Bi-stability in the Nonequilibrium Anderson-Holstein Model: Developing Tools to Study Fundamental Physics of Electron Transfer in Nonequilibrium Quantum Impurity Models

Recent developments in the field of molecular electronics have exhibited multiple steady-state solutions in nonequilibrium impurity models with strong electron-phonon (e-ph) interactions. These results have ignored the effect of electron-electron (e-e) couplings, expected to play an important role in the steady-state characteristics. To understand the effect of e-e interactions in transport and its effect on the uniqueness of the steady-state, we have developed tools to study the dynamics of a nonequilibrium quantum impurity system with e-ph and e-e interactions described by the Anderson-Holstein model. The first is a numerically exact scheme based on the generalized quantum master equation for the reduced density matrix combined with an impurity solver. We have extended the formalism to obtain the memory kernel for an arbitrary model. We have also developed an approximate scheme based on the nonequilibrium Green's function (NEGF) formalism and the equation of motion approach. Unlike previous approximations within the NEGF formalism, this approach is adequate for weak to strong e-e couplings and reduces to the self-consistent Born approximation for vanishing e-e coupling.