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\textit{Ab-initio} calculation of intrinsic spin Hall conductivity (SHC)generally requires a strict convergence criterion and a dense k-point mesh tosample the Brillouin zone, making its convergence challenging andtime-consuming. Here we present a scheme for efficiently and accuratelycalculating SHC based on maximally localized Wannier function (MLWF). Thequantities needed by the Kubo formula of SHC are derived in the space of MLWFand it is shown that only the Hamiltonian, the overlap and the spin operatormatrices are required from the initial \textit{ab-initio} calculation. Thecomputation of these matrices and the interpolation of Kubo formula on a densek-point mesh can be easily achieved. We validate our results by prototypicalcalculations on fcc Pt and GaAs, which demonstrate that the Wannierinterpolation approach is of high accuracy and efficiency. Calculations of$\alpha$-Ta and $\beta$-Ta show that SHC of $\beta$-Ta is 2.7 times of$\alpha$-Ta, while both have the opposite sign relative to fcc Pt and are anorder of magnitude smaller than Pt. The calculated spin Hall angle of $-0.156$,is quite consistent with previous experiment on $\beta$-Ta, further suggestingintrinsic contribution may dominate in $\beta$-Ta. Our approach couldfacilitate large-scale SHC calculations, and may benefit the discovery ofmaterials with high intrinsic SHC.

Calculation of intrinsic spin Hall conductivity by Wannier interpolation