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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. © 2013 American Physical Society.We acknowledge financial support of the University of the Basque Country UPV/EHU (grant No. GIC07-IT-366-07), the Departamento de Educación del Gobierno Vasco, and the Spanish Ministerio de Ciencia e Innovación (Grant No. FIS2010-19609-C02-01).Peer Reviewe

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