The energy gap Delta of superconducting Pb islands grown on Si(111) was probed in situ between 5 and 60 monolayers by low-temperature scanning tunneling spectroscopy. Delta was found to decrease from its bulk value as a function of inverse island thickness. Corresponding T_{c} values, estimated using bulk gap-to-T_{c} ratio, are in quantitative agreement with ex situ magnetic susceptibility measurements, however, in strong contrast to previous scanning probe results. Layer-dependent ab initio density functional calculations for freestanding Pb films show that the electron-phonon coupling constant, determining T_{c}, decreases with diminishing film thickness.

Over the recent years, electronic surface states have been used for a detailed spectroscopic study of the electron–phonon (e–ph) interaction, both experimentally and theoretically. This review discusses the basic physics of e–ph coupling and how information can be obtained from angle-resolved photoemission experiments and first principles calculations. Several recent results for clean and adsorbate-covered surfaces, quantum wells and free-standing monolayers are also discussed.

The influence of spin-orbit coupling ͑SOC͒ on the electron-phonon interaction and on the pairing strength is investigated for Pb and Tl within density-functional theory. For Pb we find that SOC increases the coupling constant by 44%, solving the longstanding puzzle of too small values obtained consistently in previous first-principles calculations. The origin of the SOC-induced enhancement of lies both in a softening of the phonon spectrum and in an increase in the electron-phonon coupling matrix elements. In contrast, for the neighboring element Tl only weak effects of SOC on the phonon spectrum and the electron-phonon interaction is obtained, leading to an overall reduction in by 12%. In both cases, the inclusion of SOC improves the agreement with experiment.