Delocalization and scaling properties of low-dimensional quasiperiodic systems

TL;DR

This study investigates how coupling Aubry-Andre9 chains and including next-nearest-neighbor hopping influence localization and transport in low-dimensional quasiperiodic systems, revealing a tunable metal-insulator transition and unique scaling behavior.

Contribution

It introduces a comprehensive analysis of localization and scaling in coupled quasiperiodic systems with NNN hopping, highlighting effects of dimensionality and coupling parameters.

Findings

Metal-insulator transition driven by NNN hopping and dimensionality.

Transport properties follow a single-parameter scaling function.

Scaling function can reach the value 1, differing from disordered systems.

Abstract

In this paper, we explore the localization transition and the scaling properties of both quasi-one-dimensional and two-dimensional quasiperiodic systems, which are constituted from coupling several Aubry-Andr\'{e} (AA) chains along the transverse direction, in the presence of next-nearest-neighbor (NNN) hopping. The localization length, two-terminal conductance, and participation ratio are calculated within the tight-binding Hamiltonian. Our results reveal that a metal-insulator transition could be driven in these systems not only by changing the NNN hopping integral but also by the dimensionality effects. These results are general and hold by coupling distinct AA chains with various model parameters. Furthermore, we show from finite-size scaling that the transport properties of the two-dimensional quasiperiodic system can be described by a single parameter and the scaling function can reach the value 1, contrary to the scaling theory of localization of disordered systems. The underlying physical mechanism is discussed.