Effect of spin on electron motion in a random magnetic field

TL;DR

This paper investigates how electron spin affects their motion in a two-dimensional random magnetic field, revealing that spin reduces the diffusion constant and alters correlation functions compared to spinless models.

Contribution

The authors introduce a novel approach using a Dirac Hamiltonian to derive a sigma model that incorporates electron spin effects in a random magnetic field.

Findings

Diffusion constant is halved when spin is considered.

Single-particle lifetime and transport time differ from spinless models.

Derived correlation functions show significant spin-dependent effects.

Abstract

We consider properties of a two-dimensional electron system in a random magnetic field. It is assumed that the magnetic field not only influences orbital electron motion but also acts on the electron spin. For calculations, we suggest a new trick replacing the initial Hamiltonian by a Dirac Hamiltonian. This allows us to do easily a perturbation theory and derive a supermatrix sigma model, which takes a form of the conventional sigma model with the unitary symmetry. Using this sigma model we calculate several correlation functions including a spin-spin correlation function. As compared to the model without spin, we get different expressions for the single-particle lifetime and the transport time. The diffusion constant turns out to be 2 times smaller than the one for spinless particles.