Imaging of the Cu(111) surface state in scanning tunneling microscopy.

Abstract

Scanning-tunneling-microscopy (STM) data for the Cu(111) surface have been calculated theoretically, based on Bardeen's approximation and a layer-Korringa-Kohn-Rostoker-like approach to describe the sample. The onset of the surface state gives rise to a steplike increase in the conductivity in very good agreement with recent experimental data, which demonstrates the ability of Bardeen's approximation to describe surface states in spite of its failure regarding surface states in one dimension. The STM conductivity can be approximated in terms of the local density of states (LDOS) of the sample at the voltage V, plus a background term which involves states at all energies, and which is frequently neglected in the interpretation of STM images. In the presence of a step edge, the LDOS of the Cu(111) surface state displays standing wave oscillations. In this case, the background term shows oscillations of the Friedel type which drop as ${\mathit{J}}_{1}$(2kx)/kx for a two-dimensional electron gas. This has important implications for determining the surface state dispersion relation and for the interpretation of standing wave patterns in terms of the LDOS.