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Photoconductivity in Ac-driven lateral superlattice in the presence of a magnetic field

In this work we present a model for the photoconductivity of two-dimensional electron system in a perpendicular homogeneous magnetic field, a weak lateral superlattice, and exposed to millimeter irradiation. The model includes the microwave and Landau contributions in a non-perturbative exact way, the periodic potential is treated perturbatively. The Landau-Floquet states provide a convenient base with respect to which the lattice potential becomes time-dependent, inducing transitions between the Landau-Floquet levels. Based on this formalism, we provide a Kubo-like formula that takes into account the oscillatory Floquet structure of the problem. The total conductivity exhibits strong oscillations, determined by $ε= ω/ ω_c$ with $ω$ the radiation frequency and $ω_c$ the cyclotron frequency. The oscillations follow a pattern with minima centered at $ω/ω_c =j + {1/2} (l-1) + δ$, and maxima centered at $ω/ω_c =j + {1/2} (l-1) - δ$, where $j=1,2,3.......$, $δ$ is a constant phase shift and $l$ is the dominant multipole contribution. Negative conductance states develop as the electron mobility and the intensity of the microwave power are increased. It is proposed that, depending on the geometry, negative conductance sates or negative resistance states may be observed in lateral superlattices fabricated in $GaAs/AlGa As$ heterostructures.