Efficient spin Hall conductivity calculations without wannierization using local Berry phase approach

Commonly used  first-principles calculations of spin Hall conductivity (SHC) rely heavily on methods such as the Kubo formula and Maximally Localized Wannier Functions (MLWF), which become computationally prohibitive for large-scale studies. The wannierization process, in particular, requires careful treatment of unoccupied states and poses significant computational bottlenecks for high-throughput materials screening. We develop an efficient computational approach that bypasses the wannierization step entirely by employing local Berry phase techniques. Our method adapts Prodan's spin Chern number formulation [1] and integrates it with local Berry phase methodologies previously established for anomalous Hall conductivity calculations [2,3]. This wannierization-free approach enables direct computation of intrinsic SHC with substantially reduced computational overhead, making high-throughput studies feasible. We demonstrate the method's accuracy and efficiency through calculations on Pt and Au systems, achieving excellent agreement with previous theoretical results [4]. The implementation details and computational performance advantages of this wannierization-free approach will be presented.

[1] E. Prodan, Phys. Rev. B 80, 125327 (2009).

[2] T. Fukui, Y. Hatsugai, H. Suzuki, J. Phys. Soc. Jpn. 74, 1674 (2005).

[3] H. Sawahata, N. Yamaguchi, S. Minami, F. Ishii, Phys. Rev. B 107, 024404 (2023).

[4] G. Y. Guo, S. Murakami, T.-W. Chen, N. Nagaosa, Phys. Rev. Lett. 100, 096401 (2008).