Lorentz invariance violation and the CPT-odd electromagnetic response of a tilted anisotropic Weyl semimetal

Abstract

We derive the electromagnetic response of a particular fermionic sector in the minimal QED contribution to the Standard Model Extension (SME), which can be physically realized in terms of a model describing a tilted and anisotropic Weyl semimetal (WSM). The contact is made through the identification of the Dirac-like Hamiltonian resulting from the SME with that corresponding to the WSM in the linearized tight-binding approximation. We first calculate the effective action by computing the non-perturbative vacuum polarization tensor using thermal field theory techniques, focusing upon the corrections at finite chemical potential and zero temperature. Next, we confirm our results by a direct calculation of the anomalous Hall current within a chiral kinetic theory approach. In an ideal Dirac cone picture of the WSM (isotropic and non-tilted) such response is known to be governed by axion electrodynamics, with the space-time dependent axion angle $\Theta (\mathbf{r},t)=2(\mathbf{b}\cdot \mathbf{r}-b_{0}t)$, being $2\mathbf{b}$ and $2b_0$ the separation of the Weyl nodes in momentum and energy, respectively. In this paper we demonstrate that the node tilting and the anisotropies induce novel corrections at a finite density which however preserve the structure of the axionic field theory. We apply our results to the ideal Weyl semimetal ${\mathrm{EuCd}}_2{\mathrm{As}}_2$ and to the highly anisotropic and tilted monopnictide $\mathrm{TaAs}$.

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Cited by in corpus (5)

• Optical properties and energy propagation in a dielectric medium supporting magnetic current
• Nonperturbative Lorentz Violation and Field Quantization
• Physical interpretation of large Lorentz violation via Weyl semimetals
• Optical reflection signature of an axion dielectric with magnetic current
• Effective electromagnetic Lagrangians in the derivative expansion method