• Milestone
  • Free to Read

Topological insulators with inversion symmetry

Liang Fu and C. L. Kane
Phys. Rev. B 76, 045302 – Published 2 July 2007
An article within the collection: Physical Review B 50th Anniversary Milestones

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 Z2 topological invariants, which characterize the ground state. In two dimensions, there is a single Z2 invariant that distinguishes the ordinary insulator from the quantum spin-Hall phase. In three dimensions, there are four Z2 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 Z2 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 Bi1xSbx as well as αSn 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.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Received 14 November 2006

DOI:https://doi.org/10.1103/PhysRevB.76.045302

©2007 American Physical Society

Collections

This article appears in the following collection:

Physical Review B 50th Anniversary Milestones

These Milestone studies represent lasting contributions to physics by way of reporting significant discoveries, initiating new areas of research, or substantially enhancing the conceptual tools for making progress in the burgeoning field of condensed matter physics.

Authors & Affiliations

Liang Fu and C. L. Kane

  • Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

Article Text

Click to Expand

References

Click to Expand
Issue

Vol. 76, Iss. 4 — 15 July 2007

Reuse & Permissions
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review B

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×