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 Z2 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 BaMnSb2 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.
Highlights
Finding new physical responses that signal topological quantum phase transitions is of both theoretical and experimental importance
We find that any gap closing (GC) between two gapped states that only requires 1 fine-tuning parameter is a topological quantum phase transition (TQPT) in the sense that it changes either the Z2 index[1,2] or the valley CN20
In the above Hamiltonian, the unitary transformation on the bases and the scaling/rotation of q are performed for the simplicity of the Hamiltonian; the latter generally makes q1, q2 along two non-orthogonal directions. (See Supplementary Note 3A for details.) The effective Hamiltonian at −k0 is related to h+,0 by the TR symmetry
Summary
Finding new physical responses that signal topological quantum phase transitions is of both theoretical and experimental importance. We demonstrate that the piezoelectric response can change discontinuously across a topological quantum phase transition in twodimensional time-reversal invariant systems with spin-orbit coupling, serving as a direct probe of the transition. Our work provides a general theoretical framework to classify topological quantum phase transitions, and reveals their ubiquitous relation to the piezoelectric response. A direct way to probe such TQPTs is to detect the discontinuous change of certain physical response functions. We theoretically answer this question in the affirmative: the discontinuous change of the piezoelectric response is a ubiquitous and direct signature of 2D TQPTs. The piezoelectric effect, the electric charge response induced by the applied strain, is characterized by the piezoelectric tensor (PET) to the leading order. The modern the strain tensor and ui is the theory of polarization[12,13,14] later identified the above definition as improper[15] due to the ambiguity of P in crystals, while the proper definition adds the adiabatic time dependence to ujk and relates it to the bulk current density Ji that can change the surface charge: γijk
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