RESONANT-TUNNELING WITH AN ELECTRON-PHONON INTERACTION

Using nonequilibrium quantum-statistical mechanics, we study both the equilibrium behavior and the nonlinear transport in a one-dimensional model of resonant tunneling with an electron-phonon interaction at zer o temperature. There are several unique features of our work: (1) We d emonstrate the importance of the Hartree-like electron-phonon self-ene rgy diagram in this problem lacking translational invariance. (2) We i dentify a new perturbation parameter in the study of the equilibrium p olaron shift. (3) We provide a thorough understanding of when the noni nteracting current is a poor predictor of the interacting current-volt age characteristic, which we calculate and explain in detail. Our calc ulation treats a weak electron-phonon interaction at zero temperature perturbatively in the dimensionless coupling constant, g, to lowest se lf-consistent order. Because the system is not translational invariant , we must retain both a Fock-like and a Hartree-like diagram. Dependin g of the filling condition of the resonant level, the model can be in two qualitatively different regimes: when the resonant level is empty (occupied), the polaron shift of the level with the interaction is -g Omega (-3g Omega), where Omega is the frequency of the phonon. The cro ssover occurs on a scale set by the noninteracting escape rate, Gamma, and we find that g Omega/Gamma is an additional perturbation paramete r in the study of the equilibrium polaron shift. We furthermore evalua te typical nonlinear current-voltage characteristics. When the Fermi s eas of the leads are much thicker than Omega (and Gamma), the interact ion affects the total current only near the onset of the large resonan t current and in the valley region. However, the interaction modifies the I-V characteristics at all biases when the Fermi seas are shallow. To interpret our results we separate the current densities per unit e nergy for the left and right leads into elastic and inelastic contribu tions. We finally show that the qualitative behavior of the inelastic current contributions does not depend on the filling condition of the resonant level for a system with thick Fermi seas at a typical bias wh ere a large current flows. (C) 1994 Academic Press, Inc.