Computation of intrinsic spin Hall conductivities from first principles using maximally-localized Wannier functions

Abstract

We present a method to compute the intrinsic spin Hall conductivity from first principles using an interpolation scheme based on maximally-localized Wannier functions. After obtaining the relevant matrix elements among the ab initio Bloch states calculated on a coarse k-point mesh, we Fourier transform them to find the corresponding matrix elements between Wannier states. We then perform an inverse Fourier transform to interpolate the velocity and spin-current matrix elements onto a dense k-point mesh, and use them to evaluate the spin Hall conductivity as a Brillouin-zone integral. This strategy has a much lower computational cost than a direct ab initio calculation, without sacrificing the accuracy. We demonstrate that the spin Hall conductivities of platinum and doped gallium arsenide, computed with our interpolation scheme as a function of the Fermi energy, are in good agreement with those obtained in previous first-principles studies. We also discuss certain approximations that can be made, in the spirit of the tight-binding method, to simplify the calculation of the velocity and spin-current matrix elements in the Wannier representation.

13 pages, 6 figures

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• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Restoring the density-gradient expansion for exchange in solids and surfaces
• Generalized gradient approximation for solids and their surfaces
• Spectral and Fermi surface properties from Wannier interpolation
• Intrinsic spin Hall effect in monolayers of group-VI dichalcogenides: A first-principles study
• Giant Enhancement of Intrinsic Spin Hall Conductivity in $\beta$ Tungsten via Substitutional Doping

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• Wannier Function Perturbation Theory: Localized Representation and Interpolation of Wavefunction Perturbation
• Staggered spin Hall conductivity
• Converging tetrahedron method calculations for the nondissipative parts of spectral functions