Absence of Power-Law Mid-Infrared Conductivity in Gravitational Crystals

TL;DR

This study investigates the optical conductivity of inhomogeneous holographic models and finds no evidence of power-law scaling, challenging previous claims that gravitational crystals can replicate the mid-infrared behavior of cuprate superconductors.

Contribution

The paper constructs generalized holographic models with inhomogeneous charge densities and demonstrates the absence of power-law mid-infrared conductivity scaling.

Findings

No power-law scaling observed in conductivity

Supports previous results that gravitational crystals do not mimic cuprate behavior

Provides generalized models interpolating between earlier studies

Abstract

We compute conductivities of strongly-interacting and non-uniform charge densities dual to inhomogeneous anti-de Sitter--black hole spacetimes. Backreacting bulk scalars with periodic boundary profiles, we construct generalizations of Reissner-Nordstr\"om-AdS that interpolate between those used in two previous studies --- one that reports power-law scaling for the boundary optical conductivity and one that does not. We find no evidence for power-law scaling of the conductivity, thereby corroborating the previous negative result that gravitational crystals are insufficient to generate the power-law mid-infrared conductivity observed in cuprate superconductors.