Academic literature on the topic 'Aubry-André-Harper model'

Abstract We investigate the general bounded corner states in a two-dimensional off-diagonal Aubry–André–Harper square lattice model supporting flat bands. We show that for certain values of the nearest-neighbor hopping amplitudes, triply degenerate zero-energy flat bands emerge in this lattice system. Moreover, the two-dimensional off-diagonal Aubry–André–Harper model splits into isolated fragments and hosts some general bounded corner states, and the absence of the energy gap results in that these general bounded corner states are susceptible to disorder. By adding intracellular next-nearest-neighbor hoppings, two flat bands with opposite energies split off from the original triply degenerate zero-energy flat bands and some robust general bounded corner states appear in real-space energy spectrum. Our work shows a way to obtain robust general bounded corner states in the two-dimensional off-diagonal Aubry–André–Harper model by the intracellular next-nearest-neighbor hoppings.

Ultracold atoms trapped in optical superlattices provide a simple platform for realizing the seminal Aubry–André–Harper (AAH) model. However, this model ignores the periodic modulations on the nearest-neighbor hoppings. We establish a generalized AAH model by which an optical superlattice system can be approximately described when V 1 ≫ V 2, with periodic modulations on both on-site energies and nearest-neighbor hoppings. This model supports much richer topological properties absent in the standard AAH model. Specifically, by calculating the Chern numbers and topological edge states, we show that the generalized AAH model possesses multifarious topological phases and topological phase transitions, unlike the standard AAH model supporting only a single topological phase. Our findings can uncover more opportunities for using optical superlattices to study topological and localization physics.

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.

In this work, we perform a numerical study of magnetoresistance in a one-dimensional quantum heterostructure, where the change in electrical resistance is measured between parallel and antiparallel configurations of magnetic layers. This layered structure also incorporates a non-magnetic spacer, subjected to quasi-periodic potentials, which is centrally clamped between two ferromagnetic layers. The efficiency of the magnetoresistance is further tuned by injecting unpolarized light on top of the two sided magnetic layers. Modulating the characteristic properties of different layers, the value of magnetoresistance can be enhanced significantly. The site energies of the spacer is modified through the well-known Aubry–André and Harper (AAH) potential, and the hopping parameter of magnetic layers is renormalized due to light irradiation. We describe the Hamiltonian of the layered structure within a tight-binding (TB) framework and investigate the transport properties through this nanojunction following Green’s function formalism. The Floquet–Bloch (FB) anstaz within the minimal coupling scheme is introduced to incorporate the effect of light irradiation in TB Hamiltonian. Several interesting features of magnetotransport properties are represented considering the interplay between cosine modulated site energies of the central region and the hopping integral of the magnetic regions that are subjected to light irradiation. Finally, the effect of temperature on magnetoresistance is also investigated to make the model more realistic and suitable for device designing. Our analysis is purely a numerical one, and it leads to some fundamental prescriptions of obtaining enhanced magnetoresistance in multilayered systems.

Starting with the experiment on Kondo insulator SmB6 , which shows 1/B-periodic oscillations despite the absence of gapless electronic excitations in bulk, the candidate insulators showing quantum oscillation (QO) are on the rise. But this is contrary to our conventional understanding that we need a Fermi surface to have QO. So an obvious question to ask is, ‘How can insulators show QO?’. If there is QO, then which physical quantities show QO, and what is the physical reason behind their origin? In the absence of a Fermi surface, what determines the frequency of these QO? In search of answers, we revisit recently proposed theories for this phenomenon, focusing on a minimal model of an insulator with a hybridization gap between two opposite-parity light and heavy mass bands with an inverted band structure. We show that there are characteristic differences between the QO frequencies in the magnetization and the low-energy density of states (LE-DOS) of these insulators, in marked contrast with metals where all observables exhibit oscillations at the same frequency. The temperature dependence of the amplitudes of the magnetization and DOS oscillations are also qualitatively different and show marked deviations from the Lifshitz-Kosevich form well-known in metals. The interplay of disorder and interactions in quantum systems can lead to several intriguing phenomena, amongst which many-body localization (MBL) has caught many physicists’ attention in recent times. In the second work, we investigate whether an MBL system undergoes a transition to a current-carrying non-equilibrium steady state under a drive and how the entanglement properties of the quantum states change across the transition. The drive is introduced by using a phenomenological non-Hermitian model. We also discuss the dynamics, entanglement growth, and long-time fate of a generic initial state under an appropriate time evolution of the system governed by the non-H ermitian Hamiltonian. Our study reveals rich entanglement structures of the eigenstates of the non-Hermitian Hamiltonian. We find the transition between current-carrying states with volume-law to area-law entanglement entropy as a function of disorder and the strength of the non-Hermitian term. In the third work, we take two 1D systems, namely the 1D Anderson model and Aubry-André-Harper model, that show the localization of single particle eigenstates depending on the strength of disorder and study it under a chemical potential drive. The drive is induced by connecting baths at different chemical potentials to the two edges of the system. We calculate the Green functions of the systems on the Keldysh contour that we use to calculate physical quantities like current and occupation of the non-equilibrium steady state. Our results can distinguish between the localized and delocalized phases in the non-interacting limit. In the presence of interaction, our systems can show MBL to a thermal phase transition. We end with a discussion on the possibility of probing this thermal to MBL phase boundary using dynamical mean field theory.