Negative intrinsic orbital Hall effect in group XIV materials

Abstract

Material-dependent signs of the spin Hall conductivity are a useful tool to distinguish the spin Hall effect from other spin phenomenon. Similarly, material-dependent signs of the orbital Hall effect (OHE) can be a useful tool to distinguish the OHE from other effects. But previous theoretical calculations of the orbital Hall conductivity (OHC) found mostly positive sign, making difficult the OHE detection based on the material dependence of the OHC sign. We investigate the intrinsic OHE in elemental group XIV materials Si, Ge, and $\ensuremath{\alpha}$-Sn with diamond cubic structures. We find that the OHC in these materials are gigantic $\ensuremath{\sim}{10}^{3}\phantom{\rule{4pt}{0ex}}(\ensuremath{\hbar}/e){(\mathrm{\ensuremath{\Omega}}\phantom{\rule{0.16em}{0ex}}\mathrm{cm})}^{\ensuremath{-}1}$ and negative. These materials have two pairs of valence bands interacting with each other to generate negative orbital Berry curvature. Further, we suggest the usage of these materials to measure the OHE.