Electric, thermal, and thermoelectric magnetoconductivity for Weyl/multi-Weyl semimetals in planar Hall set-ups induced by the combined effects of topology and strain

TL;DR

This paper investigates the electric, thermal, and thermoelectric responses in Weyl and multi-Weyl semimetals under combined electric, thermal, and magnetic fields, considering topology and strain effects using semiclassical Boltzmann formalism.

Contribution

It derives general response tensor expressions incorporating Berry curvature and orbital magnetic moment effects in Weyl semimetals with strain-induced pseudomagnetic fields.

Findings

Response tensors include Berry curvature and orbital magnetic moment contributions.

Orbital magnetic moment opposes Berry curvature effects in transverse responses.

Strain-induced pseudomagnetic fields influence magnetoconductivity in Weyl semimetals.

Abstract

We continue our investigation of the response tensors in planar Hall (or planar thermal Hall) configurations where a three-dimensional Weyl/multi-Weyl semimetal is subjected to the combined influence of an electric field $\mathbf E $ (and/or temperature gradient $\nabla_{\mathbf r } T$) and an effective magnetic field $\mathbf B_\chi $, generalizing the considerations of Phys. Rev. B 108 (2023) 155132 and Physica E 159 (2024) 115914. The electromagnetic fields are oriented at a generic angle with respect to each other, thus leading to the possibility of having collinear components, which do not arise in a Hall set-up. The net effective magnetic field $\mathbf B_\chi $ consists of two parts -- (a) an actual/physical magnetic field $\mathbf B $ applied externally; and (b) an emergent magnetic field $\mathbf B_5 $ which quantifies the elastic deformations of the sample. $\mathbf B_5 $ is an axial pseudomagnetic field because it couples to conjugate nodal points with opposite chiralities with opposite signs. Using a semiclassical Boltzmann formalism, we derive the generic expressions for the response tensors, including the effects of the Berry curvature (BC) and the orbital magnetic moment (OMM), which arise due to a nontrivial topology of the bandstructures. We elucidate the interplay of the BC-only and the OMM-dependent parts in the longitudinal and transverse (or Hall) components of the electric, thermal, and thermoelectric response tensors. Especially, for the co-planar transverse components of the response tensors, the OMM part acts exclusively in opposition (sync) with the BC-only part for the Weyl (multi-Weyl) semimetals.