Localization phenomena and electronic transport in irradiated Aubry–André–Harper systems

Abstract

The role of light irradiation on electronic localization is critically investigated for the first time in a tight-binding lattice where site energies are modulated in the cosine form following the Aubry–André–Harper (AAH) model. The critical point of transition from delocalized-to-localized phase can be monitored selectively by regulating the light parameters that is extremely useful to have controlled electron transmission across the system. Starting with a strictly one-dimensional (1D) AAH chain, we extend our analysis considering a two-stranded ladder model which brings peculiar signatures in presence of irradiation. Unlike 1D system, AAH ladder exhibits a mixed phase (MP) zone where both extended and localized energy eigenstates co-exist. This is the fundamental requirement to have mobility edge in energy band spectrum. A mathematical description is given for decoupling the irradiated ladder into two effective 1D AAH chains. The underlying mechanism of getting a MP zone relies on the availability of two distinct critical points (CPs) of the decoupled chains, in presence of second-neighbor hopping between the two strands. Using a minimal coupling scheme the effect of light irradiation is incorporated following the Floquet–Bloch ansatz. The localization behaviors of different energy eigenstates are studied by calculating inverse participation ratio, and, are further explained in a more compact way by calculating two-terminal transmission probabilities together with average density of states. Finally, the decoupling procedure is extended for a more general multi-stranded AAH ladders where multiple CPs and thus multiple mobility edges are found. Our analysis may provide a new route of engineering localization properties in similar kind of other fascinating quasiperiodic systems.