Dynamical effective potentials in electron tunneling: Path-integral study

Dynamical effective potential felt by an electron tunneling in the planar metal-insulator-metal system is considered. The tunneling electron coupled to the surface-plasmon modes is described within Feynman’s path-integral formalism. Self-consistent numerical results for the effective potentials, tunneling times, and tunneling rates are presented. The classical image potential is obtained in the limit of long tunneling times. It is shown that in cases when the traversal time T becomes comparable to the plasmon, i.e., screening time ${\mathrm{\omega }}_{\mathit{s}}^{\mathrm{-}1}$, considerable departure from the classical image potential appears.