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topological states constructed by two different trivial quantum wires

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Chinese Physics B 2025年第1期34卷 246-255页

作者： Jing-Run Lin Linxi Lv Zheng-Wei Zuo School of Physics and Engineering Henan University of Science and TechnologyLuoyang 471023China

The topological states of the two-leg and three-leg ladders formed by two trivial quantum wires with different lattice constants are theoretically investigated. Firstly, we take two trivial quantum wires with a lattice constant ratio of 1:2 as an example. For the symmetric nearest-neighbor intra-chain hopping two-leg ladder, the inversion symmetry protected topological insulator phase with two degenerate topological edge states appears. When the inversion symmetry is broken, the topological insulators with one or two topological edge states of different energies and topological metals with edge states embedded in the bulk states could emerge depending on the filling factor. The topological origin of these topological states in the two-leg ladders is the topological properties of the Chern insulators and Chern metals. According to the arrangement of two trivial quantum wires, we construct two types of three-leg ladders. Each type of the three-leg ladder could be divided into one trivial subspace and one topological nontrivial subspace by unitary transformation. The topological nontrivial subspace corresponds to the effective two-leg ladder model. As the filling factor changes, the system could be in topological insulators or topological metals phases. When the two-leg ladder is constructed by two trivial quantum wires with a lattice constant ratio of 1:3 and 2:3, the system could also realize rich topological states such as the topological insulators and topological metals with the topological edge states. These rich topological states in the two-leg and three-leg ladders could be confirmed by current experimental techniques.

关键词： trivial quantum wire topological invariant inversion symmetric topological insulator Chern metal

A new way to construct topological invariants of non-Hermitian systems with the non-Hermitian skin effect

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Chinese Physics B 2020年第1期29卷 119-123页

作者： J S Liu Y Z Han C S Liu Hebei Key Laboratory of Microstructural Material Physics School of ScienceYanshan UniversityQinhuangdao 066004China

The non-Hermitian skin effect breaks the conventional bulk–boundary correspondence and leads to non-Bloch topological *** by the fact that the topological protected zero modes are immune to perturbations,we construct a partner of a non-Hermitian system by getting rid of the non-Hermitian skin *** adjusting the imbalance hopping,we find that the existence of zero-energy boundary states still dictate the bulk topological invariants based on the band-theory *** non-Hermitian Su–Schrieffer–Heeger(SSH)models are used to illuminate the ***,we obtain the winding numbers in analytical form without the introduction of the generalized Brillouin *** work gives an alternative method to calculate the topological invariants of non-Hermitian systems.

关键词： non-Hermitian skin effect Su–Schrieffer–Heeger(SSH)model bulk–boundary correspondence topological invariant

topological phases and edge modes of an uneven ladder

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Chinese Physics B 2024年第8期33卷 154-168页

作者：商文创韩熠宁 Shimpei Endo 高超 Department of Physics Zhejiang Normal UniversityJinhua 321004China Key Laboratory of Optical Information Detection and Display Technology of Zhejiang Zhejiang Normal UniversityJinhua 321004China Department of Engineering Science The University of Electro-CommunicationsTokyo 182-8585Japan

We investigate the topological properties of a two-chain quantum ladder with uneven legs,i.e.,the two chains differ in their periods by a factor of *** an uneven ladder presents rich band structures classified by the closure of either direct or indirect *** also provides opportunities to explore fundamental concepts concerning band topology and edge modes,including the difference of intracellular and intercellular Zak phases,and the role of the inversion symmetry(IS).We calculate the Zak phases of the two kinds and find excellent agreement with the dipole moment and extra charge *** also find that configurations with IS feature a pair of degenerate two-side edge modes emerging as the closure of the direct bandgap,while configurations without IS feature one-side edge modes emerging as not only the closure of both direct and indirect bandgaps but also within the band ***,by projecting to the two sublattices,we find that the effective Bloch Hamiltonian corresponds to that of a generalized Su–Schrieffer–Heeger model or the Rice–Mele model whose hopping amplitudes depend on the *** this way,the topological phases can be efficiently extracted through winding *** propose that uneven ladders can be realized by spin-dependent optical lattices and their rich topological characteristics can be examined by near future experiments.

关键词： ladder model symmetry-protected topological phase topological invariant bulk-boundary correspondence

Static and dynamic properties of polymer brush with topological ring structures: Molecular dynamic simulation

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Chinese Physics B 2016年第10期25卷 252-258页

作者：万吴兵吕红红候格吴晨旭 Institute of Softmatter and Biometrics Xiamen University Collaborative Innovation Center of Chemistry for Energy Materials Xiamen University

By defining a topological constraint value（rn）,the static and dynamic properties of a polymer brush composed of moderate or short chains with different topological ring structures are studied using molecular dynamics simulation,and a comparison with those of linear polymer brush is also *** the center-of-mass height of the ring polymer brush scaled by chain length h;,there is no significant difference of exponent from that of a linear brush in the small topological constraint ***,as the topological constraint becomes stronger,one obtains a smaller *** is found that there exists a master scaling power law of the total stretching energy scaled by chain length N for moderate chain length regime,F;p;,for ring polymer brushes,but with a larger exponent v than 5/6,indicating an influence of topological constraint to the dynamic properties of the system.A topological invariant of free energy scaled by（c）;is found.

关键词： ring polymer topological invariant scaling

Simulation and detection of the topological properties of a modulated Rice-Mele model in a one-dimensional circuit-QED lattice

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Science China(Physics,Mechanics & Astronomy) 2018年第8期61卷 17-26页

作者： Lu Qi Yan Xing Ji Cao Xin-Xin Jiang Cheng-Shou An Ai-Dong Zhu Shou Zhang Hong-Fu Wang Department of Physics College of Science Yanbian University Department of Electronic Information Engineering College of Engineering Yanbian University

Here, we propose a simple scheme to realize a one-dimensional （1D） modulated Rice-Mele model （RMM） and investigate its topological properties with a 1D circuit quantum electrodynamics （QED） lattice. The system can be mapped into a Chern insulator model by introducing a period parameter. Interestingly and surprisingly, we found that the circuit-QED lattice system always exhibits topologically nonttrvial phases if both the nearest-neighbor hopping strength between two resonators and the qubitassisted on-site potentials are alternately changed in the direction of the lattice. The numerical results show that the topological phases can be obtained by introducing an additional modulation parameter and both the edge state and topological invariant can be unambiguously seen with the existence of decay and disorders, even with few resonators in the lattice.

关键词： topological phase topological invariant Rice-Mele model circuit QED

topologically protected edge gap solitons of interacting Bosons in one-dimensional superlattices

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Chinese Physics B 2018年第6期27卷 173-178页

作者： Xi-Hua Guo Tian-Fu Xu Cheng-Shi Liu Department of Physics Yanshan University Qinhuangdao 066004 China

We comprehensively investigate the nontrivial states of an interacting Bose system in a cosine potential under the open boundary condition. Our results show that there exists a kind of stable localized state： edge gap solitons. We argue that the states originate from the eigenstates of independent edge parabolas. In particular, the edge gap solitons exhibit a nonzero topological-invariant behavior. The topological nature is due to the connection of the present model to the quantized adiabatic particle transport problem. In addition, the composition relations between the gap solitons and the extended states are also discussed.

关键词： one-dimensional optical superlattices interacting Boses edge gap solitons topological invariant

Multiple surface states,nontrivial band topology,and antiferromagnetism in GdAuAl_(4)Ge_(2)

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Chinese Physics B 2023年第7期32卷 515-520页

作者：张成成王渊张发远戎洪涛蔡永青王乐马小明郭抒陈仲佳王亚南江志诚杨逸尘刘正太叶茂林君浩梅佳伟郝占阳谢子娟陈朝宇 Shenzhen Institute for Quantum Science and Engineering(SIQSE)and Department of Physics Southern University of Science and Technology(SUSTech)Shenzhen 518055China Songshan Lake Materials Laboratory Dongguan 523000China Beijing National Laboratory for Condensed Matter Physics and Institute of Physics Chinese Academy of SciencesBeijing 100190China State Key Laboratory of Functional Materials for Informatics and Center for Excellence in Superconducting Electronics Shanghai Institute of Microsystem and Information TechnologyChinese Academy of SciencesShanghai 200050China International School of Microelectronics Dongguan University of TechnologyDongguan 523000China

Magnetic topological states of matter provide a fertile playground for emerging topological physics and *** current main focus is on materials whose magnetism stems from 3d magnetic transition elements,e.g.,MnBi_(2)Te_(4),Fe_(3)Sn_(2),and Co_(3)Sn_(2)S_(2).In contrast,topological materials with the magnetism from rare earth elements remain largely *** we report rare earth antiferromagnet GdAuAl_(4)Ge_(2)as a candidate magnetic topological *** resolved photoemission spectroscopy(ARPES)and first-principles calculations have revealed multiple bulk bands crossing the Fermi level and pairs of low energy surface *** to the parity and Wannier charge center analyses,these bulk bands possess nontrivial Z2 topology,establishing a strong topological insulator state in the nonmagnetic ***,the surface band pairs exhibit strong termination dependence which provides insight into their *** results suggest GdAuAl_(4)Ge_(2)as a rare earth platform to explore the interplay between band topology,magnetism and f electron correlation,calling for further study targeting on its magnetic structure,magnetic topology state,transport behavior,and microscopic properties.

关键词： magnetic topological material surface state ARPES topological invariant

Algebraic equations and non-integer orders of fractal operators abstracted from biomechanics

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Acta Mechanica Sinica 2022年第5期38卷 113-124,I0003页

作者： Yajun Yin Gang Peng Xiaobin Yu Department of Engineering Mechanics Tsinghua UniversityBeijing 100084China

The previous study implies that the fractional operator may stem from the motion in fractal space or the motion of fractal structure abstracted from biological *** study is devoted to answering another essential question,i.e.,what determines the order of the fractional operator in fractal structure?This paper generalizes the concept of the fractal cell defined in the previous paper,explores the tree-like and net-like fractal structures with higher-order topology,abstracts two classes of higherorder fractal operators,and derives the algebraic equations satisfied by the fractal operators to answer this *** is proved that the solutions of the algebraic equations for fractal operators are deterministically related to the fractional-time operators that are usually of fractional *** the Vieta theorem,the relation between the solutions of algebraic equations for fractal operators and the physical-component operators is clarified,and the duality constraints between them are *** solutions of the fractal operators show that the topological invariants of the fractal cells are one of the essential factors in determining the fractional orders.A conjecture on the specific order of the fractional-time operator in fractal structure is proposed.

关键词： Fractal cell topological invariant Fractal operator(fractional-time operator) Fractional order