Transport properties of a $3$-dimensional holographic effective theory with gauge-axion coupling

TL;DR

This paper develops a 3D holographic effective theory with gauge-axion coupling, revealing temperature-dependent DC electric conductivity, a metal-insulator transition, and violation of the Wiedemann-Franz law, differing from 4D models.

Contribution

It introduces a novel 3D holographic model with gauge-axion coupling, analyzing its unique transport properties and phase transition behavior.

Findings

DC electric conductivity depends on temperature when gauge-axion coupling vanishes

The model exhibits a metal-insulator transition at zero temperature

The Wiedemann-Franz law is violated in this holographic setup

Abstract

In this paper, we implement a $3$-dimensional holographic effective theory with gauge-axion coupling. The analytical black hole solution is worked out. We investigate the Direct current (DC) thermoelectric conductivities. A novel property is that DC electric conductivity for vanishing gauge-axion coupling is temperature dependent. It is different from that of $4$-dimensional axion model whose DC electric conductivity is temperature independent. In addition, the gauge-axion coupling induces a metal insulator transition (MIT) at zero temperature. The properties of other DC thermoelectric conductivities are also discussed. Moreover we find that the Wiedemann-Franz (WF) law is violated in our model.