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-Andr\'{e}-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 critical points 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.

Thermoelectric Effect in a Fibonacci Chain with AAH Modulation: A Theoretical Study

“…In our calculation we set $$b=(1+\sqrt {5})/2$$, and this is most commonly used in literature. [ 36, 37 ]…”

“…In our calculation we set b = (1 + √ 5)∕2, and this is most commonly used in literature. [36,37] The contact electrodes are also described within a TB framework. The electrodes are assumed to be perfect, 1D and reflection less.…”

Helical Molecule as an Efficient Rectifier: Effects of Molecular Conformation and Transverse Electric Field

“…In order to have an asymmetric molecule between two contact electrodes, for current rectification operation, we apply an electric field perpendicular to the helix axis (see Figure 1). In presence of the electric field, site energies of the molecule become field dependent obeying a cosine relation, [44][45][46] analogous to the well known Aubry-André-Harper (AAH) [47][48][49][50][51][52][53][54][55] form. Because of this external electric field, the system becomes a correlated disordered one, exhibiting atypical fragmented and gapped energy spectrum, which might play a crucial role to get a favorable response.…”

Bias-induced circular current in a loop nanojunction with AAH modulation: Role of hopping dimerization

“…In condensed matter systems different kinds of disorder are taken into account. Among them, correlated disorder in the form of Aubry-André-Harper (AAH) models [19][20][21][22][23][24][25][26][27] nowadays draws significant attention due to its unique and diverse characteristic features, compared to usual random (uncorrelated) disordered lattices [28][29][30][31]. For a correlated disorder, the disorder profile is deterministic, viz., it is fully defined, whereas, for the uncorrelated case, the profile is not known and thus, unlike a correlated case, an averaging over a large number of different disordered configurations needs to be considered, which may weaken the response in some cases.…”