Unconventional topological phase transition in two-dimensional systems with space-time inversion symmetry

TL;DR

This paper reveals an unconventional topological phase transition in 2D systems with space-time inversion symmetry, mediated by a stable Weyl semimetal phase, contrasting with traditional transitions in time-reversal invariant systems.

Contribution

It introduces a novel topological phase transition mechanism involving Weyl semimetals in 2D systems with space-time inversion symmetry, supported by theoretical and material examples.

Findings

Weyl points are stabilized by space-time inversion symmetry.

Topological invariant changes via Weyl point pair-creation/annihilation.

HgTe/CdTe quantum wells exhibit this transition within specific thickness ranges.

Abstract

We study a topological phase transition between a normal insulator and a quantum spin Hall insulator in two-dimensional (2D) systems with time-reversal and two-fold rotation symmetries. Contrary to the case of ordinary time-reversal invariant systems where a direct transition between two insulators is generally predicted, we find that the topological phase transition in systems with an additional two-fold rotation symmetry is mediated by an emergent stable two-dimensional Weyl semimetal phase between two insulators. Here the central role is played by the so-called space-time inversion symmetry, the combination of time-reversal and two-fold rotation symmetries, which guarantees the quantization of the Berry phase around a 2D Weyl point even in the presence of strong spin-orbit coupling. Pair-creation/pair-annihilation of Weyl points accompanying partner exchange between different pairs induces a jump of a 2D $Z_{2}$ topological invariant leading to a topological phase transition. According to our theory, the topological phase transition in HgTe/CdTe quantum well structure is mediated by a stable 2D Weyl semimetal phase since the quantum well, lacking inversion symmetry intrinsically, has two-fold rotation about the growth direction. Namely, the HgTe/CdTe quantum well can show 2D Weyl semimetallic behavior within a small but finite interval in the thickness of HgTe layers between a normal insulator and a quantum spin Hall insulator. We also propose that few-layer black phosphorus under perpendicular electric field is another candidate system to observe the unconventional topological phase transition mechanism accompanied by emerging 2D Weyl semimetal phase protected by space-time inversion symmetry.