Piezoelectricity and topological quantum phase transitions in two-dimensional spin-orbit coupled crystals with time-reversal symmetry

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.