CCA)-based resonators provides a potential solution for this purpose, although continuous oscillation at super large incident angle remains challenging. In this work, we employ the CCA resonator to generate continuous oscillation within $\pm$20${}_{}^{\circ }$ angular misalignment of cavity mirror in experiment. On the basis of retroreflection theory, the retroreflectivity of a CCA is analyzed by using optical simulation software. Notably, the experiment verifies the advantage of using a CCA over a plane mirror in laser resonator, thereby providing a promising approach for ECDLs. The threshold characteristic curves measured at different incident angles in the experiment verify that the CCA possesses an obvious anti-angle misalignment performance. This research introduces an alternative solution of using CCA resonator instead of parallel plane cavity, thereby realizing an adjustment-free ECDL with enhanced mechanical stability.

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Symmetry-protected and Brillouin zone folding driven bound states in the continuum in dielectric nanorod arrays for efficient third harmonic generation Wen-Jing Wang(王文静), Shi-Jie Liang(梁世杰), Jia-Qi Zou(邹家祺), Yan-Yan Huo(霍燕燕), and Ting-Yin Ning(宁廷银) Chin. Phys. B, 2025, 34 (3):  034202.  DOI: 10.1088/1674-1056/ada2f0 Abstract ( 102 )   HTML ( 0 )   PDF (1611KB) ( 5 )   Two types of bound states in continuum (BICs), symmetry-protected and Brillouin zone folding driven, are identified in hollow Si nanorod arrays. By modulating the direction and distance of the air holes from the center of the nanorods, it is possible to achieve either a single quasi-BIC or three quasi-BICs. The transmission spectra exhibit ultra-narrow lines, and the quasi-BICs demonstrate ultra-high Q factors. Additionally, efficient third-harmonic generation occurs at low pump intensities. The results indicate that the proposed nanostructures of two types of BICs with a flexible modulation hold great potential applications for nonlinear photonic devices.

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Pure-quartic soliton molecules in normal fourth-order dispersion regimes based on spectral filtering effect Han-Yang Shen(申翰阳), Rui-Bo Lan(蓝睿博), Hong-Bin Hu(胡洪彬), Yang Li(李阳), Rui Zhou(周瑞), and Zu-Xing Zhang(张祖兴) Chin. Phys. B, 2025, 34 (3):  034203.  DOI: 10.1088/1674-1056/ada43c Abstract ( 106 )   HTML ( 0 )   PDF (896KB) ( 8 )   Recent theoretical verification of self-similar and dissipative pure-quartic solitons (PQSs) emphasized the similarity between PQS lasers and conventional fiber lasers, but the unique equilibrium mechanism hinders the formation of PQS molecules in normal fourth-order dispersion (FOD) regimes. In this paper, we investigated the effect of filters on shaping PQSs in normal FOD based on a passively mode-locked fiber laser model. A bandpass filter eliminates the time pedestal of dissipative PQSs, thus realizing a multi-pulsing state. When the filter bandwidth is appropriate, the effective spectral filtering effect can lower the pulse splitting threshold and enable the coherent restoration from chaotic PQSs to PQS molecules. Additionally, changing the central wavelength of the filter can generate PQSs and PQS molecules with asymmetric intensity distributions. These results are important guides for the manipulation of PQSs and the construction of high repetition-frequency fiber lasers.

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Passive on-chip isolators based on the thin-film lithium niobate platform Jiacheng Liu(刘嘉成), Gongyu Xia(夏功榆), Qilin Hong(洪琦琳), Pingyu Zhu(朱枰谕), Kai-Kai Zhang(张凯凯), Keyu Xia(夏可宇), Ping Xu(徐平), Shiqiao Qin(秦石乔), and Zhihong Zhu (朱志宏) Chin. Phys. B, 2025, 34 (3):  034204.  DOI: 10.1088/1674-1056/ada2ef Abstract ( 99 )   HTML ( 0 )   PDF (906KB) ( 9 )   Optical isolators, the photonic analogs of electronic diodes, are essential for ensuring the unidirectional flow of light in optical systems, thereby mitigating the destabilizing effects of back reflections. Thin-film lithium niobate (TFLN), hailed as "the silicon of photonics," has emerged as a pivotal material in the realm of chip-scale nonlinear optics, propelling the demand for compact optical isolators. We report a breakthrough in the development of a fully passive, integrated optical isolator on the TFLN platform, leveraging the Kerr effect to achieve an impressive 10.3 dB of isolation with a minimal insertion loss of 1.87 dB. Further theoretical simulations have demonstrated that our design, when applied to a microring resonator with a $Q$ factor of 5$\times {10}^6$, can achieve 20 dB of isolation with an input power of merely 8 mW. This advancement underscores the immense potential of lithium niobate-based Kerr-effect isolators in propelling the integration and application of high-performance on-chip lasers, heralding a new era in integrated photonics.

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Controlled propagation and particle manipulation of off-axis-rotating elliptical Gaussian beams in strong nonlocal media Rong-Quan Chen(陈荣泉), Rui-Lin Xiao(肖瑞林), Wei Wang(王伟), Xi-Xi Chu(储茜茜), Yu-Qing Song(宋雨晴), Xu-Dong Hu(胡旭东), and Ming Chen(陈明) Chin. Phys. B, 2025, 34 (3):  034205.  DOI: 10.1088/1674-1056/ada9dd Abstract ( 91 )   HTML ( 0 )   PDF (2155KB) ( 12 )   Off-axis-rotating elliptical Gaussian beams (OareGB) oblique incidence in strong nonlocal medium exhibit novel propagation properties. The analytical expressions of semi-axial beam widths, and center-of-mass trajectory equations for transmitting off-axis-rotating elliptical Gaussian beams in strong nonlocal media are obtained using the $ABCD$ transfer matrix method. The study revealed that the trajectory of the mass's center in the cross-section can be controlled by changing the sizes of the OareGB parameters $c$, $d$, $\zeta$, and $f$. The gradient force of the light field causes the spot region to form a spatial potential well in the media, and this spatial potential well can effectively capture nanoparticles. The particles captured by the light field can move along with the beam, realizing the effective manipulation of the particle trajectory. These laws may be applied to modulating the propagation path of light beams and optical tweezer technology.

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Topological transmission and topological corner states combiner in all-dielectric honeycomb valley photonic crystals Ming Sun(孙铭), Xiao-Fang Xu(许孝芳), Yun-Feng Shen(沈云峰), Ya-Qing Chang(常雅箐), and Wen-Ji Zhou(周文佶) Chin. Phys. B, 2025, 34 (3):  034206.  DOI: 10.1088/1674-1056/ada9d9 Abstract ( 83 )   HTML ( 0 )   PDF (2933KB) ( 7 )   We study the topological states (TSs) of all-dielectric honeycomb valley photonic crystals (VPCs). Breaking the space inversion symmetry of the honeycomb lattice by varying the filling ratio of materials for circular ring dielectric columns in the unit cell, which triggers topological phase transitions and thus achieves topological edge states (TESs) and topological corner states (TCSs). The results demonstrate that this structure has efficient photon transmission characteristics and anti-scattering robustness. In particular, we have found that changing the type of edge splicing between VPCs with different topological properties produces a change in the frequency of TCSs, and then based on this phenomenon, we have used a new method of adjusting only the type of edge splicing of the structure to design a novel TCSs combiner that can integrate four TCSs with different frequencies. This work not only expands the variety and number of unexplored TCSs that may exist in a fixed photonic band gap and can be rationalized to be selectively excited in the fixed configuration. Our study provides a feasible pathway for the design of integrated optical devices in which multiple TSs coexist in a single photonic system.

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A WKB method based on parabolic cylinder function for very-low-frequency sound propagation in deep ocean Jian-Kang Zhan(詹建康), Sheng-Chun Piao(朴胜春), Li-Jia Gong(龚李佳), Yang Dong(董阳), Yong-Chao Guo(郭永超), and Guang-Xue Zheng(郑广学) Chin. Phys. B, 2025, 34 (3):  034301.  DOI: 10.1088/1674-1056/ada886 Abstract ( 79 )   HTML ( 0 )   PDF (2145KB) ( 6 )   A Wentzel-Kramers-Brillouin (WKB) method is introduced for obtaining a uniform asymptotic solution for underwater sound propagation at very low frequencies in deep ocean. The method utilizes a mode sum and employs the reference functions method to describe the solution to the depth-separated wave equation approximately using parabolic cylinder functions. The conditions for the validity of this approximation are also discussed. Furthermore, a formula that incorporates waveguide effects for the modal group velocity is derived, revealing that boundary effects at very low frequencies can have a significant impact on the propagation characteristics of even low-order normal modes. The present method not only offers improved accuracy compared to the classical WKB approximation and the uniform asymptotic approximation based on Airy functions, but also provides a wider range of depth applicability. Additionally, this method exhibits strong agreement with numerical methods and offers valuable physical insights. Finally, the method is applied to the study of very-low-frequency sound propagation in the South China Sea, leading to sound transmission loss predictions that closely align with experimental observations.

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Motion of a rigid particle in the lid-driven cavity flow Fan Yang(杨帆), Zhe Yan(闫喆), Wencan Wang(汪文灿), and Ren Shi(施任) Chin. Phys. B, 2025, 34 (3):  034701.  DOI: 10.1088/1674-1056/ada438 Abstract ( 110 )   HTML ( 0 )   PDF (1834KB) ( 9 )   The motion of an elliptical rigid particle in a lid-driven cavity flow was numerically simulated using the immersed boundary lattice Boltzmann method (IB-LBM). The effects of the particle's initial orientation angle, initial position, aspect ratio, and size on the motion characteristics were investigated. The computational results indicate that the particle's motion undergoes two distinct stages: a starting stage that involves moving from the release position to a limit cycle, and a periodic stage that involves moving on the limit cycle. The initial orientation of the particle has a minimal impact on both stages of motion. In contrast, the time it takes for the particle to reach the limit cycle may vary depending on the release position. Furthermore, particles with a larger aspect ratio exhibit a greater maximum velocity magnitude; an increase in particle size causes the particle trajectory to contract more toward the center of the cavity, decreasing the centrifugal force experienced by the particle.

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Learning complex nonlinear physical systems using wavelet neural operators Yanan Guo(郭亚楠), Xiaoqun Cao(曹小群), Hongze Leng(冷洪泽), and Junqiang Song(宋君强) Chin. Phys. B, 2025, 34 (3):  034702.  DOI: 10.1088/1674-1056/ada7dc Abstract ( 68 )   HTML ( 0 )   PDF (10845KB) ( 5 )   Nonlinear science is a fundamental area of physics research that investigates complex dynamical systems which are often characterized by high sensitivity and nonlinear behaviors. Numerical simulations play a pivotal role in nonlinear science, serving as a critical tool for revealing the underlying principles governing these systems. In addition, they play a crucial role in accelerating progress across various fields, such as climate modeling, weather forecasting, and fluid dynamics. However, their high computational cost limits their application in high-precision or long-duration simulations. In this study, we propose a novel data-driven approach for simulating complex physical systems, particularly turbulent phenomena. Specifically, we develop an efficient surrogate model based on the wavelet neural operator (WNO). Experimental results demonstrate that the enhanced WNO model can accurately simulate small-scale turbulent flows while using lower computational costs. In simulations of complex physical fields, the improved WNO model outperforms established deep learning models, such as U-Net, ResNet, and the Fourier neural operator (FNO), in terms of accuracy. Notably, the improved WNO model exhibits exceptional generalization capabilities, maintaining stable performance across a wide range of initial conditions and high-resolution scenarios without retraining. This study highlights the significant potential of the enhanced WNO model for simulating complex physical systems, providing strong evidence to support the development of more efficient, scalable, and high-precision simulation techniques.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

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Simulation on atmospheric pressure barrier discharge with varying relative position between two wavy dielectric surfaces Xue-Chen Li(李雪辰), Wen-Jie Wan(万文杰), Xiao-Qian Liu(刘晓倩), Mo Chen(陈墨), Kai-Yue Wu(吴凯玥), Jun-Xia Ran(冉俊霞), Xue-Xia Pang(庞学霞), Xue-Xue Zhang(张雪雪), Jia-Cun Wu(武珈存), Peng-Ying Jia(贾鹏英), and Hui Sun(孙辉) Chin. Phys. B, 2025, 34 (3):  035202.  DOI: 10.1088/1674-1056/ada43d Abstract ( 33 )   HTML ( 0 )   PDF (1294KB) ( 9 )   As a popular approach to producing atmospheric pressure non-thermal plasma, dielectric barrier discharge (DBD) has been extensively used in various application fields. In this paper, DBD with wavy dielectric layers is numerically simulated in atmospheric pressure helium mixed with trace nitrogen based on a fluid model. With varying relative position (phase difference ($\mathrm{\Delta }\phi$)) of the wavy surfaces, there is a positive discharge and a negative discharge per voltage cycle, each of which consists of a pulse stage and a hump stage. For the pulse stage, maximal current increases with increasing $\mathrm{\Delta }\phi$. Results show that DBD with the wavy surfaces appears as discrete micro-discharges (MDs), which are self-organized to different patterns with varying $\mathrm{\Delta }\phi$. The MDs are vertical and uniformly-spaced with $\mathrm{\Delta }\phi =$0, which are self-organized in pairs with $\mathrm{\Delta }\phi =\pi /4$. These MD pairs are merged into some bright wide MDs with $\mathrm{\Delta }\phi =\pi /2$. In addition, narrow MDs appear between tilted wide MDs with $\mathrm{\Delta }\phi =3\pi /4$. With $\mathrm{\Delta }\phi =\pi$, the pattern is composed of wide and narrow MDs, which are vertical and appear alternately. To elucidate the formation mechanism of the patterns with different $\mathrm{\Delta }\phi$, temporal evolutions of electron density and electric field are investigated for the positive discharge. Moreover, surface charge on the wavy dielectric layers has also been compared with different $\mathrm{\Delta }\phi$.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

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Atomic origin of minor alloying element effect on glass forming ability of metallic glass Shan Zhang(张珊), Qingan Li(李庆安), Yong Yang(杨勇), and Pengfei Guan(管鹏飞) Chin. Phys. B, 2025, 34 (3):  036105.  DOI: 10.1088/1674-1056/ada756 Abstract ( 44 )   HTML ( 0 )   PDF (2095KB) ( 3 )   The glass-forming ability (GFA) of metallic glasses is a key scientific challenge in their development and application, with compositional dependence playing a crucial role. Experimental studies have demonstrated that the addition of specific minor elements can greatly enhance the GFA of parent alloys, yet the underlying mechanism remains unclear. In this study, we use the ZrCuAl system as a model to explore how the addition of minor Al influences the crystallization rate by modulating the properties of the crystal-liquid interface, thereby affecting the GFA. The results reveal that the minor addition of Al significantly reduces the crystal growth rate, a phenomenon not governed by particle density fluctuations at the interface. The impact of minor element additions extends beyond a modest increase in crystal-unfavorable motifs in the bulk supercooled liquid. More importantly, it leads to a significant enrichment of these motifs at the crystal-supercooled liquid interface, forming a dense topological network of crystal-unfavorable structures that effectively prevent the growth of the crystalline interface and enhance GFA. Our results provide valuable insights for the design and development of high-performance metallic glasses.

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First-principles study of electronic and magnetic properties of self-intercalated van der Waals magnet Cr3Ge2Te6 Jia-wan Li(李家万), Shi-Bo Zhao(赵世博), Lin Zhuang(庄琳), and Yusheng Hou(侯玉升) Chin. Phys. B, 2025, 34 (3):  036301.  DOI: 10.1088/1674-1056/adab67 Abstract ( 27 )   HTML ( 0 )   PDF (4040KB) ( 5 )   Self-intercalated van der Waals magnets, characterized by self-intercalating native atoms into van der Waals layered structures with intrinsic magnetism, exhibit a variety of novel physical properties. Here, using first-principles calculations and Monte Carlo simulations, we report a self-intercalated van der Waals ferromagnet, Cr${}_3$Ge${}_2$Te${}_6$, which has a high Curie temperature of 492 K. We find that Cr${}_3$Ge${}_2$Te${}_6$ is nearly half-metallic with a spin polarization reaching up to 90.9%. Due to the ferromagnetism and strong spin-orbit coupling effect in Cr${}_3$Ge${}_2$Te${}_6$, a large anomalous Hall conductivity of $138{\mathrm{\Omega }}^{-1}\cdot {\mathrm{c}\mathrm{m}}^{-1}$ and $305{\mathrm{\Omega }}^{-1}\cdot {\mathrm{c}\mathrm{m}}^{-1}$ can be realized when its magnetization is along its magnetic easy axis and hard axis, respectively. By doping electrons (holes) into Cr${}_3$Ge${}_2$Te${}_6$, these anomalous Hall conductivities can be increased up to $318{\mathrm{\Omega }}^{-1}\cdot {\mathrm{c}\mathrm{m}}^{-1}$ ($648{\mathrm{\Omega }}^{-1}\cdot {\mathrm{c}\mathrm{m}}^{-1}$). Interestingly, a five-layer Cr${}_3$Ge${}_2$Te${}_6$ thin film retains room-temperature ferromagnetism with a higher spin polarization and larger anomalous Hall conductivity. Our study demonstrates that Cr${}_3$Ge${}_2$Te${}_6$ is a novel room-temperature self-intercalated ferromagnet with high-spin polarization and large anomalous Hall conductivity, offering great opportunities for designing nano-scale electronic devices.

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A thermodynamically complete multi-phase equation of state for dense and porous metals at wide ranges of temperature and pressure Yanhong Zhao(赵艳红), Li-Fang Wang(王丽芳), Qili Zhang(张其黎), Le Zhang(张乐), Hongzhou Song(宋红州), Xingyu Gao(高兴誉), Bo Sun(孙博), Haifeng Liu(刘海风), and Haifeng Song(宋海峰) Chin. Phys. B, 2025, 34 (3):  036401.  DOI: 10.1088/1674-1056/ada54b Abstract ( 37 )   HTML ( 0 )   PDF (791KB) ( 6 )   A thermodynamically complete multi-phase equation of state (EOS) applicable to both dense and porous metals at wide ranges of temperature and pressure is constructed. A standard three-term decomposition of the Helmholtz free energy as a function of specific volume and temperature is presented, where the cold component models both compression and expansion states, the thermal ion component introduces the Debye approximation and melting entropy, and the thermal electron component employs the Thomas-Fermi-Kirzhnits (TFK) model. The porosity of materials is considered by introducing the dynamic porosity coefficient $\alpha$ and the constitutive $P$-$\alpha$ relation, connecting the thermodynamic properties between dense and porous systems, allowing for an accurate description of the volume decrease caused by void collapse while maintaining the quasi-static thermodynamic properties of porous systems identical to the dense ones. These models enable the EOS applicable and robust at wide ranges of temperature, pressure and porosity. A systematic evaluation of the new EOS is conducted with aluminum (Al) as an example. 300 K isotherm, shock Hugoniot, as well as melting curves of both dense and porous Al are calculated, which shows great agreements with experimental data and validates the effectiveness of the models and the accuracy of parameterizations. Notably, it is for the first time Hugoniot $P$-$\sigma$ curves up to 10${}^6$ GPa and shock melting behaviors of porous Al are derived from analytical EOS models, which predict much lower compression limit and shock melting temperatures than those of dense Al.

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Barocaloric effect in ferroelastic Pb3(VO4)2 Pengtao Cheng(程鹏涛), Zuhua Chen(陈祖华), Chengliang Zhang(张成亮), Zhengming Zhang(张正明), Bing Li(李昺), and Dunhui Wang(王敦辉) Chin. Phys. B, 2025, 34 (3):  036801.  DOI: 10.1088/1674-1056/ada9d8 Abstract ( 21 )   HTML ( 0 )   PDF (1089KB) ( 12 )   The barocaloric effect is considered as one of the most promising refrigeration with the potential to replace traditional gas compression refrigeration. One of the main obstacles to the application of barocaloric materials lies in the requirement for high driving pressures. In this paper, we report on the barocaloric effect of Pb${}_3$(VO${}_4$)${}_2$, which exhibits a ferroelastic transition from a high-temperature trigonal structure to a low-temperature monoclinic structure at 357 K, accompanied by a substantial volume change. The entropy change induced by hydrostatic pressure can reach up 14 J$\cdot$kg${}^{-1}\cdot$K${}^{-1}$ under a relatively low pressure of 80 MPa. This work is expected to expand the selection range of barocaloric materials.

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

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Merging and separation of polarization singularities in complex lattices Mengyao Wang(王梦瑶), Tian Shi(石天), Luhui Ning(宁鲁慧), Peng Liu(刘鹏), Liangsheng Li(李粮生), and Ning Zheng(郑宁) Chin. Phys. B, 2025, 34 (3):  037303.  DOI: 10.1088/1674-1056/ada9da Abstract ( 21 )   HTML ( 0 )   PDF (3004KB) ( 3 )   The evolution in momentum space of bound states in the continuum (BICs) and circularly polarized states (CPSs) - as far-field polarization singularities - can be observed by controlling the geometric parameters of photonic crystals. This offers significant potential in optics and photonics. Here, we reveal that in complex lattices far-field polarization singularities can be flexibly manipulated while preserving structural symmetry. A change in topological charge for the at-$\Gamma$ BIC can generate new BICs or CPSs. At an off-$\Gamma$ point, a BIC can spawn from the collision of two CPSs. As the thickness of the structure increases, this BIC will meet the at-$\Gamma$ BIC. The merging of BICs can induce topological charge transition and yield a large wavevector space around the $\Gamma$ point with ultra-high quality ($Q$) factors. Our findings provide a novel degree of freedom for manipulating polarization singularities, which holds great promise in radiation modulation and singular optics.

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Magnetic flux transitions in two-band single-junction superconductors with time-reversal symmetry breaking Guo Wang(王果), Tian-Yi Han(韩天意), and Hai Huang(黄海) Chin. Phys. B, 2025, 34 (3):  037401.  DOI: 10.1088/1674-1056/ada431 Abstract ( 47 )   HTML ( 1 )   PDF (690KB) ( 19 )   Based on Ginzburg-Landau theory, we investigate the electromagnetic properties of two-band superconductors with broken time-reversal symmetry. We propose an apparatus of a superconducting ring integrated with a microbridge structure to probe the peculiar topological excitations in the chiral system. The phase difference of two order parameters in the superconductor satisfies the double sine-Gordon equation, and a linear relationship between the phase difference at the two ends of the junction and the total magnetic flux in the ring can be obtained. Then with the Josephson current-phase relation, we establish the dependence of the circulating current and magnetic flux on the applied external magnetic field. Our results show that this single-junction system will exhibit the irreversible behaviors and two different types of fractional flux transitions can clearly manifest the time-reversal symmetry breaking in two-component superconductors.

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Electronic structure and coexisting topological states in ferromagnetic and antiferromagnetic phases of MnBi2Te4 quantum wires Jian Li(李健), Zhu-Cai Yin(尹柱财), Qing-Xu Li(李清旭), and Jia-Ji Zhu(朱家骥) Chin. Phys. B, 2025, 34 (3):  037501.  DOI: 10.1088/1674-1056/ada551 Abstract ( 50 )   HTML ( 0 )   PDF (3394KB) ( 1 )   We theoretically investigate the electronic structure of cylindrical magnetic topological insulator quantum wires in $\mathrm{M}\mathrm{n}\mathrm{B}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_4$. Our study reveals the emergence of topological surface states in the ferromagnetic phase, characterized by spin-polarized subbands resulting from intrinsic magnetization. In the antiferromagnetic phase, we identify the coexistence of three distinct types of topological states, encompassing both surface states and central states.

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Perpendicular magnetic anisotropy of Pd/Co2MnSi/Co/Pd multilayer Xiaoqi Qin(秦晓奇), Jiaxing Tan(谭家兴), Xianwu Xiu(修显武), Wentian Cao(曹文田), and Shuyun Wang(王书运) Chin. Phys. B, 2025, 34 (3):  037502.  DOI: 10.1088/1674-1056/ada694 Abstract ( 21 )   HTML ( 0 )   PDF (951KB) ( 3 )   Pd/Co${}_2$MnSi (CMS)/Co/Pd multilayer films were designed based on the idea of combining highly spin-polarized materials with strong perpendicular magnetic anisotropy (PMA) films. The PMA of Pd/CMS/Co/Pd multilayer films was studied by optimizing the growth conditions and thickness of each film layer. The optimal structure of the multilayer films was Pd(6 nm)/CMS(5 nm)/Co(2 nm)/Pd(1 nm). Its abnormal Hall resistance ($R_{\mathrm{H}\mathrm{a}\mathrm{l}\mathrm{l}}$), coercivity ($H_{\mathrm{c}}$) and effective magnetic anisotropy constant ($K_{\mathrm{e}\mathrm{f}\mathrm{f}}$) are 0.08 $\mathrm{\Omega }$, 284 Oe and 1.36 Merg/cm${}^3$, respectively, which are 100%, 492%, and 183% higher than the corresponding values (0.04 $\mathrm{\Omega }$, 48 Oe, and 0.48 Merg/cm${}^3$) of the Pd(6 nm)/Co(1 nm)/Pd(3 nm) trilayer films. The analysis shows that the increases of the above values are the result of the Pd/CMS interface effect and CMS/Co interface ferromagnetic (FM) coupling, and that it is closely related to the thickness of each film layer in the multilayer films and the growth conditions of the multilayer films.

INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

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Turing instability-induced oscillations in coupled reaction-diffusion systems Nan Wang(王楠), Yuan Tong(仝源), Fucheng Liu(刘富成), Xiaoxuan Li(李晓璇), Yafeng He(贺亚峰), and Weili Fan(范伟丽) Chin. Phys. B, 2025, 34 (3):  038201.  DOI: 10.1088/1674-1056/ada42b Abstract ( 36 )   HTML ( 0 )   PDF (1464KB) ( 10 )   A new type of localized oscillatory pattern is presented in a two-layer coupled reaction-diffusion system under conditions in which no Hopf instability can be discerned in either layer. The transitions from stationary patterns to asynchronous and synchronous oscillatory patterns are obtained. A novel method based on decomposing coupled systems into two associated subsystems has been proposed to elucidate the mechanism of formation of oscillating patterns. Linear stability analysis of the associated subsystems reveals that the Turing pattern in one layer induces the other layer locally, undergoes a supercritical Hopf bifurcation and gives rise to localized oscillations. It is found that the sizes and positions of oscillations are determined by the spatial distribution of the Turing patterns. When the size is large, localized traveling waves such as spirals and targets emerge. These results may be useful for deeper understanding of pattern formation in complex systems, particularly multilayered systems.

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Signal estimation bias in x-ray dark-field imaging using dual phase grating interferometer Zhi-Li Wang(王志立), Zun Zhang(张尊), Heng Chen(陈恒), and Xin Ge(葛昕) Chin. Phys. B, 2025, 34 (3):  038701.  DOI: 10.1088/1674-1056/ada430 Abstract ( 36 )   HTML ( 0 )   PDF (710KB) ( 6 )   In x-ray dark-field imaging using dual phase grating interferometer, multi-contrast signals are extracted from a set of acquired phase-stepping data by using the least-squares fitting algorithm. The extracted mean intensity, amplitude and visibility signals may be intrinsically biased. However, it is still unclear how large these biases are and how the data acquisition parameters influence the biases in the extracted signals. This work set out to address these questions. Analytical expressions of the biases of the extracted signals were theoretically derived by using a second-order Taylor series expansion. Extensive numerical simulations were performed to validate the theoretical results. It is illustrated that while the estimated mean intensity signal is always unbiased, the estimated amplitude and visibility signals are both positively biased. While the biases of the estimated amplitude signals are proportional to the inverse of the total number of phase steps, the biases of the estimated visibility signals are inversely proportional to the product of the total number of phase steps and the mean number of photons counted per phase step. Meanwhile, it is demonstrated that the dependence of the biases on the mean visibility is quite different from that of Talbot-Lau interferometer due to the difference in the intensity model. We expect that these results can be useful for data acquisition optimizations and interpretation of x-ray dark-field images.

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Dynamics of zebrafish locomotion being independent of spatial size Zhen Wang(王震), Jian Gao(高见), Yongshang Long(龙永尚), Huaping Lv(吕华平), and Qun Wang(王群) Chin. Phys. B, 2025, 34 (3):  038702.  DOI: 10.1088/1674-1056/ada54c Abstract ( 38 )   HTML ( 0 )   PDF (1357KB) ( 3 )   Zebrafish are increasingly being utilized as a laboratory animal species to study various biological processes, both normal and pathological. It is crucial to comprehend the dynamics of zebrafish locomotion and put forth realistic models since their locomotion characteristics are employed as feedback indicators in diverse experiments. In this study, we conducted experimental research on the locomotion of zebrafish across various spatial sizes, focusing on the analysis of motion step size and motion direction. The results indicated that the motion step exhibits long-range correlations, the motion direction shows unbiased randomness, and the data characteristics are not influenced by spatial size. The dynamic mechanisms are complicated dynamical processes rather than fractional Brownian or Lévy processes motion. Based on the experimental results, we proposed a model for describing the movement of zebrafish in a circular container. Our findings shed light on the locomotion characteristics of zebrafish, and have the potential to benefit both the biological outcomes of animal tests and the welfare of the subjects.

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Characteristics of complex network of heatwaves over China Xuemin Shen(沈雪敏), Xiaodong Hu(胡晓东), Aixia Feng(冯爱霞), Qiguang Wang(王启光), and Changgui Gu(顾长贵) Chin. Phys. B, 2025, 34 (3):  038903.  DOI: 10.1088/1674-1056/ada43a Abstract ( 23 )   HTML ( 0 )   PDF (7595KB) ( 10 )   Using complex network methods, we construct undirected and directed heatwave networks to systematically analyze heatwave events over China from 1961 to 2023, exploring their spatiotemporal evolution patterns in different regions. The findings reveal a significant increase in heatwaves since the 2000s, with the average occurrence rising from approximately 3 to 5 times, and their duration increasing from 15 to around 30 days, nearly doubling. An increasing trend of "early onset and late withdrawal" of heatwaves has become more pronounced each year. In particular, eastern regions experience heatwaves that typically start earlier and tend to persist into September, exhibiting greater interannual variability compared to western areas. The middle and lower reaches of the Yangtze River and Xinjiang are identified as high-frequency heatwave areas. Complex network analysis reveals the dynamics of heatwave propagation, with degree centrality and synchronization distance indicating that the middle and lower reaches of the Yangtze River, Northeast China, and Xinjiang are key nodes in heatwave spread. Additionally, network divergence analysis shows that Xinjiang acts as a "source" area for heatwaves, exporting heat to surrounding regions, while the central region functions as a major "sink," receiving more heatwave events. Further analysis from 1994 to 2023 indicates that heatwave events exhibit stronger network centrality and more complex synchronization patterns. These results suggest that complex networks provide a refined framework for depicting the spatiotemporal dynamics of heatwave propagation, offering new avenues for studying their occurrence and development patterns.