Electromagnetic response of interacting Weyl semimetals

TL;DR

This paper investigates the electromagnetic behavior of strongly interacting Weyl semimetals by coupling Weyl fermions to a quantum critical system and using holographic methods to derive their effective electromagnetic response.

Contribution

It introduces a holographic framework to analyze the electromagnetic properties of interacting Weyl semimetals, including anomalous magnetic moments and conductivity with vertex corrections.

Findings

Derived frequency and momentum-dependent anomalous magnetic moment.

Calculated conductivity including vertex corrections.

Connected holographic model to Coulomb interactions in Weyl semimetals.

Abstract

We study the electromagnetic properties of Weyl semimetals with strong interactions. Focusing on a single Weyl cone in the band structure, we induce strong interactions by coupling the Weyl fermion with a tunable coupling constant $g_f$ to a quantum critical system. The critical fluctuations are described by a conformal field theory containing fermionic operators with scaling dimension $\Delta$. Employing the methods of the holographic correspondence, we then derive the effective theory of the Weyl fermion in the presence of external electric and magnetic fields. In particular, we determine the frequency and momentum-dependent anomalous magnetic moment of the Weyl fermions. We also determine the conductivity of the Weyl semimetal including the vertex corrections consistent with the Ward identity. Finally, we connect our construction to the case of Coulomb interactions in Weyl semimetals by tuning the parameters $\Delta \rightarrow 5/2$ and $g_f^2 \rightarrow e/\sqrt{\hbar c\epsilon_0$.