Intrinsic Orbital and Spin Hall Effect in Bismuth Semimetal

We investigate the intrinsic orbital Hall conductivity (OHC) and spin Hall conductivity (SHC) in Bismuth semimetal, by employing sp-orbital tight-binding model. We report a substantial difference between anisotropy of OHC and SHC whose orbital and spin polarization lie within the basal plane. We do not observe substantial correlation between the orbital and spin Berry curvature via spin orbit coupling (SOC) at Fermi energy, disproving the correlation between OHC and SHC in strong SOC regime. We argue the huge SHC in Bi semimetal attributes 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 mean to differentiate the two effects in experiments.