Application of Intermediate Representation basis in Migdal-Eliashberg calculations for low-T_c superconductors

Over the past few years, the anisotropic Migdal-Eliashberg formalism has been successfully used to compute the superconducting properties from low- to high-temperature superconductors. However, computing the superconducting gap function at very low temperatures is extremely difficult as a large number of sampling points are required to convergence the summation over the Matsubara frequency on the imaginary axis. To overcome this problem, we have recently implemented the intermediate Representation (IR) basis method [1] in the EPW code [2] which enables the reduction in the number of sampling points for the Matsubara frequency summation. This methodology also allows one to accurately evaluate the Coulomb retardation effects by taking into account in the Migdal-Eliashberg equations the contributions coming from the high energy bands. In this talk, I will show the performance of this approach in the case of representative low-temperature superconductors.

[1] M. Wallerberger, S. Badr, S. Hoshino et al., Software X 21 101266 (2023).

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