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We propose an alternative formulation of the $Z_2$ topological index for quantum spin Hall systems and band insulators when time reversal invariance is not broken. The index is expressed in terms of the Chern numbers of the bands of the…

介观与纳米尺度物理 · 物理学 2009-11-01 Rahul Roy

The Hall effect, the anomalous Hall effect and the spin Hall effect are fundamental transport processes in solids arising from the Lorentz force and the spin-orbit coupling respectively. The quantum versions of the Hall effect and the spin…

介观与纳米尺度物理 · 物理学 2010-07-13 Rui Yu , Wei Zhang , H. J. Zhang , S. C. Zhang , Xi Dai , Zhong Fang

The quantum spin Hall (QSH) state is a topologically non-trivial state of quantum matter which preserves time-reversal symmetry; it has an energy gap in the bulk, but topologically robust gapless states at the edge. Recently, this novel…

介观与纳米尺度物理 · 物理学 2009-11-13 Chaoxing Liu , Taylor L. Hughes , Xiao-Liang Qi , Kang Wang , Shou-Cheng Zhang

Quantum anomalous Hall (QAH) phase is a two-dimensional bulk ferromagnetic insulator with a nonzero Chern number in presence of spin-orbit coupling (SOC) but absence of applied magnetic fields. Associated metallic chiral edge states host…

强关联电子 · 物理学 2016-06-28 Jian Zhou , Qi-Feng Liang , Hongming Weng , Y. B. Chen , Shu-Hua Yao , Yan-Feng Chen , Jinming Dong , Guang-Yu Guo

We consider a system of weakly coupled one-dimensional wires forming a three-dimensional stack in the presence of a spatially periodic modulation of the chemical potential along the wires, equivalent to a charge density wave (CDW). An…

介观与纳米尺度物理 · 物理学 2020-09-23 Paweł Szumniak , Daniel Loss , Jelena Klinovaja

Quantum spin Hall (QSH) insulators are versatile platforms for exploring exotic quantum phases, especially when combined with high-order van Hove singularities (VHSs) that enhance electron correlations. However, perfect spin Hall…

材料科学 · 物理学 2025-10-16 Rahul Verma , Yash Vardhan , Hsin Lin , Bahadur Singh

We introduce a quantum spin Hall semimetal or Fermi liquid characterized with a Z2 topological invariant, measurable through circularly polarized light. We propose its engineering through two topological metallic band structures in crystals…

介观与纳米尺度物理 · 物理学 2025-08-19 Karyn Le Hur

Topological invariants are a significant ingredient in the study of topological phases of matter that intertwines the supposedly contradicting concepts of bulk and boundary. The nature of the invariants differ depending on the dimension of…

介观与纳米尺度物理 · 物理学 2023-11-28 Srijata Lahiri , Saurabh Basu

Topological order can be found in a wide range of physical systems, from crystalline solids, photonic meta-materials and even atmospheric waves to optomechanic, acoustic and atomic systems. Topological systems are a robust foundation for…

量子气体 · 物理学 2023-07-04 A. Valdés-Curiel , D. Trypogeorgos , Q. -Y. Liang , R. P. Anderson , I. B. Spielman

Quantum spin Hall effect is usually realized in two-dimensional materials with time-reversal symmetry, but whether it can be realized without symmetry protection remains unexplored. Here, we propose type-II quantum spin Hall insulator with…

介观与纳米尺度物理 · 物理学 2025-04-01 Panjun Feng , Chao-Yang Tan , Miao Gao , Xun-Wang Yan , Zheng-Xin Liu , Peng-Jie Guo , Fengjie Ma , Zhong-Yi Lu

Atomically thin topological materials are attracting growing attention for their potential to radically transform classical and quantum electronic device concepts. Amongst them is the quantum spin Hall (QSH) insulator - a two-dimensional…

介观与纳米尺度物理 · 物理学 2021-04-28 Michael S. Lodge , Shengyuan A. Yang , Shantanu Mukherjee , Bent Weber

We show that edges of Quantum Spin Hall topological insulators represent a natural platform for realization of exotic supersolid phase. On one hand, fermionic edge modes are helical due to the nontrivial topology of the bulk. On the other…

介观与纳米尺度物理 · 物理学 2018-09-12 O. M. Yevtushenko , A. M. Tsvelik

We consider weak topological insulators with a twofold rotation symmetry around the dark direction, and show that these systems can be endowed with the topological crystalline structure of a higher-order topological insulator protected by…

介观与纳米尺度物理 · 物理学 2020-08-04 Sander H. Kooi , Guido van Miert , Carmine Ortix

Quantum spin Hall (QSH) insulators are two-dimensional electronic materials that have a bulk band gap like an ordinary insulator but have topologically protected pairs of edge modes of opposite chiralities. To date, experimental studies…

介观与纳米尺度物理 · 物理学 2024-02-13 Kaifei Kang , Bowen Shen , Yichen Qiu , Kenji Watanabe , Takashi Taniguchi , Jie Shan , Kin Fai Mak

Topologically protected surface modes of classical waves hold the promise to enable a variety of applications ranging from robust transport of energy to reliable information processing networks. The integer quantum Hall effect has delivered…

介观与纳米尺度物理 · 物理学 2020-08-25 Weiyin Deng , Xueqin Huang , Jiuyang Lu , Valerio Peri , Feng Li , Sebastian D. Huber , Zhengyou Liu

The inverted band structure discovered in InAs/GaSb quantum well (QW) is found to host the topological quantum spin Hall (QSH) states. A QSH insulator hosts counterpropagating spin-polarized edge states that are protected by the…

介观与纳米尺度物理 · 物理学 2022-08-30 Sushmita Saha , Alestin Mawrie

Topological insulating states in two-dimensional (2D) materials are ideal systems to study different types of quantized response signals due to their in gap metallic states. Very recently, the quantum spin Hall (QSH) effect was discovered…

介观与纳米尺度物理 · 物理学 2024-04-23 Junwen Lai , Xiangyang Liu , Jie Zhan , Tianye Yu , Peitao Liu , Xing-Qiu Chen , Yan Sun

The interplay between non-Hermiticity and topology opens an exciting avenue for engineering novel topological matter with unprecedented properties. While previous studies have mainly focused on one-dimensional systems or Chern insulators,…

介观与纳米尺度物理 · 物理学 2021-05-12 Junpeng Hou , Ya-Jie Wu , Chuanwei Zhang

Magnetic orders characterized by multiple ordering vectors harbor noncollinear and noncoplanar spin textures and can be a source of unusual electronic properties through the spin Berry phase mechanism. We theoretically show that such…

强关联电子 · 物理学 2016-07-22 Satoru Hayami , Ryo Ozawa , Yukitoshi Motome

We propose a scheme to realize a new Z_2 topological insulator in a square optical lattice. Different from the conventional topological insulator protected by the time-reversal symmetry, here, the optical lattice possesses a novel hidden…

量子气体 · 物理学 2016-06-22 Jing-Min Hou , Wei Chen