Spatial Modulation and Conductivities in Effective Holographic Theories

We analyze a class of bottom-up holographic models for low energy thermo-electric transport. The models we focus on belong to a family of Einstein-Maxwell-dilaton theories parameterized by two scalar functions, characterizing the dilaton self-interaction and the gauge coupling function. We impose spatially inhomogeneous lattice boundary conditions for the dilaton on the AdS boundary and study the resulting phase structure attained at low energies. We find that as we dial the scalar functions at our disposal (changing thus the theory under consideration), we obtain either (i) coherent metallic, or (ii) insulating, or (iii) incoherent metallic phases. We chart out the domain where the incoherent metals appear in a restricted parameter space of theories. We also analyze the optical conductivity, noting that non-trivial scaling behaviour at intermediate frequencies appears to only be possible for very narrow regions of parameter space.