Mimic the optical conductivity in disordered solids via gauge/gravity duality

TL;DR

This paper uses gauge/gravity duality to model disordered solids and finds that the optical conductivity exhibits universal non-power law scaling at high frequencies, similar to real disordered materials.

Contribution

It demonstrates a holographic model that reproduces non-power law optical conductivity scaling in disordered solids, highlighting the role of dilaton-gauge couplings and boundary behaviors.

Findings

Optical AC conductivity shows non-power law scaling at high frequencies for z>1.

Scaling behavior is robust against temperature variations.

The model suggests dilaton-gauge couplings influence conductivity scaling.

Abstract

We study the optical conductivity in a (2+1)-dimensional non-relativistic field theory holographically dual to a (3+1)-dimensional charged Lifshitz black brane with the Einstein-Maxwell-dilaton theory. Surprisingly, we find that the optical AC conductivity satisfies the nontrivial (non-)power law scaling in the high frequency regime rather than approaching to a constant when the dynamical critical exponent $z>1$, which is qualitatively similar to those in various disordered solids in condensed matter systems. Besides, this (non-)power law scaling behavior shows some universality, which is robust against the temperatures. We argue that the peculiar scaling behavior of AC conductivity may stem from the couplings of the dilaton field with the gauge fields and also the logarithmic behavior near the boundary in the Lifshitz spacetime.