Motions of electrons in adiabatically perturbed periodic structures

TL;DR

This paper analyzes how electrons move in crystalline structures under slow external or structural changes, focusing on the effective dynamics within decoupled subspaces of the quantum state space.

Contribution

It provides a detailed theoretical framework for understanding electron motion in adiabatically perturbed periodic potentials, including the decoupling of Hilbert space into invariant subspaces.

Findings

Decoupling of Hilbert space into almost invariant subspaces.

Effective dynamics within these subspaces.

Applicability to both non-magnetic and magnetic regimes.

Abstract

We study the motion of electrons in a periodic background potential (usually resulting from a crystalline solid). For small velocities one would use either the non-magnetic or the magnetic Bloch hamiltonian, while in the relativistic regime one would use the Dirac equation with a periodic potential. The dynamics, with the background potential included, is perturbed either through slowly varying external electromagnetic potentials or through a slow deformation of the crystal. In either case we discuss how the Hilbert space of states decouples into almost invariant subspaces and explain the effective dynamics within such a subspace.