Abstract
Intrinsic spin Hall conductivities are calculated for strong spin-orbit Bi(1-x)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 (ℏ/e)(Ω cm)^{-1} for bismuth to 96 (ℏ/e)(Ω 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 Bi(0.83)Sb(0.17). The spin Hall conductivity could be changed by a factor of 5 for doped Bi, or for Bi(0.83)Sb(0.17), by changing the chemical potential by 0.5 eV, suggesting the potential for doping or voltage tuned spin Hall current.
Highlights
Intrinsic spin Hall conductivities are calculated for strong spin-orbit Bi1−xSbx semimetals, from the Kubo formula and using Berry curvatures evaluated throughout the Brillouin zone from a tight-binding Hamiltonian
The spin Hall conductivity, which is the ratio of the spin Hall current to the longitudinal electric field, depends on details of the electronic band structure such as the strength of the spin-orbit interaction, the Fermi energy, the direction of current relative to crystal axes, and the strain [4,5,6,7,8,9,10,11,12,13,14,15,16,17]
Measurements of the variation of the spin Hall conductivity with these quantities have been done in most detail for noncentrosymmetric semiconductor quantum wells [8,16]; other phenomena, including current-induced spin polarization [18,19] and precessional spin-orbit fields [20] complicate the interpretation
Summary
Week ending 13 MARCH 2015 pockets at the T points for bismuth and the H points for antimony. For the electronic structure of the Bi1−xSbx alloy [39], the band energies and overlap integrals are averaged using the virtual crystal approximation. The electronic band structure of Bi1−xSbx around the Fermi energy is shown in Fig. 1 for four different compositions, using the parametrization of Refs. At around 9% antimony the band overlap disappears and a semimetal-semiconductor (SMSC) transition occurs. The spin Hall conductivity can be calculated for convenience under conditions where the edge current contribution vanishes, but the value obtained will be the appropriate one for the sum of edge and bulk currents in a Energy eV
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