Anomalous Hall conductivity of the holographic $\mathbb{Z}_2$ Dirac semimetals

TL;DR

This paper uses holographic models to study anomalous Hall conductivity in $ ext{Z}_2$ Dirac semimetals, revealing phase transitions between topologically trivial and non-trivial phases with Hall conductivity as an order parameter.

Contribution

It introduces a holographic model incorporating two gauge fields and their coupling to analyze topological phase transitions in $ ext{Z}_2$ Dirac semimetals.

Findings

Hall conductivity depends on gauge coupling $ ext{alpha}$ and Chern-Simons terms.

Phase transition characterized by Hall conductivity as an order parameter.

Topologically non-trivial phase exhibits a distinct Hall conductivity prefactor.

Abstract

The anomalous spin Hall conductivity in the holographic model of Dirac semimetals with two Dirac nodes protected by the crystal symmetry has been elaborated. Such system besides the chiral anomaly possesses another anomaly which is related to the $\mathbb{Z}_2$ topological charge of the system. The holographic model of the system contains matter action with two $U(1)$-gauge fields as well as the appropriate combination of the Chern-Simons gauge terms. We also allow for the coupling of two gauge fields {\it via} the kinetic mixing parametrised by the coupling $\alpha$. The holographic approach in the probe limit enables us to obtain Hall conductivity. The aim of this work is to describe the phase transitions in the $\mathbb{Z}_2$ Dirac semimetals between the topologically trivial and non-trivial phases. Interestingly the anomalous Hall conductivity plays a role of the order parameter of this phase transition. The holographically found prefactor of the Hall conductivity in the topologically non-trivial phase, depends on the coupling $\alpha$ and the Chern - Simons couplings.