Axial Hall effect and universality of holographic Weyl semi-metals

TL;DR

This paper explores the properties of holographic Weyl semimetals, focusing on their topological phase transition, axial Hall conductivity, and universality, including validation through a supergravity model.

Contribution

It demonstrates the persistence of the topological phase transition across parameter space and confirms the universality of the axial Hall conductivity in holographic models.

Findings

Topological phase transition persists over a wide parameter range.

Axial Hall conductivity is 1/3 of electric Hall conductivity after renormalization.

Phase transition occurs in a top-down supergravity model.

Abstract

The holographic Weyl semimetal is a model of a strongly coupled topological semi-metal. A topological quantum phase transition separates a topological phase with non-vanishing anomalous Hall conductivity from a trivial state. We investigate how this phase transition depends on the parameters of the scalar potential (mass and quartic self coupling) finding that the quantum phase transition persists for a large region in parameter space. We then compute the axial Hall conductivity. The algebraic structure of the axial anomaly predicts it to be 1/3 of the electric Hall conductivity. We find that this holds once a non-trivial renormalization effect on the external axial gauge fields is taken into account. Finally we show that the phase transition also occurs in a top-down model based on a consistent truncation of type IIB supergravity.