Query: Topological Insulators

Candidate papers:

abstract: Topological insulators are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time reversal symmetry. These topological materials have been theoretically predicted and experimentally observed in a variety of systems, including HgTe quantum wells, BiSb alloys, and Bi2Te3 and Bi2Se3 crystals. Theoretical models, materials properties, and experimental results on two dimensional and three dimensional topological insulators are reviewed, and both the topological band theory and the topological field theory are discussed. Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. The theory of topological superconductors is reviewed, in close analogy to the theory of topological insulators.
author_names: Xiao-liang Qi

Shou-Cheng Zhang
title: Topological insulators and superconductors
year: 2011

abstract: 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. These states are possible due to the combination of spin orbit interactions and time reversal symmetry. The two dimensional (2D) topological insulator is a quantum spin Hall insulator, which is a close cousin of the integer quantum Hall state. A three dimensional (3D) topological insulator supports novel spin polarized 2D Dirac fermions on its surface. In this Colloquium the theoretical foundation for topological insulators and superconductors is reviewed and recent experiments are described in which the signatures of topological insulators have been observed. Transport experiments on \mathrm{Hg}\mathrm{Te}\mathrm{Cd}\mathrm{Te} quantum wells are described that demonstrate the existence of the edge states predicted for the quantum spin Hall insulator. Experiments on \mathrm{Bi}}_{1\ensuremath{ }x}\mathrm{Sb}}_{x} \mathrm{Bi}}_{2}\mathrm{Se}}_{3} \mathrm{Bi}}_{2}\mathrm{Te}}_{3} and \mathrm{Sb}}_{2}\mathrm{Te}}_{3} are then discussed that establish these materials as 3D topological insulators and directly probe the topology of their surface states. Exotic states are described that can occur at the surface of a 3D topological insulator due to an induced energy gap. A magnetic gap leads to a novel quantum Hall state that gives rise to a topological magnetoelectric effect. A superconducting energy gap leads to a state that supports Majorana fermions and may provide a new venue for realizing proposals for topological quantum computation. Prospects for observing these exotic states are also discussed, as well as other potential device applications of topological insulators.
author_names: M Zahid Hasan

C L Kane
title: Colloquium Topological insulators
year: 2010

abstract: We study three dimensional generalizations of the quantum spin Hall (QSH) effect. Unlike two dimensions, where a single Z2 topological invariant governs the effect, in three dimensions there are 4 invariants distinguishing 16 phases with two general classes: weak (WTI) and strong (STI) topological insulators. The WTI are like layered 2D QSH states, but are destroyed by disorder. The STI are robust and lead to novel "topological metal" surface states. We introduce a tight binding model which realizes the WTI and STI phases, and we discuss its relevance to real materials, including bismuth.
author_names: Liang Fu

C L Kane

Eugene J Mele
title: Topological insulators in three dimensions.
venue: Physical review letters
year: 2007

abstract: Topological insulators are materials with a bulk excitation gap generated by the spin orbit interaction that are different from conventional insulators. This distinction is characterized by {Z}_{2} topological invariants, which characterize the ground state. In two dimensions, there is a single {Z}_{2} invariant that distinguishes the ordinary insulator from the quantum spin Hall phase. In three dimensions, there are four {Z}_{2} invariants that distinguish the ordinary insulator from `weak' and `strong' topological insulators. These phases are characterized by the presence of gapless surface (or edge) states. In the two dimensional quantum spin Hall phase and the three dimensional strong topological insulator, these states are robust and are insensitive to weak disorder and interactions. In this paper, we show that the presence of inversion symmetry greatly simplifies the problem of evaluating the {Z}_{2} invariants. We show that the invariants can be determined from the knowledge of the parity of the occupied Bloch wave functions at the time reversal invariant points in the Brillouin zone. Using this approach, we predict a number of specific materials that are strong topological insulators, including the semiconducting alloy \mathrm{Bi}}_{1\ensuremath{ }x}\mathrm{Sb}}_{x} as well as \ensuremath{\alpha}\text{\ensuremath{ \mathrm{Sn} and HgTe under uniaxial strain. This paper also includes an expanded discussion of our formulation of the topological insulators in both two and three dimensions, as well as implications for experiments.
author_names: Liang Fu

C L Kane
title: Topological insulators with inversion symmetry
year: 2007

abstract: anyone with a healthy fear of sticking their fingers into a plug socket will know, the behaviour of electrons in different materials varies dramatically. The first " electronic phases " of matter to be defined were the electrical conductor and insulator, and then came the semiconductor, the magnet and more exotic phases such as the superconductor. Recent work has, however now uncovered a new electronic phase called a topological insulator. Putting the name to one side for now, the meaning of which will become clear later, what is really getting everyone excited is the behaviour of materials in this phase. Strangely, they can insulate on the inside but conduct on the outside acting like a thick plastic cable covered with a layer of metal, except that the material is actually the same throughout. What is more, the conducting electrons arrange themselves into spin up electrons travelling in one direction and spin down electrons travelling in the other; this " spin current " is a milestone in the realization of practical " spintronics " Topological insulators have a rather unusual history because unlike almost every other exotic phase of matter they were characterized theoretically before being discovered experimentally. Both of the present authors, among others, were involved in that early work, which was based on the band theory of solids the standard quantum mechanical framework for understanding the electronic properties of materials. We showed two things. First, special edge states (in 2D objects) or surface states (in 3D objects) allow electrons to conduct at the surface of a material that otherwise behaves as an insulator. Second, these states necessarily occur when the band structure has a certain property a value associated with an abstract quantity called the topology (more about this later) For one of us (CK) it was an attempt to contribute to the theory of graphene the one atom thick sheets of carbon celebrated by the 2010 Nobel prize that inspired these new ideas about topology. But only when topological insulators were discovered experimentally in 2007 did the attention of the condensed matter physics community become firmly focused on this new class of materials. A related topo logical property known as the quantum Hall effect had already been found in 2D ribbons in the early 1980s, but the discovery of the first example of a 3D topologi cal phase reignited that earlier interest. Given that the 3D topological insulators
author_names: Yize Jin

Lu Zheng
title: Topological Insulators
year: 2013

abstract: When electrons are subject to a large external magnetic field, the conventional charge quantum Hall effect dictates that an electronic excitation gap is generated in the sample bulk, but metallic conduction is permitted at the boundary. Recent theoretical models suggest that certain bulk insulators with large spin orbit interactions may also naturally support conducting topological boundary states in the quantum limit, which opens up the possibility for studying unusual quantum Hall like phenomena in zero external magnetic fields. Bulk Bi1 xSbx single crystals are predicted to be prime candidates for one such unusual Hall phase of matter known as the topological insulator. The hallmark of a topological insulator is the existence of metallic surface states that are higher dimensional analogues of the edge states that characterize a quantum spin Hall insulator. In addition to its interesting boundary states, the bulk of Bi1 xSbx is predicted to exhibit three dimensional Dirac particles, another topic of heightened current interest following the new findings in two dimensional graphene and charge quantum Hall fractionalization observed in pure bismuth. However, despite numerous transport and magnetic measurements on the Bi1 xSbx family since the 1960s, no direct evidence of either topological Hall states or bulk Dirac particles has been found. Here, using incident photon energy modulated angle resolved photoemission spectroscopy (IPEM ARPES) we report the direct observation of massive Dirac particles in the bulk of Bi0.9Sb0.1, locate the Kramers points at the sample's boundary and provide a comprehensive mapping of the Dirac insulator's gapless surface electron bands. These findings taken together suggest that the observed surface state on the boundary of the bulk insulator is a realization of the 'topological metal' They also suggest that this material has potential application in developing next generation quantum computing devices that may incorporate 'light like' bulk carriers and spin textured surface currents.
author_names: D Hsieh

Dong Qian

L Andrew Wray

Y Y Xia

Yew San Hor

Robert J Cava

M Zahid Hasan
title: A topological Dirac insulator in a quantum spin Hall phase
venue: Nature
year: 2008

abstract: Topological insulators are new states of quantum matter in which surface states residing in the bulk insulating gap of such systems are protected by time reversal symmetry. The study of such states was originally inspired by the robustness to scattering of conducting edge states in quantum Hall systems. Recently, such analogies have resulted in the discovery of topologically protected states in two dimensional and three dimensional band insulators with large spin orbit coupling. So far, the only known three dimensional topological insulator is BixSb1 x, which is an alloy with complex surface states. Here, we present the results of first principles electronic structure calculations of the layered, stoichiometric crystals Sb2Te3, Sb2Se3, Bi2Te3 and Bi2Se3. Our calculations predict that Sb2Te3, Bi2Te3 and Bi2Se3 are topological insulators, whereas Sb2Se3 is not. These topological insulators have robust and simple surface states consisting of a single Dirac cone at the G point. In addition, we predict that Bi2Se3 has a topologically non trivial energy gap of 0.3 eV, which is larger than the energy scale of room temperature. We further present a simple and unified continuum model that captures the salient topological features of this class of materials. First principles calculations predict that Bi2Se3, Bi2Te3 and Sb2Te3 are topological insulators three dimensional semiconductors with unusual surface states generated by spin orbit coupling whose surface states are described by a single gapless Dirac cone. The calculations further predict that Bi2Se3 has a non trivial energy gap larger than the energy scale kBT at room temperature.
author_names: Haijun Zhang

Chaoxing Liu

Xiao-liang Qi

Xi Dai

Zhong Fang

Shou-Cheng Zhang
title: Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface
year: 2009

abstract: Recent experiments and theories have suggested that strong spin orbit coupling effects in certain band insulators can give rise to a new phase of quantum matter, the so called topological insulator, which can show macroscopic quantum entanglement effects. Such systems feature two dimensional surface states whose electrodynamic properties are described not by the conventional Maxwell equations but rather by an attached axion field, originally proposed to describe interacting quarks. It has been proposed that a topological insulator with a single Dirac cone interfaced with a superconductor can form the most elementary unit for performing fault tolerant quantum computation. Here we present an angle resolved photoemission spectroscopy study that reveals the first observation of such a topological state of matter featuring a single surface Dirac cone realized in the naturally occurring Bi_2Se_3 class of materials. Our results, supported by our theoretical calculations, demonstrate that undoped Bi_2Se_3 can serve as the parent matrix compound for the long sought topological device where in plane carrier transport would have a purely quantum topological origin. Our study further suggests that the undoped compound reached via n to p doping should show topological transport phenomena even at room temperature.
author_names: Yuqi Xia

Dong Qian

D Hsieh

L Andrew Wray

Arijeet Pal

Hsin Lin

Arun Bansil

D Grauer

Yew San Hor

Robert J Cava

M Zahid Hasan
title: Observation of a large gap topological insulator class with a single Dirac cone on the surface
year: 2009

abstract: The recent discovery of topological insulators has revived interest in the band topology of insulators. In this Letter, we extend the topological classification of band structures to include certain crystal point group symmetry. We find a class of three dimensional "topological crystalline insulators" which have metallic surface states with quadratic band degeneracy on high symmetry crystal surfaces. These topological crystalline insulators are the counterpart of topological insulators in materials without spin orbit coupling. Their band structures are characterized by new topological invariants. We hope this work will enlarge the family of topological phases in band insulators and stimulate the search for them in real materials.
author_names: Liang Fu
title: Topological crystalline insulators.
venue: Physical review letters
year: 2011

abstract: Certain insulators have exotic metallic states on their surfaces. These states are formed by topological effects that also render the electrons travelling on such surfaces insensitive to scattering by impurities. Such topological insulators may provide new routes to generating novel phases and particles, possibly finding uses in technological applications in spintronics and quantum computing.
author_names: Joel E Moore
title: The birth of topological insulators
venue: Nature
year: 2010