Anisotropic fixed points in Dirac and Weyl semimetals

TL;DR

This paper investigates how anisotropy and tilt in Dirac and Weyl semimetals affect their low-energy electrodynamics, revealing persistent anisotropy and emergent magnetoelectric effects at the fixed point.

Contribution

It provides a renormalization group analysis showing anisotropy persists and tilt induces magnetoelectric terms in these semimetals at the infrared fixed point.

Findings

Anisotropy remains at the infrared fixed point.

Tilt induces a magnetoelectric term in the electrodynamics.

Magnetoelectric magnitude matches electronic tilt at the fixed point.

Abstract

The effective low energy description of interacting Dirac and Weyl semimetals is that of massless quantum electrodynamics with several Lorentz breaking material parameters. We perform a renormalization group analysis of Coulomb interaction in anisotropic Dirac and Weyl semimetals and show that the anisotropy persists in the material systems at the infrared fixed point. In addition, a tilt of the fermion cones breaking inversion symmetry induces a magnetoelectric term in the electrodynamics of the material whose magnitude runs to match that of the electronic tilt at the fixed point.