Geometrodynamics of electrons in a crystal under position and time dependent deformation

TL;DR

This paper develops a geometric framework for understanding the semiclassical dynamics of electrons in deformed crystals, revealing new effects like strain-induced polarization and magnetization.

Contribution

It introduces a lattice bundle geometric approach incorporating Berry curvatures and strain gradients to analyze electron behavior under deformation.

Findings

Identification of an effective post-Newtonian gravity at band bottom

Prediction of polarization induced by strain gradients

Discovery of orbital magnetization due to strain rate

Abstract

Semiclassical dynamics of Bloch electrons in a crystal under slowly varying deformation is developed in the geometric language of a lattice bundle. Berry curvatures and gradients of energy are introduced in terms of lattice covariant derivatives, with the corresponding connections given by the gradient and rate of strain. A number of physical effects are discussed: an effective post-Newtonian gravity at band bottom, polarization induced by spatial gradient of strain, orbital magnetization induced by strain rate, and electron energy stress tensor.