Yang-Mills Structure for Electron-Phonon Interactions

TL;DR

This paper develops an SU(2) gauge theory framework for electron-phonon interactions in polar crystals, linking spin, phonons, and superconductivity, and providing a unified theoretical approach to complex electron-phonon phenomena.

Contribution

It introduces a novel SU(2) gauge theory model for electron-phonon interactions, incorporating spin and phonon modes, and connects it to superconductivity mechanisms.

Findings

Gauge charge identified as electron spin

Massive spinors and vector bosons in crystals with band gaps

Recovery of BCS mechanism in a specific limit

Abstract

This work presents a method of grouping the electron spinors and the acoustic phonon modes of polar crystals such as metal oxides into an SU(2) gauge theory. The gauge charge is the electron spin, which is assumed to couple to the transverse acoustic phonons on the basis of spin ordering phenomena in crystals such as V$_{2}$O$_{3}$ and VO$_{2}$, while the longitudinal mode is neutral. A generalization the Peierls mechanism is presented based on the discrete gauge invariance of crystals and the corresponding Ward-Takahashi identity. The introduction of a band index violates the Ward-Takahashi identity for interband transitions resulting in a longitudinal component appearing in the upper phonon band. Thus both the spinors and the vector bosons acquire mass and a crystal with an electronic band gap and optical phonon modes results. In the limit that the coupling of bosons charged under the SU(2) gauge group goes to zero, breaking the electron U(1) symmetry recovers the BCS mechanism. In the limit that the neutral boson decouples, a Cooper instability mediated by spin-wave exchange results from symmetry breaking, i.e. unconventional superconductivity mediated by magnetic interactions.