Spatial Modulation and Conductivities in Effective Holographic Theories

TL;DR

This paper explores holographic models with scalar fields to understand different low-energy transport phases, revealing conditions for metallic, insulating, and incoherent metallic behaviors and their optical conductivity characteristics.

Contribution

It introduces a family of Einstein-Maxwell-dilaton holographic models with inhomogeneous boundary conditions to classify various low-energy transport phases and analyze their optical properties.

Findings

Identification of parameter regions for metallic, insulating, and incoherent phases.

Observation of narrow parameter space with non-trivial optical conductivity scaling.

Mapping of phase structure based on scalar function variations.

Abstract

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.