Resonant states and wavepacket super-diffusion in intra-chain correlated ladders with diluted disorder

In this work, we study a tight-binding Hamiltonian model system of a binary correlated ladder with diluted disorder. We introduce intra-chain correlations between the on-site potentials by imposing that ϵ(i, s) = - ϵ(i, - s) where s = ± 1 indexes the two ladder chains. Further, we consider each ladder chain as composed of inter-penetrating ordered and random sub-chains. We show that the presence of a random on-site distribution in one of the inter-penetrating chains leads to Anderson localization except at a specific symmetric pair of energy eigenmodes. Further, by integrating the time-dependent Schroedinger equation, we follow the time-evolution of an initially localized one-electron wavepacket. We report that the remaining delocalized resonant modes are responsible for a super-diffusive spread of the wavepacket dispersion while the wavepacket participation function remains finite. A scaling analysis of the wavepacket distribution shows that it obeys a universal scaling form with the development of a power-law tail followed by a super-diffusively evolving cutoff. We obtain three exponents characterizing this super-diffusive dynamics and show that they satisfy a simple scaling relation.