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 which is constructed from a quasi-one-dimensional chain with 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 combined with the finite-size scaling analysis. 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 $I_{p_c}(s)\propto \exp (-A_c{s}^{\alpha })$, with $A_c\simeq 1.50$ and $\alpha \simeq 1.0$. This reveals the possible existence of metal-insulator transition in materials with chains as the backbones.

12 pages, 4 figures

References in corpus (1)

• Spreading and shortest paths in systems with sparse long-range connections

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