On the $Z_2$ classification of Quantum Spin Hall Models

Abstract

We propose an alternative formulation of the $Z_2$ topological index for quantum spin Hall systems and band insulators when time reversal invariance is not broken. The index is expressed in terms of the Chern numbers of the bands of the model, and a connection with the number of pairs of robust edge states is thus established. The alternative index is easy to compute in most cases of interest. We also discuss connections with the recently proposed spin Chern number for quantum spin Hall models.

Presentation changed to improve clarity, some technical aspects of the topological arguments including material previously cited as unpublished notes have now been added as an appendix

References in corpus (4)

• Dissipationless Quantum Spin Current at Room Temperature
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• Topological aspects of quantum spin Hall effect in graphene: Z${}_2$ topological order and spin Chern number

Cited by in corpus (2)

• Topological Surface States Protected From Backscattering by Chiral Spin Texture
• Fractional Quantum Hall Effect via Holography: Chern-Simons, Edge States, and Hierarchy