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

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.