TUNNELING IN PRESENCE OF COUPLING TO OTHER MODES - APPLICATION TO SCANNING-TUNNELING-MICROSCOPY

Using path integral techniques, we investigate the problem of estimating the tunneling probability in the case where the tunneling particle is coupled to the medium through which it tunnels. We develop methods for estimating the tunneling probability in the cases where (1) the tunneling is elastically and the medium is at zero temperature and (2) the medium is at a finite temperature and the tunneling could happen inelastically. We point out that the second method makes clearer the basis for the approach of Persson and Baratoff [Phys. Rev. B 38, 9616 (1988)], in which they heuristically extended the method of Caldeira and Leggett [Phys. Rev. Lett. 46, 211 (1981)] to account for dynamical image effects in scanning tunneling microscopy. Our analysis, however, brings out a defect of their approach. It leads to an energy loss to the system of plasmons, even when there is no possibility of exciting plasmons, because the tunneling particle does not have enough energy to cause this. Therefore, for this problem, we suggest that one has to make use of a method which has the condition that the tunneling is elastically built into it. We demonstrate how this can be done and find that the dynamical effects are more important than pointed out by Persson and Baratoff. We have also investigated the tunneling of an electron through a liquid in between the electrode and the tip, a situation of great interest in the study of the electrochemical interface. It has been suggested that the solvent might play a dynamical role in the tunneling, leading to a lowering of the barrier height for tunneling. We find that the time spent by the electron inside the liquid is much shorter than the time needed for the orientational polarization of the liquid to respond. Consequently, the tunneling has to be thought of as occurring through a random distribution of stationary solvent molecules. The randomness leads to an enhancement of the tunneling probability, due to which the tunneling current increases with temperature. We have investigated the temperature dependence and found it to be rather weak. We conclude that coupling to the orientational polarization of the liquid cannot explain the large lowering of the barrier that has been observed in some experiments.