| An approach to non-equilibrium sequential quantum charge transport through a quantum dot by means of the reduced density matrix and master equation formalism, has been used to obtain the population of states of the system in both the Markovian and non-Markovian regimes. In both regimes, it is found that the anisotropy of the tunneling rates (into and out of the dot) significantly influences the population of states. Specifically, an intrinsic asymmetry due to spatial localization of the wavefunction inside the dot, and an extrinsic asymmetry, due to the difference in tunneling barrier widths between source and drain reservoirs, strongly affect the occupation probability distribution of the dot. In the symmetric case, under both the Markovian and non-Markovian derivations, we find that the barrier widths significantly affect the time necessary to reach the steady state. However, the transient behavior is markedly different under both derivations: under the Markov approximation the decay is a monotonic exponential, while in the non-Markovian derivation is oscillatory with an exponential envelope. The analysis in the Markovian case is further extended to obtain a regime where Negative Differential Conductance (NDC) arises, characterized by an interplay between the extrinsic and intrinsic asymmetries. Expressions for the currents characterizing NDC are analytically obtained in terms of the anisotropy parameters. We also investigate the limits where the steady state current through the dot may be suppressed through ground state channels but not through excited states channels, as well as where the current may be suppressed altogether even when available channels reside inside the transport window (these results appear to be in agreement with a number of transport experiments showing NDC signatures in 2DEG heterostructures). |
