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We investigate the spectral and transport properties of a two-armtight-binding ladder perturbed by an external magnetic field following anAubry-Andr\'e-Harper profile. The varying magnetic flux trapped in consecutiveladder-cells simulates an axial twist that enables us, in principle, to probe awide variety of systems ranging from a ribbon Hofstadter geometry to helicalDNA chains. We perform an in-depth numerical analysis, using a directdiagonalization of the lattice Hamiltonian to study the electronic spectra andtransport properties of the model. We show that such a geometry creates aself-similar multifractal pattern in the energy landscape. The spectralproperties are analyzed using the local density of states and a Green'sfunction formalism is employed to obtain the two-terminal transmissionprobability. With the standard multifractal analysis and the evaluation ofinverse participation ratio we show that, the system hosts both critical andextended phase for a slowly varying aperiodic sequence of flux indicating apossible mobility edge. Finally, we report signatures of topological edge modesthat are found to be robust against a correlated perturbation given to thenearest neighbor hopping integrals. Our results can be of importance inexperiments involving ladder-like quantum networks, realized with cold atoms inan optical trap setup.

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