Effects of Virtual Electron Transitions between Image States on Electron Dynamics at Metal Surfaces

Abstract

Electron dynamics in image states of metals are investigated by taking notice of the effects of virtual electron transitions between different image states, which are represented by off-diagonal elements of self-energy functions. Analytical formulae of both the diagonal and off-diagonal elements of the Green functions, which represent the electron densities of the image states and the probability of electron propagation between the image states, respectively, are obtained from Dyson's equations. The virtual electron transitions cause energy repulsion between the image states, and hence the decay of the electron densities can be accelerated or decelerated as compared with the decay rates given by the imaginary parts of the self-energies of the image states. Moreover, the virtual electron transitions can account for quantum beats exhibited in both the diagonal and off-diagonal elements of the Green functions. By numerical analysis, we show how the above effects are enhanced as the lifetimes of the image sta...