Related papers: Anomalous mobility edges in one-dimensional quasip…
We introduce a two-dimensional generalisation of the quasiperiodic Aubry-Andr\'e model. Even though this model exhibits the same duality relation as the one-dimensional version, its localisation properties are found to be substantially more…
Mobility edges (ME), defined as critical energies that separate the extended states from the localized states, are a significant topic in quantum physics. In this paper, we demonstrate the existence of two exact new mobility edges for two…
Mobility edge transitions from localized to extended states have been observed in two and three dimensional systems, for which sound theoretical explanations have also been derived. One-dimensional lattice models have failed to predict…
A basis of Bloch waves, distorted locally by the random potential, is introduced for electrons in the Anderson model. Matrix elements of the Hamiltonian between these distorted waves are averages over infinite numbers of independent…
We investigate the effect of an additional modulation parameter $\delta$ on the mobility properties of quasiperiodic lattices described by a generalized Ganeshan-Pixley-Das Sarma model with two on site modulation parameters. For the case…
The mobility edges (MEs) that separate localized, multifractal and ergodic states in energy are a central concept in understanding Anderson localization. In this work we study the effect of several mutually commensurate quasiperiodic…
Localization in non-Hermitian quasicrystals can differ fundamentally from its Hermitian counterpart when non-reciprocity is spatially disordered. Here we study a one-dimensional non-Hermitian Aubry-Andr\'{e}-Harper chain with a Bernoulli…
In this work we analytically explain the origin of the mobility edge in the partially disordered random regular graphs of degree d, i.e., with a fraction $\beta$ of the sites being disordered, while the rest remain clean. It is shown that…
We study a one-dimensional system that includes both a commensurate off-diagonal modulation of the hopping amplitude and an incommensurate, slowly varying diagonal on-site modulation. By using asymptotic heuristic arguments, we identify…
A single-particle mobility edge (SPME) marks a critical energy separating extended from localized states in a quantum system. In one-dimensional systems with uncorrelated disorder, a SPME cannot exist, since all single-particle states…
We propose a solvable class of 1D quasiperiodic tight-binding models encompassing extended, localized, and critical phases, separated by nontrivial mobility edges. Limiting cases include the Aubry-Andr\'e model and the models of PRL 114,…
Quasiperiodic systems host exotic transport regimes that are distinct from those found in periodic or disordered lattices. In this work, we study quantum transport in the Aubry-Andr\'e-Harper lattice in a two-terminal setup coupled to…
We demonstrate the existence of generalized Aubry-Andr\'e self-duality in a class of non-Hermitian quasi-periodic lattices with complex potentials. From the self-duality relations, the analytical expression of mobility edges is derived.…
Periodically driven systems have a longstanding reputation for establishing rich topological phenomena beyond their static counterpart. In this work, we propose and investigate a periodically driven extended Su-Schrieffer-Heeger model with…
Whether the many-body mobility edges can exist in a one-dimensional interacting quantum system is a controversial problem, mainly hampered by the limited system sizes amenable to numerical simulations. We investigate the transition from…
We analyse the anomalous properties of specific electronic states in the Kronig-Penney model with weak compositional and structural disorder. Using the Hamiltonian map approach, we show that the localisation length of the electronic states…
We address edge states and rich localization regimes available in the one-dimensional (1D) dynamically modulated superlattices, both theoretically and numerically. In contrast to conventional lattices with straight waveguides, the…
We present analytical results on transport properties of many-mode waveguides with randomly stratified disorder having long-range correlations. To describe such systems, the theory of 1D transport recently developed for a correlated…
Within the framework of the Aubry-Andre model, one kind of self-dual quasiperiodic lattice, it is known that a sharp transition occurs from \emph{all} eigenstates being extended to \emph{all} being localized. The common perception for this…
Mobility edge, a critical energy separating localized and extended excitations, is a key concept for understanding quantum localization. Aubry-Andr\'{e} (AA) model, a paradigm for exploring quantum localization, does not naturally allow…