Scale-dependent correction to the dynamical conductivity of a disordered system at unitary symmetry

TL;DR

This paper calculates the leading scale-dependent correction to the dynamical conductivity in disordered systems at unitary symmetry, revealing significant corrections at three dimensions that surpass traditional Drude predictions.

Contribution

It provides the first calculation of the leading scale-dependent correction to conductivity in three-dimensional disordered systems at unitary symmetry.

Findings

Leading correction to conductivity at d=3 is proportional to |omega|.

Correction dominates over the Drude omega^2 term at low frequencies.

Determines the leading correction to the RG beta-function in the metallic phase at d=3.

Abstract

Anderson localization has been studied extensively for more than half a century. However, while our understanding has been greatly enhanced by calculations based on a small epsilon expansion in d = 2 + epsilon dimensions in the framework of non-linear sigma models, those results can not be safely extrapolated to d = 3. Here we calculate the leading scale-dependent correction to the frequency-dependent conductivity sigma(omega) in dimensions d <= 3. At d = 3 we find a leading correction Re{sigma(omega)} ~ |omega|, which at low frequency is much larger than the omega^2 correction deriving from the Drude law. We also determine the leading correction to the renormalization group beta-function in the metallic phase at d = 3.