First-principles calculation of the electron-phonon coupling in ultrathin Pb superconductors: Suppression of the transition temperature by surface phonons

We present a first-principles calculation of the electron-phonon coupling for thin layered lead systems. Using our Wannier-Fourier approach we show that the superconductivity in these systems is accounted for by traditional isotropic Migdal-Eliasberg theory through phonon-induced electron pairing. It is found that the transition temperature of Pb is suppressed by the presence of surface phonons which have been stiffened by an increased electronic spring constant. Superconductivity persists in ultrathin layered Pb despite the suppression from a decreased electronic density of states and weakened coupling to surface phonons.