Linear response in planar Hall and thermal Hall setups for Rarita-Schwinger-Weyl semimetals

We investigate the nature of the linear-response tensors in planar Hall and planar thermal Hall setups, where we subject a Rarita-Schwinger-Weyl (RSW) semimetal to the combined influence of an electric field E (and/or temperature gradient ∇ᵣ T) and a weak (i.e., non-quantizing) magnetic field B. For computing the in-plane transport components, we have added an elastic deformation which gives rise to a chirality-dependent effective magnetic field Bᵗᵒᵗ = B + χ \, B₅, where χ is the chirality of an RSW node. We have included the effects of orbital magnetic moment (OMM), in conjunction with the Berry curvature (BC), both of which appear as a consequence of nontrivial topology of the bandstructure. Due to the presence of four bands, RSW semimetals provide a richer structure for obtaining the linear-response coefficients, compared to the Weyl semimetals. In particular, we have found that the OMM-contributed terms may oppose or add up to the BC-only parts, depending on which band we are considering. We have also considered the response arising from internode scatterings. Last, but not the least, we have determined the out-of-plane response comprising the intrinsic anomalous Hall and the Lorentz-force-contributed currents, whose nature corroborates the findings of some recent experimental results.