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Topological materials host fascinating low dimensional gapless states at the boundary. As a prominent example, helical topological edge states (TESs) of two-dimensional topological insulators (2DTIs) and their stacked three-dimensional (3D)…

The scientific interest in two-dimensional topological insulators (2D TIs) is currently shifting from a more fundamental perspective to the exploration and design of novel functionalities. Key concepts for the use of 2D TIs in spintronics…

The bulk-boundary correspondence is a generic feature of topological states of matter, reflecting the intrinsic relation between topological bulk and boundary states. For example, robust edge states propagate along the edges and corner…

Mesoscale and Nanoscale Physics · Physics 2022-11-15 Ai-Lei He , Wei-Wei Luo , Yuan Zhou , Yi-Fei Wang , Hong Yao

Topological insulators are a recently discovered class of materials with fascinating properties: While the inside of the solid is insulating, fundamental symmetry considerations require the surfaces to be metallic. The metallic surface…

The topological insulator is a fundamentally new phase of matter, with the striking property that the conduction of electrons occurs only on its surface, not within the bulk, and that conduction is topologically protected. Topological…

Three-dimensional topological insulators are characterized by the presence of protected gapless spin helical surface states. In realistic samples these surface states are extended from one surface to another, covering the entire sample.…

Mesoscale and Nanoscale Physics · Physics 2011-11-08 Ken-Ichiro Imura , Yositake Takane , Akihiro Tanaka

Topological insulators (TIs) are a new quantum state of matter discovered recently, which are characterized by unconventional bulk topological invariants. Proposals for practical applications of the TIs are mostly based upon their metallic…

Mesoscale and Nanoscale Physics · Physics 2016-01-15 M. N. Chen , L. Sheng , R. Shen , D. N. Sheng , D. Y. Xing

A three-dimensional strong-topological-insulator or -semimetal hosts topological surface states which are often said to be gapless so long as time-reversal symmetry is preserved. This narrative can be mistaken when surface state…

Strongly Correlated Electrons · Physics 2015-06-29 A. P. Weber , Q. D. Gibson , Huiwen Ji , A. N. Caruso , A. V. Fedorov , R. J. Cava , T. Valla

Gapless topological boundary states characterize nontrivial topological phases arising from the bulk-boundary correspondence in symmetry-protected topological materials, such as the emergence of helical edge states in a two-dimensional…

Materials Science · Physics 2024-04-19 Yueh-Ting Yao , Xiaoting Zhou , Yi-Chun Hung , Hsin Lin , Arun Bansil , Tay-Rong Chang

Three-dimensional (3D) topological insulators (TIs) are known to carry 2D Dirac-like topological surface states in which spin-momentum locking prohibits backscattering. When thinned down to a few nanometers, the hybridization between the…

In this paper we review some connections recently discovered between topological insulators and certain classes of quantum spin liquids, focusing on two and three spatial dimensions. In two dimensions we show the integer quantum Hall effect…

Strongly Correlated Electrons · Physics 2012-03-29 Gregory A. Fiete , Victor Chua , Mehdi Kargarian , Rex Lundgren , Andreas Ruegg , Jun Wen , Vladimir Zyuzin

We consider a one-dimensional, time-reversal-invariant system with attractive interactions and spin-orbit coupling. Such a system is gapless due to the strong quantum fluctuations of the superconducting order parameter. However, we show…

Mesoscale and Nanoscale Physics · Physics 2015-06-18 Anna Keselman , Erez Berg

The recent discovery of topological insulators with exotic metallic surface states has garnered great interest in the fields of condensed matter physics and materials science. A number of spectacular quantum phenomena have been predicted…

Materials Science · Physics 2011-01-07 Wanxiang Feng , Jun Ding , Di Xiao , Yugui Yao

A topological insulator is characterized by spin-momentum locking on its boundary. The spin momentum locking on the surface of a three dimensional topological insulator leads to the existence of a non-trivial Berry's phase which leads to…

Mesoscale and Nanoscale Physics · Physics 2012-06-06 Su-Yang Xu , L. A. Wray , Y. Xia , R. Shankar , S. Jia , A. Fedorov , J. H. Dil , F. Meier , B. Slomski , J. Osterwalder , R. J. Cava , M. Z. Hasan

Recently discovered materials called three-dimensional topological insulators constitute examples of symmetry protected topological states in the absence of applied magnetic fields and cryogenic temperatures. A hallmark characteristic of…

Spin-orbital textures in topological insulators due to the spin locking with the electron momentum, play an important role in spintronic phenomena that arise from the interplay between charge and spin degrees of freedom. We have explored…

Mesoscale and Nanoscale Physics · Physics 2024-04-16 A. L. Araújo , F. Crasto de Lima , C. H. Lewenkopf , A. Fazzio

Quantum spin Hall insulators, or synonymously known as 2D topological insulators, are crucial 2D systems hosting topologically protected edge states. The working temperature of this topological quantum phase is dictated by the inverted…

Three dimensional topological insulators embody a newly discovered state of matter characterized by conducting spin-momentum locked surface states that span the bulk band gap as demonstrated via spin-resolved ARPES measurements . This…

Mesoscale and Nanoscale Physics · Physics 2012-05-09 L. Andrew Wray , Su-Yang Xu , Yuqi Xia , David Hsieh , Alexei V. Fedorov , Hsin Lin , Arun Bansil , Yew San Hor , Robert J. Cava , M. Zahid Hasan

We show how to engineer enhanced skew scattering and gap-like opening in the surface state of three-dimensional topological insulators using only non-magnetic impurities. Enhanced skew scattering off non-magnetic impurities is obtained as a…

Mesoscale and Nanoscale Physics · Physics 2014-12-11 J. Fransson , A. M. Black-Schaffer , A. V. Balatsky

Noninteracting insulating electronic states of matter can be classified according to their symmetries in terms of topological invariants which can be related to effective surface theories. These effective surface theories are in turn…

Mesoscale and Nanoscale Physics · Physics 2015-06-19 Bart de Leeuw , Carolin Küppersbusch , Vladimir Juricic , Lars Fritz