Intrinsic spin Hall conductivities are calculated for strong spin-orbit ${\mathrm{Bi}}_{1-x}{\mathrm{Sb}}_x$ semimetals, from the Kubo formula and using Berry curvatures evaluated throughout the Brillouin zone from a tight-binding Hamiltonian. Nearly crossing bands with strong spin-orbit interaction generate giant spin Hall conductivities in these materials, ranging from 474 $(\hslash /\mathrm{e})(\mathrm{\Omega }\mathrm{cm}{)}^{-1}$ for bismuth to 96 $(\hslash /\mathrm{e})(\mathrm{\Omega }\mathrm{cm}{)}^{-1}$ for antimony; the value for bismuth is more than twice that of platinum. The large spin Hall conductivities persist for alloy compositions corresponding to a three-dimensional topological insulator state, such as ${\mathrm{Bi}}_{0.83}{\mathrm{Sb}}_{0.17}$. The spin Hall conductivity could be changed by a factor of 5 for doped Bi, or for ${\mathrm{Bi}}_{0.83}{\mathrm{Sb}}_{0.17}$, by changing the chemical potential by 0.5 eV, suggesting the potential for doping or voltage tuned spin Hall current.

• Received 27 October 2014

DOI:https://doi.org/10.1103/PhysRevLett.114.107201

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Published by the American Physical Society