Fourier-transform scanning tunneling microscopy investigation of the energy versus wave vector dispersion of electrons at the Au(111) surface

We have investigated the contributions of surface-state electrons and bulk state electrons to the spatially oscillating local density of states (LDOS) of the Au(111) surface by scanning tunneling microscopy and spectroscopy at low temperatures. Based on the Fourier-transform images of LDOS maps obtained at various energies, we were able to determine the dispersion of the surface-state electrons in a broad range of energies, up to 3 eV. The energy versus wave vector dispersion relation was found to clearly deviate from the parabolic free-electron-like behavior at higher energies above 1 eV. Moreover, relying on two-dimensional Fourier-transform analysis, we develop an original approach to determine the dispersion behavior of bulk state electrons that are scattered at (sub)surface defects in the top atomic layers of the Au(111) surface. This ``additional set'' of electrons is found to exhibit a dispersion for the occupied states that is consistent with the calculated band structure of bulk Au and previous photoemission experiments. On the other hand, an anomalous bulk state dispersion behavior occurs in the empty state regime, where the wavelength of the spatial oscillations of the LDOS is observed to remain constant for the investigated energy range. This behavior is inconsistent with previous band-structure calculations and requires further theoretical investigation that takes into account the influence of inelastic electron scattering.