Dynamics theory of deformable solids with quasiparticle excitations in the presence of electromagnetic fields

TL;DR

This paper develops a comprehensive, self-consistent theoretical framework combining elasticity, quasiparticle kinetics, and electromagnetism to describe the behavior of charged quasiparticles in deformable crystalline solids under electromagnetic fields.

Contribution

It introduces a unified set of equations that incorporate nonlinear elasticity, a generalized kinetic equation valid across the entire Brillouin zone, and Maxwell's equations, extending traditional models.

Findings

The kinetic equation includes a new term beyond the classical Boltzmann equation.

The theory applies to metals, semiconductors, and quantum crystals.

It is exact within the quasiparticle approximation.

Abstract

A full selfconsistent set of equations is deduced to describe the kinetics and dynamics of charged quasiparticles (electrons, holes etc.) with arbitrary dispersion law in crystalline solids subjected to time-varying deformations. The set proposed unifies the nonlinear elasticity theory equation, a kinetic equation for quasiparticle excitations and Maxwell's equations supplemented by the constitute relations. The kinetic equation used is valid for the whole Brillouin zone. It is compatible with the requirement for periodicity in k-space and contains an essential new term compared to the traditional form of the Boltzmann equation. The theory is exact in the frame of the quasiparticle approach and can be applied to metals, semiconductors, as well as to other crystalline solids including quantum crystals and low-dimensional lattice structures.