Mass enhancement parameter in free-standing ultrathin Pb(111) films: The effect of spin-orbit coupling

The influence of spin-orbit interaction on the electron-phonon coupling strength at the Fermi level of thin lead films is investigated using first-principles calculations in the density functional perturbation formalism. The calculations both scalar relativistic and including spin-orbit coupling (SOC) have been carried out for free-standing Pb(111) films consisting of four to ten atomic layers. It is shown that the spin-orbit interaction produces a large enhancement of the electron-phonon coupling strength regardless of the film thickness. This partly reflects a strong SOC-induced softening of the film phonon spectra, and partly a SOC-mediated increase in electron-phonon coupling matrix elements. For thin films, quantum size effects result in pronounced oscillations of the average coupling constant with the number of layers, which become damped for thicker films. DOI: 10.1103/PhysRevB.87.085440