Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase

TL;DR

This paper investigates phase transitions in three-dimensional systems, revealing a topological gapless phase between quantum spin Hall and insulator phases in inversion-asymmetric materials, contrasting with two-dimensional cases.

Contribution

It demonstrates the emergence of a topological gapless phase in 3D systems, highlighting the role of diabolical points and topological properties in phase transitions.

Findings

Gapless phase appears in 3D inversion-asymmetric systems

Topological nature of diabolical points causes the gapless phase

Contrast with 2D systems where such a phase does not occur

Abstract

Phase transitions between the quantum spin Hall and the insulator phases in three dimensions are studied. We find that in inversion-asymmetric systems there appears a gapless phase between the quantum spin Hall and insulator phases in three dimensions, which is in contrast with the two-dimensional case. Existence of this gapless phase stems from a topological nature of gapless points (diabolical points) in three dimensions, but not in two dimensions.