Our objective is to study resonant tunneling of an electron in the presence of inelastic scattering by optical phonons. Using a recently developed technique, based on exact mapping of a many-body problem onto a one-body problem, we compute transmission through a single site at finite temperatures. We also compute current through a single site at finite temperatures and an arbitrary strength of the potential drop over the tunneling region. Transmission vs incident electron energy at finite temperatures displays additional peaks due to phonon absorption processes. Current at a voltage bias smaller than the phonon frequency is dominated by elastic processes. We apply the method to an electron tunneling through the Aharonov-Bohm ring coupled to optical phonons. The elastic part of electron-phonon scattering does not affect the phase of the electron. Dephasing occurs only through inelastic processes.

• Received 4 August 1998

DOI:https://doi.org/10.1103/PhysRevB.59.13087