Holographic description of an anisotropic Dirac semimetal

TL;DR

This paper develops a holographic model for an anisotropic Dirac semimetal in 2+1 dimensions, revealing a rich phase diagram with semi-metallic, insulating, and semi-Dirac phases characterized by distinct fermionic dispersion relations.

Contribution

It introduces a novel holographic framework for anisotropic Dirac semimetals, capturing topological phase transitions and diverse fermionic phases with explicit symmetry breaking.

Findings

Identification of semi-metallic phases with Dirac cones

Discovery of an insulating phase with a mass gap and mild anisotropy

Observation of an anisotropic semi-Dirac phase with mixed dispersion relations

Abstract

Holographic quantum matter exploits the AdS/CFT correspondence to study systems in condensed matter physics. An example of these systems are strongly correlated semimetals, which feature a rich phase diagram structure. In this work, we present a holographic model for a Dirac semimetal in $2+1$ dimensions that features a topological phase transition. Our construction relies on deforming a relativistic UV fixed point with some relevant operators that explicitly break rotations and some internal symmetries. The phase diagram for different values of the relevant coupling constants is obtained. The different phases are characterized by distinct dispersion relations for probe fermionic modes in the AdS geometry. We find semi-metallic phases characterized by the presence of Dirac cones and an insulating phase featuring a mass gap with a mild anisotropy. Remarkably, we find as well an anisotropic semi-Dirac phase characterized by a massless a fermionic excitation dispersing linearly in one direction while quadratically in the other.