Topological Insulators with Inversion Symmetry

TL;DR

This paper demonstrates how inversion symmetry simplifies the calculation of Z_2 topological invariants in topological insulators, enabling prediction of new strong topological insulators from material properties.

Contribution

It introduces a method to determine Z_2 invariants from parity at time reversal invariant points, facilitating identification of strong topological insulators.

Findings

Inversion symmetry simplifies Z_2 invariant calculations.

Predicted strong topological insulators include Bi_{1-x}Sb_x, -Sn, and strained HgTe.

The method is applicable to both 2D and 3D topological insulators.

Abstract

Topological insulators are materials with a bulk excitation gap generated by the spin orbit interaction, and which are different from conventional insulators. This distinction is characterized by Z_2 topological invariants, which characterize the groundstate. In two dimensions there is a single Z_2 invariant which distinguishes the ordinary insulator from the quantum spin Hall phase. In three dimensions there are four Z_2 invariants, which 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 2D quantum spin Hall phase and the 3D 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 wavefunctions at the time reversal invariant points in the Brillouin zone. Using this approach, we predict a number of specific materials are strong topological insulators, including the semiconducting alloy Bi_{1-x} Sb_x as well as \alpha-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.