The electron-phonon interaction from fundamental local gauge symmetries in solids

TL;DR

This paper develops a gauge theory framework for electron-phonon interactions in solids, linking elastic properties to local gauge symmetries and revealing new couplings relevant for spintronics.

Contribution

It introduces a gauge invariance-based approach to describe electron-phonon interactions and predicts novel couplings involving spin currents in solids.

Findings

Identification of elastic waves as gauge fields (phonons)

Standard electron-phonon interaction derived from gauge invariance

Emergence of new strain-spin current couplings with spin-orbit effects

Abstract

The elastic properties of solids are described in close analogy with General Relativity, by locally gauging the translational group of space-time. Electron interactions with the crystal lattice are thus generated by enforcing full gauge invariance, with the introduction of a gauge field. Elementary excitations are associated with the local gauge, contrasting to the usual interpretation as being Goldstone bosons emerging from global symmetry breaking. In the linear limit of the theory, the gauge field displays elastic waves, that we identify with acoustic phonons, when the field is quantized. Coupling with the electronic part of the system yields the standard electron-phonon interaction. If spin-orbit effects are included, unusual couplings emerge between the strain field and the electronic spin current, leading to novel physics that may be relevant for spintronic applications.