Intrinsic orbital and spin Hall effect in bismuth semimetal

Abstract

We investigate the intrinsic orbital Hall conductivity (OHC) and spin Hall conductivity (SHC) in a bismuth semimetal, by employing an $sp$-orbital tight-binding model. We report a notable difference between the anisotropy of OHC and SHC whose orbital and spin polarizations lie within the basal plane. We do not observe a substantial correlation between the orbital and spin Berry curvatures with spin-orbit coupling (SOC) at the Fermi energy, disproving the correlation between OHC and SHC in a strong SOC regime. We argue the huge SHC in a Bi semimetal is attributed to its gigantic SOC which strongly affects the hybridization of the $p$ orbitals, despite its relatively small magnitude of OHC. We hope the distinct anisotropy of OHC and SHC provides a feasible means to differentiate between the two effects in experiments.