Anistrotropic two-gap superconductivity and electron-phonon coupling in 2H-NbS$_2$

We investigate from first principles the nature of the superconducting state of 2$H$-NbS$_2$ using the fully anisotropic Migdal-Eliashberg theory, including Coulomb interactions. In agreement with experiment we find two superconducting gaps, which we map onto the Fermi surface and analyse in terms of the electronic orbital character. In addition, we investigate the electron-phonon interaction underlying the superconducting pairing and compare it to similar transition-metal dicalchogenides.