Gap closing and universal phase diagrams in topological insulators

TL;DR

This paper classifies how energy gaps close in topological insulators, linking these closures to topological phase transitions and revealing a gapless phase in certain three-dimensional systems.

Contribution

It provides a comprehensive classification of gap closing phenomena in 2D and 3D topological insulators, highlighting the topological nature of these transitions.

Findings

Gap closings are associated with changes in Z_2 topological numbers.

Inversion-asymmetric 3D systems exhibit a gapless phase between phases.

Gap-closing points in 3D have a topological origin.

Abstract

We study a general problem how the gap in a nonmagnetic band insulator closes by tuning a parameter. We review our recent results on the classification of all the possible gap closing in two and three dimensions. We show that they accompany the change of Z_2 topological numbers, and that the gap closings correspond to phase transitions between the quantum spin Hall and the insulator phases. Interestingly, in inversion-asymmetric three-dimensional systems there appears a gapless phase between the quantum spin Hall and insulator phases. This gapless phase is due to a topological nature of gap-closing points in three dimensions, but not in two dimensions.