Electron-phonon coupling and pairing mechanism in $\beta$--Bi${}_2$Pd centrosymmetric superconductor

We report first-principles calculations of the superconducting properties of $\beta$–Bi${}_2$Pd within the fully anisotropic Migdal-Eliashberg formalism. We find a single anisotropic superconducting gap of $s$–wave symmetry which varies in magnitude on the different regions of the Fermi surface. The calculated superconducting energy gap on the Fermi surface, the superconducting transition temperature, the specific heat, and the quasi-particle density of states are in good agreement with the corresponding experimental results and support the view that $\beta$–Bi${}_2$Pd is a phonon-mediated single anisotropic gap superconductor.