Topological insulators with inversion symmetry

Abstract

Topological insulators are materials with a bulk excitation gap generated by\nthe spin orbit interaction, and which are different from conventional\ninsulators. This distinction is characterized by Z_2 topological invariants,\nwhich characterize the groundstate. In two dimensions there is a single Z_2\ninvariant which distinguishes the ordinary insulator from the quantum spin Hall\nphase. In three dimensions there are four Z_2 invariants, which distinguish the\nordinary insulator from "weak" and "strong" topological insulators. These\nphases are characterized by the presence of gapless surface (or edge) states.\nIn the 2D quantum spin Hall phase and the 3D strong topological insulator these\nstates are robust and are insensitive to weak disorder and interactions. In\nthis paper we show that the presence of inversion symmetry greatly simplifies\nthe problem of evaluating the Z_2 invariants. We show that the invariants can\nbe determined from the knowledge of the parity of the occupied Bloch\nwavefunctions at the time reversal invariant points in the Brillouin zone.\nUsing this approach, we predict a number of specific materials are strong\ntopological insulators, including the semiconducting alloy Bi_{1-x} Sb_x as\nwell as \\alpha-Sn and HgTe under uniaxial strain. This paper also includes an\nexpanded discussion of our formulation of the topological insulators in both\ntwo and three dimensions, as well as implications for experiments.\n

Keywords

Affiliated Institutions

• University of Pennsylvania US

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