Localization, transport and edge states in a two-strand ladder network in an aperiodically staggered magnetic field

TL;DR

This paper explores the spectral, transport, and topological properties of a two-leg ladder network under an aperiodic magnetic field, revealing multifractal energy spectra, mobility edges, and robust edge modes with potential experimental relevance.

Contribution

It introduces a detailed numerical analysis of a ladder network with an Aubry-André-Harper magnetic flux profile, uncovering multifractal spectra, mobility edges, and topological edge states.

Findings

Multifractal energy landscape observed.

Presence of mobility edges indicating critical and extended phases.

Robust topological edge modes against perturbations.

Abstract

We investigate the spectral and transport properties of a two-arm tight-binding ladder perturbed by an external magnetic field following an Aubry-Andr\'e-Harper profile. The varying magnetic flux trapped in consecutive ladder-cells simulates an axial twist that enables us, in principle, to probe a wide variety of systems ranging from a ribbon Hofstadter geometry to helical DNA chains. We perform an in-depth numerical analysis, using a direct diagonalization of the lattice Hamiltonian to study the electronic spectra and transport properties of the model. We show that such a geometry creates a self-similar multifractal pattern in the energy landscape. The spectral properties are analyzed using the local density of states and a Green's function formalism is employed to obtain the two-terminal transmission probability. With the standard multifractal analysis and the evaluation of inverse participation ratio we show that, the system hosts both critical and extended phase for a slowly varying aperiodic sequence of flux indicating a possible mobility edge. Finally, we report signatures of topological edge modes that are found to be robust against a correlated perturbation given to the nearest neighbor hopping integrals. Our results can be of importance in experiments involving ladder-like quantum networks, realized with cold atoms in an optical trap setup.