Charge transport in holography with momentum dissipation

TL;DR

This work develops a holographic framework for charge transport with momentum dissipation implemented by linear axions coupled to a dilaton, enabling hyperscaling-violating IR geometries. By deriving a two-term DC conductivity and performing a detailed IR analysis, it classifies possible low-temperature transport regimes into four classes based on whether the current and axions are (marginally) relevant. The study reveals rich scaling behaviors for resistivity and optical conductivity, including coherent/incoherent metals and insulators, and uncovers violations of naive scale-invariant AC predictions due to the running dilaton. It also connects the results to random-field disorder physics and discusses analytic AdS completions and future extensions to anisotropic or helical phases.

Abstract

In this work, we examine how charge is transported in a theory where momentum is relaxed by spatially dependent, massless scalars. We analyze the possible IR phases in terms of various scaling exponents and the (ir)relevance of operators in the IR effective holographic theory with a dilaton. We compute the (finite) resistivity and encounter broad families of (in)coherent metals and insulators, characterized by universal scaling behaviour. The optical conductivity at zero temperature and low frequencies exhibits power tails which can violate scaling symmetries, due to the running of the dilaton. At low temperatures, our model captures features of random-field disorder.