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

Topological quantum phase transitions can be reflected by the sudden jump of certain physical response functions, e.g., the transition between quantum spin Hall state and normal insulator state featured by the jump of the two-terminal conductance. In this work, we demonstrate that the piezoelectric response can also change discontinuously across a topological quantum phase transition in two-dimensional time-reversal invariant systems with spin-orbit coupling. We study all gap closing cases for all 7 plane groups that allow non-vanishing piezoelectric tensor and find that any gap closing with 1 fine-tuning parameter between two gapped states changes either the Z2 invariant (characterizing the quantum spin Hall phase) or the "locally" stable valley Chern number (characterizing the valley Hall phase). The jump of the piezoelectric response is found to exist for all these transitions, and we propose the HgTe/CdTe quantum well and BaMnSb2 as two potential experimental platforms.