Optical second-harmonic spectroscopy of Au(887) and Au(443) surfaces

Abstract

In order to investigate the electronic states of step sites on Au surfaces, we have observed the reflected optical second-harmonic (SH) intensity from Au(887) and Au(443) surfaces in ultrahigh vacuum with a normal incident excitation light beam, as a function of the photon energy and the incident and SH light polarizations. The second-order surface nonlinear susceptibility elements observed in this measurement configuration were ${\ensuremath{\chi}}_{xxx}^{(2)}$, ${\ensuremath{\chi}}_{xyy}^{(2)}$, and ${\ensuremath{\chi}}_{yxy}^{(2)}$, where $x$ and $y$ are defined as the $[11\overline{2}]$ and $[\overline{1}10]$ directions, respectively. The step edges lie in the $y$ direction. The ratios of the nonlinear susceptibility elements $|{\ensuremath{\chi}}_{xyy}^{(2)}|/|{\ensuremath{\chi}}_{xxx}^{(2)}|$ and $|{\ensuremath{\chi}}_{yxy}^{(2)}|/|{\ensuremath{\chi}}_{xxx}^{(2)}|$ were different on the two surfaces in the photon energy range from $2\ensuremath{\hbar}\ensuremath{\omega}=2.5$ to 3.3 eV. The deviation of the SH response from that of an ideal $3m$ symmetric Au(111) surface was found to be larger for the Au(443) surface than for the Au(887) surface. This deviation is attributed to the atomic steps created by the miscut of the samples. In order to analyze the observed SH spectra, we calculated the electronic states of a Au(554) slab using a density-functional theory. We found that the low-energy onset of the SH intensity caused by the steps can be qualitatively interpreted by referring to the calculated partial density of the $d$-electronic states of the step and terrace atoms on the Au slab.