Direction-dependent conductivity in planar Hall set-ups with tilted Weyl/multi-Weyl semimetals

Abstract

We compute the magnetoelectric conductivity tensors in planar Hall set-ups, which are built with tilted Weyl semimetals (WSMs) and multi-Weyl semimetals (mWSMs), considering all possible relative orientations of the electromagnetic fields ($\mathbf{E}$ and $\mathbf{B}$) and the direction of the tilt. The non-Drude part of the response arises from a nonzero Berry curvature in the vicinity of the WSM/mWSM node under consideration. Only in the presence of a nonzero tilt do we find linear-in-$|\mathbf{B}|$ terms in set-ups where the tilt-axis is not perpendicular to the plane spanned by $\mathbf{E}$ and $\mathbf{B}$. The advantage of the emergence of the linear-in-$|\mathbf{B}|$ terms is that, unlike the various $|\mathbf{B}{|}^2$-dependent terms that can contribute to experimental observations, they have purely a topological origin, and they dominate the overall response-characteristics in the realistic parameter regimes. The important signatures of these terms are that they (1) change the periodicity of the response from $\ddot{I}€$ to $2\ddot{I}€$, when we consider their dependence on the angle $\hat{I}¸$ between $\mathbf{E}$ and $\mathbf{B}$; and (2) lead to an overall change in sign of the conductivity depending on $\hat{I}¸$, when measured with respect to the $\mathbf{B}=0$ case.

some typos/errors involving units and parameter-values corrected; corrigendum appears at https://doi.org/10.1088/1361-648X/adc866