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

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