Topological insulators with inversion symmetry

By Liang Fu, C. L. Kane. 2006

2,910 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/47e27e738df8c325432086adb16c9555a7bb77d7

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Citations in the corpus

Dirac Surface States in Intrinsic Magnetic Topological Insulators EuSn2As2 and MnBi2nTe3n+1 (2019, background): “try [1, 2, 3]. The thinking and research on time-reversal symmetry in condensed matter systems directly led to the discovery of time-reversal-invariant (TRI) Z 2 TIs with the quantum spin Hall effect [4, 5, 6, 7]. The introduction of magnetism into the Z 2 TIs can produce more exotic topological qua”
Unexpected mass acquisition of Dirac fermions at the quantum phase transition of a topological insulator (2011, background): “Strong spin–orbit coupling can lead to an inversion of the character of valence- and conduction-band wave functions, resulting in an odd Z 2 invariant that characterizes the topological insulato”
Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface (2009, methodology): “For systems with inversion symmetry, a method based on the parity eigenvalues of band states at time-reversal-invariant points can be applie”
Topological Semimetals from First Principles (2018, background): “e parity eigenvalues, and corresponding to dierent surfaces Sabcd, are quite similar to the (strong and weak) topological indices „0;123”characterizing topological insulators in three dimensions (122, 123). We comment on this connection in more detail below. The Z2 invariant of Dirac nodal line semi”