On the theory of difference frequency generation and light rectification in the scanning tunnelling microscope

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Abstract
The problem of currents induced in the scanning tunnelling microscope due to incident laser radiation is analysed. The authors uses a light-binding description of the microscope tunnelling junction, and the interaction with the laser field is taken into account by an effective time-dependent coupling between tip and sample. The currents generated at frequencies that are linear combinations of the incident frequencies are then obtained with the help of a nonequilibrium Green's function formalism. Particular attention is paid to the rectification and difference frequency generation effects. In this work they extend previous results for the rectified current to the case where a direct bias is applied in addition to the laser field. It is shown that in the limit of very low frequencies the dynamical response may be deduced from the static characteristic curve. In order to compare with recent experimental data, they perform model calculations for a graphite sample and study the induced photocurrent as a function of bias voltage, tip-sample distance and photon energy. The limitations of the adiabatic approximation are discussed. Finally, they present results for the rectified current in the presence of an adsorbed molecule with a characteristic vibrational mode. The contribution from inelastic processes is obtained to the lowest order in the electron-phonon coupling. It is shown that the onset of inelastic tunnelling should be reflected as a singularity in the rectified current as a function of both bias voltage and photon energy.