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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

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…

Mesoscale and Nanoscale Physics · Physics 2021-04-28 Michael S. Lodge , Shengyuan A. Yang , Shantanu Mukherjee , Bent Weber

Topological insulators in three dimensions are nonmagnetic insulators that possess metallic surface states as a consequence of the nontrivial topology of electronic wavefunctions in the bulk of the material. They are the first known…

Strongly Correlated Electrons · Physics 2012-01-26 M. Zahid Hasan , Joel E. Moore

Topological insulators are new class of materials which are characterized by a bulk band gap like ordinary band insulator but have protected conducting states on their edge or surface. These states emerge out due to the combination of…

Mesoscale and Nanoscale Physics · Physics 2017-08-18 Arijit Saha , Arun M. Jayannavar

Topological phases with insulating bulk and gapless surface or edge modes have attracted much attention because of their fundamental physics implications and potential applications in dissipationless electronics and spintronics. In this…

Materials Science · Physics 2016-05-18 Yafei Ren , Zhenhua Qiao , Qian Niu

Topological Surface States (TSS) represent new types of two dimensional electron systems with novel and unprecedented properties distinct from any quantum Hall-like or spin-Hall effects. Their Z$_2$ topological order can be realized at room…

Mesoscale and Nanoscale Physics · Physics 2014-01-07 M. Zahid Hasan , Su-Yang Xu , David Hsieh , L. Andrew Wray , Yuqi Xia

In this Book Chapter (invited) we briefly review the basic concepts defining topological insulators and focus on elaborating on the key experimental results that revealed and established their symmetry protected (SPT) topological nature. We…

Mesoscale and Nanoscale Physics · Physics 2015-02-17 M. Zahid Hasan , Su-Yang Xu , Madhab Neupane

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

2D topological insulators promise novel approaches towards electronic, spintronic, and quantum device applications. This is owing to unique features of their electronic band structure, in which bulk-boundary correspondences enforces the…

Topology is now securely established as a means to explore and classify electronic states in crystalline solids. This review provides a gentle but firm introduction to topological electronic band structure suitable for new researchers in…

Strongly Correlated Electrons · Physics 2023-09-28 Andrew T. Boothroyd

The three-dimensional topological insulator (originally called "topological insulators") is the first example in nature of a topologically ordered electronic phase existing in three dimensions that cannot be reduced to multiple copies of…

Mesoscale and Nanoscale Physics · Physics 2011-05-03 M. Zahid Hasan , David Hsieh , Yuqi Xia , L. Andrew Wray , Su-Yang Xu , Charles L. Kane

We investigate the effect of disorder on topologically nontrivial states in a two dimension (2D) mechanical system. We first propose a quantum spin Hall (QSH) insulator based on an out-of-plane spring-mass model and analytically study the…

Applied Physics · Physics 2023-09-01 Xiaotian Shi , Rajesh Chaunsali , Georgios Theocharis , Huaqing Huang , Rui Zhu , Jinkyu Yang

Topological matter has become one of the most important subjects in contemporary condensed matter physics. Here, I would like to provide a pedagogical review explaining some of the main ideas, which were pivotal in establishing topological…

Strongly Correlated Electrons · Physics 2018-09-24 Kwon Park

The twin discoveries of the quantum Hall effect, in the 1980's, and of topological band insulators, in the 2000's, were landmarks in physics that enriched our view of the electronic properties of solids. In a nutshell, these discoveries…

Strongly Correlated Electrons · Physics 2017-05-24 P. A. McClarty , F. Krüger , T. Guidi , S. F. Parker , K. Refson , A. W. Parker , D. Prabakharan , R. Coldea

Noncollinear and noncoplanar magnetic orders lead to unusual electronic structures and transport properties. We here investigate two types of multiple-Q magnetically ordered states and a topological phase transition between them in two…

Strongly Correlated Electrons · Physics 2015-02-10 Satoru Hayami , Yukitoshi Motome

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

Modern condensed matter physics relies on the concept of topology to classify matter, from quantum Hall systems to topological insulators. Engineered systems, benefiting from synthetic dimensions, can potentially give access to novel…

A three-dimensional (3D) topological insulator (TI) is a quantum state of matter with a gapped insulating bulk yet a conducting surface hosting topologically-protected gapless surface states. One of the most distinct electronic transport…

Mesoscale and Nanoscale Physics · Physics 2015-01-06 Yang Xu , Ireneusz Miotkowski , Chang Liu , Jifa Tian , Hyoungdo Nam , Nasser Alidoust , Jiuning Hu , Chih-Kang Shih , M. Zahid Hasan , Yong P. Chen

Ultracold atom research presents many avenues to study problems at the forefront of physics. Due to their unprecedented controllability, these systems are ideally suited to explore new exotic states of matter, which is one of the key…

Quantum Gases · Physics 2015-03-19 Indubala I Satija , Erhai Zhao

The interplay between interactions and topology in quantum materials is of extensive current interest. Strong correlations are known to be important for insulating topological states, as exemplified by the fractional quantum Hall effect.…

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