Time-dependent partition-free approach in resonant tunneling systems

Abstract

An extended Keldysh formalism, well suited to properly take into account the initial correlations, is used in order to deal with the time-dependent current response of a resonant tunneling system. We use a partition-free approach by Cini in which the whole system is in equilibrium before an external bias is switched on. No fictitious partitions are used. Despite a more involved formulation, this partition-free approach has many appealing features being much closer to what is experimentally done. In particular, besides the steady-state responses one can also calculate physical dynamical responses. In the noninteracting case we clarify under what circumstances a steady-state current develops and compare our result with the one obtained in the partitioned scheme. We prove a theorem of asymptotic equivalence between the two schemes for arbitrary time-dependent disturbances. We also show that the steady-state current is independent of the history of the external perturbation (memory-loss theorem). In the so-called wide-band limit an analytic result for the time-dependent current is obtained. In the interacting case we work out the lesser Green function in terms of the self-energy and we recover a well-known result in the long-time limit. In order to overcome the complications arising from a self-energy which is nonlocal in time we propose an exact nonequilibrium Green-function approach based on time-dependent density-functional theory. The equations are no more difficult than an ordinary mean-field treatment. We show how the scattering-state scheme by Lang follows from our formulation. An exact formula for the steady-state current of an arbitrary interacting resonant tunneling system is obtained. As an example the time-dependent current response is calculated in the random-phase approximation.