Conductivity of weakly disordered strange metals: from conformal to hyperscaling-violating regimes

TL;DR

This paper develops a semi-analytic holographic method to model the crossover from strange metal to conformal physics, enabling detailed calculations of conductivity and instabilities in hyperscaling-violating geometries.

Contribution

It introduces a new holographic technique to construct interpolating geometries between AdS and hyperscaling-violating regimes, facilitating analysis of strange metal conductivity under disorder.

Findings

Conductivity calculations align with scaling predictions.

Logarithmic corrections appear in certain holographic cases.

Insights into superconducting instabilities in hyperscaling-violating backgrounds.

Abstract

We present a semi-analytic method for constructing holographic black holes that interpolate from anti-de Sitter space to hyperscaling-violating geometries. These are holographic duals of conformal field theories in the presence of an applied chemical potential, $\mu$, at a non-zero temperature, $T$, and allow us to describe the crossover from `strange metal' physics at $T \ll \mu$, to conformal physics at $T \gg \mu$. Our holographic technique adds an extra gauge field and exploits structure of the Einstein-Maxwell system to manifestly find 1-parameter families of solutions of the Einstein-matter system in terms of a small family of functions, obeying a nested set of differential equations. Using these interpolating geometries, we re-consider holographically some recent questions of interest about hyperscaling-violating field theories. Our focus is a more detailed holographic computation of the conductivity of strange metals, weakly perturbed by disorder coupled to scalar operators, including both the average conductivity as well as sample-to-sample fluctuations. Our findings are consistent with previous scaling arguments, though we point out logarithmic corrections in some special (holographic) cases. We also discuss the nature of superconducting instabilities in hyperscaling-violating geometries with appropriate choices of scalar couplings.