Coupling to real and virtual phonons in tunneling spectroscopy of superconductors

Fine structures in the tunneling spectra of superconductors have been widely used to identify fingerprints of the interaction responsible for Cooper pairing. Here, we show that for scanning tunneling microscopy (STM) of Pb, the inclusion of inelastic tunneling processes is essential for the proper interpretation of these fine structures. For STM the usual McMillan inversion algorithm of tunneling spectra must therefore be modified to include inelastic tunneling events, an insight that is crucial for the identification of the pairing glue in conventional and unconventional superconductors alike.