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Inelastic tunneling spectroscopy of Pb islands on Cu(111) obtained byscanning tunneling microscopy below 1K provides a direct access to the localEliashberg function of the islands with high energy resolution. The Eliashbergfunction describes the electron-phonon interaction causing conventionalsuperconductivity. The measured Eliashberg function strongly depends on thelocal thickness of the Pb nanostructures and shows a sharp maximum when quantumwell states of the Pb islands come close to the Fermi energy. Ab initiocalculations reveal that this is related to enhanced electron-phonon couplingat these thicknesses.

Local measurement of the Eliashberg function of Pb islands: enhancement of electron-phonon coupling by quantum well states