Piezoelectricity and Topological Quantum Phase Transitions in Two-Dimensional Spin-Orbit Coupled Crystals with Time-Reversal Symmetry

TL;DR

This paper shows that piezoelectric response can serve as a direct indicator of topological quantum phase transitions in 2D time-reversal invariant systems with spin-orbit coupling, providing a new experimental probe.

Contribution

It introduces a theoretical framework linking piezoelectric response discontinuities to topological quantum phase transitions in 2D materials with specific symmetry properties.

Findings

Piezoelectric response changes discontinuously across topological transitions.

All gap closing cases in certain symmetry groups alter topological invariants.

Proposed experimental platforms include HgTe/CdTe quantum wells and BaMnSb₂.

Abstract

Finding new physical responses that signal topological quantum phase transitions is of both theoretical and experimental importance. Here, we demonstrate that the piezoelectric response can change discontinuously across a topological quantum phase transition in two-dimensional time-reversal invariant systems with spin-orbit coupling, thus serving as a direct probe of the transition. We study all gap closing cases for all 7 plane groups that allow non-vanishing piezoelectricity and find that any gap closing with 1 fine-tuning parameter between two gapped states changes either the $Z_2$ invariant or the locally stable valley Chern number. The jump of the piezoelectric response is found to exist for all these transitions, and we propose the HgTe/CdTe quantum well and BaMnSb$_2$ as two potential experimental platforms. Our work provides a general theoretical framework to classify topological quantum phase transitions and reveals their ubiquitous relation to the piezoelectric response.