Two-strand ladder network variants: localization, multifractality, and quantum dynamics under an Aubry-Andr\'e-Harper kind of quasiperiodicity

TL;DR

This study explores how quasiperiodic Aubry-André-Harper modulation affects electronic localization, multifractality, and quantum dynamics in two variants of two-strand ladder networks, revealing unique spectral and dynamical behaviors.

Contribution

It introduces two ladder network variants under AAH modulation, demonstrating their distinct localization, multifractality, and quantum dynamical properties, especially in relation to an ultrathin graphene nanoribbon model.

Findings

Eigenstates become localized beyond a threshold modulation in the simple ladder.

The graphene nanoribbon variant retains extended states at the spectrum center.

Quantum dynamics show different MSD behavior depending on the network and modulation strength.

Abstract

In this paper we demonstrate, using a couple of variants of a two-strand ladder network that, a quasiperiodic Aubry-Andr\'e-Harper (AAH) modulation applied to the vertical strands, mimicking a deterministic distortion in the network, can give rise to certain exotic features in the electronic spectrum of such systems. While, for the simplest ladder network all the eigenstates become localized as the modulation strength crosses a threshold, for the second variant, modelling an ultrathin graphene nano-ribbon, the central part of the energy spectrum remains populated by extended wavefunctions. The multifractal character in the energy spectrum is observed for both these networks close to the critical values of the modulation. We substantiate our findings also by studying the quantum dynamics of a wave packet on such decorated lattices. Interestingly, while the mean square displacement (MSD) changes in the usual manner in a pure two-strand ladder network as the modulation strength varies, for the ultrathin graphene nanoribbon the temporal behaviour of the MSD remains unaltered only up to a strong modulation strength. This, we argue, is due to the extendedness of the wavefunction at the central part of the energy spectrum. Other measurements like the return probability, temporal autocorrelation function, the time dependence of the inverse participation ratio, and the information entropy are calculated for both networks with different modulation strengths and corroborate our analytical findings.