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

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.