Predicting superconducting transition temperatures via the anisotropic Migdal-Eliashberg calculations with ab initio Coulomb interaction

We have developed an efficient framework for solving the anisotropic Migdal-Eliashberg equations by implementing the intermediate representation (IR) basis in the EPW code [1,2]. This approach drastically reduces the computational cost of Matsubara-frequency summations while preserving quantitative accuracy. By incorporating the ab initio screened Coulomb interaction obtained from the GW approximation, we treat electron-phonon and Coulomb interactions on an equal footing. For MgB₂, the calculated superconducting transition temperature shows excellent agreement with experiment, demonstrating the predictive capability of our method. We further apply the framework to MgB₂-type superconductors to explore the role of anisotropic Coulomb effects in shaping the superconducting multigap structure.

[1] H. Lee, S. Poncé, K. Bushick et al., npj Comput. Mater. 9, 156 (2023).

[2] H. Mori, T. Nomoto, R. Arita, and E. R. Margine, Phys. Rev. B. 110, 064505 (2024).