Absence of power-law mid-infrared conductivity in gravitational crystals

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 ReissnerNordström-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.