Quantum theory of mechanical deformations

TL;DR

This paper develops a quantum framework for analyzing inhomogeneous adiabatic deformations in crystalline insulators, revealing new insights into the dynamic response and its relation to magnetic effects, with applications to flexoelectricity.

Contribution

It introduces a metric-tensor approach to quantum deformations, deriving an effective Schrödinger equation and clarifying the dynamic response in flexoelectric phenomena.

Findings

Dynamic response acts as a gauge field in the Hamiltonian.

Dynamic currents do not produce bound charges at surfaces.

The formalism resolves previous puzzles in flexoelectric theory.

Abstract

We construct a general metric-tensor framework for treating inhomogenous adiabatic deformations applied to crystalline insulators, by deriving an effective time-dependent Schr\"odinger equation in the undistorted frame. The response can be decomposed into "static" and "dynamic" terms that correspond, respectively, to the amplitude and the velocity of the distortion. We then focus on the dynamic contributon, which takes the form of a gauge field entering the effective Hamiltonian, in the linear-response limit. We uncover an intimate relation between the dynamic response to the rotational component of the inhomogeneous deformation and the diamagnetic response to a corresponding inhomogeneous magnetic field. We apply this formalism to the theory of flexoelectric response, where we resolve a previous puzzle by showing that the currents generated by the dynamic term, while real, generate no bound charges even at surfaces, and so may be dropped from a practical theory of flexoelectricity.