Linear-in-$T$ resistivity from semiholographic non-Fermi liquid models

TL;DR

This paper develops a semiholographic model combining critical holographic sectors with Fermi liquids to explain linear-in-temperature resistivity, revealing a universal ratio of couplings that yields this behavior across various conditions.

Contribution

It introduces a novel semiholographic framework that captures linear-in-$T$ resistivity in non-Fermi liquids, unifying holographic and Fermi-liquid effects with tunable parameters.

Findings

Linear-in-$T$ resistivity achieved over wide temperature range

Existence of a coupling ratio producing universal resistivity behavior

Approaching $ u=1$ yields marginal Fermi liquid characteristics

Abstract

We construct a semiholographic effective theory in which the electron of a two-dimensional band hybridizes with a fermionic operator of a critical holographic sector, while also interacting with other bands that preserve quasiparticle characteristics. Besides the scaling dimension $\nu$ of the fermionic operator in the holographic sector, the effective theory has two {dimensionless} couplings $\alpha$ and $\gamma$ determining the holographic and Fermi-liquid-type contributions to the self-energy respectively. We find that irrespective of the choice of the holographic critical sector, there exists a ratio of the effective couplings for which we obtain linear-in-$T$ resistivity for a wide range of temperatures. This scaling persists to arbitrarily low temperatures when $\nu$ approaches unity in which limit we obtain a marginal Fermi liquid with a specific temperature dependence of the self-energy.