  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.
