Lorentz invariance violation and the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi><mml:mi>T</mml:mi></mml:math>-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 nonperturbative 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 nontilted) such response is known to be governed by axion electrodynamics, with the space-time dependent axion angle <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="normal">Θ</a:mi><a:mo stretchy="false">(</a:mo><a:mi mathvariant="bold-italic">r</a:mi><a:mo>,</a:mo><a:mi>t</a:mi><a:mo stretchy="false">)</a:mo><a:mo>=</a:mo><a:mn>2</a:mn><a:mo stretchy="false">(</a:mo><a:mi mathvariant="bold-italic">b</a:mi><a:mo>·</a:mo><a:mi mathvariant="bold-italic">r</a:mi><a:mo>−</a:mo><a:msub><a:mi>b</a:mi><a:mn>0</a:mn></a:msub><a:mi>t</a:mi><a:mo stretchy="false">)</a:mo></a:math>, being <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mn>2</k:mn><k:mi mathvariant="bold-italic">b</k:mi></k:math> and <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mn>2</n:mn><n:msub><n:mi>b</n:mi><n:mn>0</n:mn></n:msub></n:math> 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 <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:msub><p:mi>EuCd</p:mi><p:mn>2</p:mn></p:msub><p:msub><p:mi>As</p:mi><p:mn>2</p:mn></p:msub></p:math> and to the highly anisotropic and tilted monopnictide TaAs. Published by the American Physical Society 2024

Topics & Concepts