Theory of orbital magnetization in disordered systems

TL;DR

This paper develops a gauge-invariant formula for orbital magnetization in disordered systems using Keldysh Green's functions, applicable to both insulators and metals, and demonstrates its use on a 2D electron gas with Rashba coupling.

Contribution

It introduces a general, gauge-invariant formula for orbital magnetization in disordered systems that includes vertex corrections and applies to metals and insulators.

Findings

The formula recovers previous results in the absence of disorder.

Disorder causes a shift in the orbital magnetization distribution.

Application to a 2D electron gas shows disorder mainly renormalizes quasiparticle energies.

Abstract

We present a general formula of the orbital magnetization of disordered systems based on the Keldysh Green's function theory in the gauge-covariant Wigner space. In our approach, the gauge invariance of physical quantities is ensured from the very beginning, and the vertex corrections are easily included. Our formula applies not only for insulators but also for metallic systems where the quasiparicle behavior is usually strongly modified by the disorder scattering. In the absence of disorders, our formula recovers the previous results obtained from the semiclassical theory and the perturbation theory. As an application, we calculate the orbital magnetization of a weakly disordered two-dimensional electron gas with Rashba spin-orbit coupling. We find that for the short range disorder scattering, its major effect is to the shifting of the distribution of orbital magnetization corresponding to the quasiparticle energy renormalization.