A MATRIX-METHOD FOR TREATING THE COUPLING BETWEEN AN ELECTRON AND A SURFACE-PLASMON - A DYNAMICAL IMAGE POTENTIAL IN MODEL TUNNELING JUNCTIONS

In this paper, we present a method for treating in a general manner th e coupling between a single electron and boson fields represented by h armonic oscillators. The (general) solution of the corresponding many- body Schrodinger equation in real space is obtained by means of a prop agation matrix method without using any ansatz for the many-body wave functions. We study the particular case of coupling between electrons and surface plasmons in tunnelling junctions. The electron is coupled inside the tunnelling barrier to a few surface plasmon modes. We prese nt results for the dynamical effective potential felt by an electron t unnelling in model one-dimensional tunnelling junctions as well as for the various traversal times. As expected, significant differences fro m the corresponding static image potential are obtained when the tunne lling times tau are shorter than the characteristic response time of t he surface charge (i.e. the inverse of the surface plasmon frequency o mega). Examples of such dynamical effective potentials are given for v arious typical tunnelling conditions in the presence and absence of an applied bias voltage. The behaviour of the potential is studied versu s the tunnelling times tau. It is also shown that the apparent barrier height that can be deduced from experiments does not always contain u seful information about the dynamics of the coupled electron-plasmon s ystem. On the other hand, the absolute values of the current in the tu nnelling junctions are strongly dependent on the characteristic parame ters of this dynamics.