Spin and orbital effects in a 2D electron gas in a random magnetic field

TL;DR

This paper develops a superbosonization approach to analyze a 2D electron gas in a random magnetic field, revealing spin and orbital effects, and deriving a nonlinear sigma model with implications for transport properties.

Contribution

It introduces a superbosonization method for a 2D electron gas in a random magnetic field, accounting for spin and orbital effects, and derives a nonlinear sigma model including spin modes.

Findings

Transport time is twice smaller than for spinless particles.

Additional soft spin excitations appear for fixed RMF direction.

Derived a nonlinear sigma model with orbital, spin, and spin-orbital collision terms.

Abstract

Using the method of superbosonization we consider a model of a random magnetic field (RMF) acting on both orbital motion and spin of electrons in two dimensions. The method is based on exact integration over one particle degrees of freedom and reduction of the problem to a functional integral over supermatrices $Q({\bf r},{\bf r^{\prime}})$. We consider a general case when both the direction of the RMF and the g-factor of the Zeeman splitting are arbitrary. Integrating out fast variations of $Q$ we come to a standard collisional unitary non-linear $\sigma$-model. The collision term consists of orbital, spin and effective spin-orbital parts. For a particular problem of a fixed direction of RMF, we show that additional soft excitations identified with spin modes should appear. Considering $\delta $% -correlated weak RMF and putting g=2 we find the transport time $\tau_{tr} $. This time is 2 times smaller than that for spinless particles.