TIME-DEPENDENT TRANSPORT IN INTERACTING AND NONINTERACTING RESONANT-TUNNELING SYSTEMS

We consider a mesoscopic region coupled to two leads under the influen ce of external time-dependent voltages. The time dependence is coupled to source and drain contacts, the gates controlling the tunnel-barrie r heights, or to the gates that define the mesoscopic region. We deriv e, with the Keldysh nonequilibrium-Green-function technique, a formal expression for the fully nonlinear, time-dependent current through the system. The analysis admits arbitrary interactions in the mesoscopic region, but the leads are treated as noninteracting. For proportionate coupling to the leads, the time-averaged current is simply the integr al between the chemical potentials of the time-averaged density of sta tes, weighted by the coupling to the leads, in close analogy to the ti me-independent result of Meir and Wingreen [Phys. Rev. Lett. 68, 2512 (1992)]. Analytical and numerical results for the exactly solvable non interacting resonant-tunneling system are presented. Due to the cohere nce between the leads and the resonant site, the current does not foll ow the driving signal adiabatically: a ''ringing'' current is found as a response to a voltage pulse, and a complex time dependence results in the case of harmonic driving voltages. We also establish a connecti on to recent linear-response calculations, and to earlier studies of e lectron-phonon scattering effects in resonant tunneling.