The nature of electronic states in a disordered chain with long-ranged hopping amplitudes

In this work we investigate the nature of the electronic states in a one-dimensional tight-binding model with on-site energetic disorder and long-ranged hopping amplitudes. These are assumed to follow a power-law decay behavior with distance in the form h(r)∝1/rα, with α>1. Direct numerical diagonalization, finite-size scaling and a spectral statistics analysis show that as α→1 the localization length exhibits an exponential growth as the upper band edge is approached. Strong finite-size corrections are present in this regime near the upper band edge with the one-electron states displaying a strong level repulsion even at large, although finite, chains.