Surface imaging of inelastic Friedel oscillations

Impurities that are present on the surface of a metal often have internal degrees of freedom. Inelastic scattering due to impurities can be revealed by observing local features seen in the tunneling current with a scanning tunneling microscope (STM). We consider localized vibrational modes coupled to the electronic structure of a surface. We argue that vibrational modes of impurities produce Fermi momentum k(F) oscillations in second derivative of current with respect to voltage partial derivative I-2(r,V)/partial derivative V-2. These oscillations are similar to the well-known Friedel oscillations of screening charge on the surface. We propose to measure inelastic scattering generated by the presence of the vibrational modes with STM by imaging the partial derivative I-2/partial derivative V-2 oscillations on the metal surface.