Exploration of the memory effect on the photon-assisted tunneling via a single quantum dot: A generalized Floquet theoretical approach

The generalized Floquet approach is developed to study memory effect on electron transport phenomena through a periodically driven single quantum dot in an electrode-multi-level dot-electrode nanoscale quantum device. The memory effect is treated using a multi-function Lorentzian spectral density (LSD) model that mimics the spectral density of each electrode in terms of multiple Lorentzian functions. For the symmetric single-function LSD model involving a single-level dot, the underlying single-particle propagator is shown to be related to a 2 x 2 effective time-dependent Hamiltonian that includes both the periodic external field and the electrode memory effect. By invoking the generalized Van Vleck (GVV) nearly degenerate perturbation theory, an analytical Tien-Gordon-like expression is derived for arbitrary order multi- photon resonance d.c. tunneling current. Numerically converged simulations and the GVV analytical results are in good agreement, revealing the origin of multi- photon coherent destruction of tunneling and accounting for the suppression of the staircase jumps of d.c. current due to the memory effect. Specially, a novel blockade phenomenon is observed, showing distinctive oscillations in the field-induced current in the large bias voltage limit.