Localization-delocalization transition of electron states in a disordered quantum small-world network

Abstract

We investigate the localization behavior of electrons in a random lattice that is constructed from a quasi-one-dimensional chain with a large coordinate number Z and rewired bonds, resembling the small-world network proposed recently, but with site-energy disorder and quantum links instead of classical ones. The random rewiring of bonds in the chain with large Z enhances both the topological disorder and the effective dimensionality. From the competition between disorder and dimensionality enhancement a transition from localization to delocalization is found by using the level statistics method. The critical value of the rewiring rate for this transition is determined numerically. We obtain a universal critical integrated distribution of level spacing s in the form ${I}_{{p}_{c}}(s)\ensuremath{\propto}\mathrm{exp}(\ensuremath{-}{A}_{c}{s}^{\ensuremath{\alpha}}),$ with ${A}_{c}\ensuremath{\simeq}1.50$ and $\ensuremath{\alpha}\ensuremath{\simeq}1.0.$ This reveals the possible existence of metal-insulator transition in materials with chains as the backbones.