Quantifying many-body effects by high-resolution Fourier transform scanning tunneling spectroscopy

High-resolution Fourier transform scanning tunneling spectroscopy (FT-STS) is used to study many-body effects on the surface state of Ag(111). Our results reveal a kink in the otherwise parabolic band dispersion of the surface electrons and an increase in the quasiparticle lifetime near the Fermi energy ${E}_{f}$. The experimental data are accurately modeled with the $T$-matrix formalism for scattering from a single impurity, assuming that the surface electrons are dressed by the electron-electron and electron-phonon interactions. We confirm the latter as the interaction responsible for the deviations from bare dispersion. We further show how FT-STS can be used to simultaneously extract real and imaginary parts of the self-energy for both occupied and unoccupied states with a momentum and energy resolution competitive with angle-resolved photoemission spectroscopy. From our quantitative analysis of the data we extract a Debye energy of $\ensuremath{\hbar}{\ensuremath{\Omega}}_{D}=14\ifmmode\pm\else\textpm\fi{}1\text{ }\text{ }\mathrm{meV}$ and an electron-phonon coupling strength of $\ensuremath{\lambda}=0.13\ifmmode\pm\else\textpm\fi{}0.02$, consistent with previous results. This proof-of-principle measurement advances FT-STS as a method for probing many body effects, which give rise to a rich array of material properties.