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Room-temperature realization of macroscopic quantum phenomena is one of the major pursuits in fundamental physics. The quantum spin Hall state, a topological quantum phenomenon that features a two-dimensional insulating bulk and a helical…

Symmetry-protected topological crystalline insulators (TCIs) have primarily been characterized by their gapless boundary states. However, in time-reversal- ($\mathcal{T}$-) invariant (helical) 3D TCI$\unicode{x2014}$termed higher-order TCIs…

Topological insulators are a newly discovered phase of matter characterized by a gapped bulk surrounded by novel conducting boundary states. Since their theoretical discovery, these materials have encouraged intense efforts to study their…

Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator, but have protected conducting states on their edge or surface. The 2D topological insulator is a quantum spin Hall insulator, which is a…

Mesoscale and Nanoscale Physics · Physics 2015-03-13 M. Z. Hasan , C. L. Kane

In principle the stacking of different two-dimensional (2D) materials allows the construction of 3D systems with entirely new electronic properties. Here we propose to realize topological crystalline insulators (TCI) protected by mirror…

Mesoscale and Nanoscale Physics · Physics 2019-04-24 Sanjib Kumar Das , Binghai Yan , Jeroen van den Brink , Ion Cosma Fulga

The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Recently, a new class of topological insulators has been proposed. These topological insulators have an insulating gap in…

Mesoscale and Nanoscale Physics · Physics 2009-11-13 Markus Koenig , Hartmut Buhmann , Laurens W. Molenkamp , Taylor L. Hughes , Chao-Xing Liu , Xiao-Liang Qi , Shou-Cheng Zhang

Electronic edge states in topological insulators have become a major paradigm in physics. The oldest and primary example is that of quantum Hall (QH) edge channels that propagate along the periphery of two-dimensional electron gases (2DEGs)…

The quantum spin Hall (QSH) effect, characterized by topologically protected spin-polarized edge states, was recently demonstrated in monolayers of the transition metal dichalcogenide (TMD) WTe$_2$. However, the robustness of this…

Mesoscale and Nanoscale Physics · Physics 2024-05-07 Felix Lüpke , Dacen Waters , Anh D. Pham , Jiaqiang Yan , David G. Mandrus , Panchapakesan Ganesh , Benjamin M. Hunt

The quantum spin hall (QSH) phase, also known as the 2D topological insulator, is characterized by protected helical edge modes arising from time reversal symmetry. While initially proposed for band insulators, this phase can also manifest…

Strongly Correlated Electrons · Physics 2024-03-26 Yixin Ma , Shenghan Jiang , Chao Xu

It has been demonstrated that topological quantum spin Hall (QSH) state exist in twisted bilayers of transition metal dichalcogenides. However, a comprehensive theoretical characterization of the topological edge states remains a topic of…

Mesoscale and Nanoscale Physics · Physics 2025-08-08 Hao He , Zhao Gong , Shuai Li , Jian-Jun Liu , Hui-Ying Mu , Xing-Tao An

Quantum spin Hall (QSH) insulator materials feature topologically protected edge states that can drastically reduce dissipation and are useful for the next-generation electronics. However, the nonvolatile control of topological edge state…

Materials Science · Physics 2020-12-30 Hua Bai , Xinwei Wang , Weikang Wu , Pimo He , Zhu'an Xu , Shengyuan A. Yang , Yunhao Lu

The hallmark of a time-reversal symmetry protected topologically insulating state of matter in two-dimensions (2D) is the existence of chiral edge modes propagating along the perimeter of the system. To date, evidence for such electronic…

Mesoscale and Nanoscale Physics · Physics 2014-09-22 Ilya K. Drozdov , A. Alexandradinata , Sangjun Jeon , Stevan Nadj-Perge , Huiwen Ji , R. J. Cava , B. A. Bernevig , Ali Yazdani

While two-dimensional topological insulators (2D TI) initiated the field of topological materials, only very few materials were discovered to date and the direct access to their quantum spin Hall edge states has been challenging due to…

Mesoscale and Nanoscale Physics · Physics 2016-04-12 Sung Hwan Kim , Kyung-Hwan Jin , Joonbum Park , Jun Sung Kim , Seung-Hoon Jhi , Han Woong Yeom

The recently synthesized ternary quasi-2D material TaRhTe$_4$ is a bulk Weyl semimetal with an intrinsically layered structure, which poses the question how the topology of its electronic structure depends on layers separations.…

Materials Science · Physics 2025-09-18 Xiao Zhang , Ning Mao , Oleg Janson , Jeroen van den Brink , Rajyavardhan Ray

Atomic monolayers on semiconductor surfaces represent a new class of functional quantum materials at the ultimate two-dimensional limit, ranging from superconductors [1, 2] to Mott insulators [3, 4] and ferroelectrics [5] to quantum spin…

We study three dimensional generalizations of the quantum spin Hall (QSH) effect. Unlike two dimensions, where the QSH effect is distinguished by a single $Z_2$ topological invariant, in three dimensions there are 4 invariants…

Mesoscale and Nanoscale Physics · Physics 2015-06-25 Liang Fu , C. L. Kane , E. J. Mele

Topological phases, especially topological crystalline insulators (TCIs), have been intensively explored observed experimentally in three-dimensional (3D) materials. However, the two-dimensional (2D) films are explored much less than 3D…

Materials Science · Physics 2017-11-22 Yi-zhen Jia , Wei-xiao Ji , Chang-wen Zhang , Ping Li , Shu-feng Zhang , Pei-ji Wang , Sheng-shi Li , Shi-shen Yan

Evidence for the quantum spin Hall (QSH) effect has been reported in several experimental systems in the form of approximately quantized edge conductance. However, the most fundamental feature of the QSH effect, spin-momentum locking in the…

We report on a class of quantum spin Hall insulators (QSHIs) in strained-layer InAs/GaInSb quantum wells, in which the bulk gaps are enhanced by up to five folds as compared to the binary InAs/GaSb QSHI. Remarkably, with consequently…

Mesoscale and Nanoscale Physics · Physics 2017-08-09 Lingjie Du , Tingxin Li , Wenkai Lou , Xingjun Wu , Xiaoxue Liu , Zhongdong Han , Chi Zhang , Gerard Sullivan , Amal Ikhlassi , Kai Chang , Rui-Rui Du

Topological phases of matter have been extensively studied for their intriguing bulk and edge properties. Recently, higher-order topological insulators with boundary states that are two or more dimensions lower than the bulk states, have…

Mesoscale and Nanoscale Physics · Physics 2020-01-08 Xiujuan Zhang , Bi-Ye Xie , Hong-Fei Wang , Xiangyuan Xu , Yuan Tian , Jian-Hua Jiang , Ming-Hui Lu , Yan-Feng Chen