Electric and thermoelectric response for Weyl and multi-Weyl semimetals in planar Hall configurations including the effects of strain

Abstract

We investigate the response tensors in planar Hall (thermal Hall) configurations such that a three-dimensional Weyl or multi-Weyl semimetal is subjected to the influence of an electric field E (temperature gradient ∇rT) and an effective magnetic field Btot oriented at a generic angle with respect to each other. The effective magnetic field consists of two parts — (a) an actual/physical magnetic field B, and (b) an emergent magnetic field B5 which quantifies the elastic deformations of the sample. B5 is an axial pseudomagnetic field because it couples to conjugate nodal points with opposite chiralities with opposite signs. We study the interplay of the orientations of these two components of Btot with respect to the direction of the electric field (temperature gradient) and elucidate how it affects the characteristics involving the chirality of the node. Additionally, we show that the magnitude and sharpness of the conductivity tensor profiles strongly depend on the value of the topological charge at the node in question.