Spectral Correlations in Disordered Electronic Systems: Crossover from Metal to Insulator Regime

Abstract

We use the semiclassical approach combined with the scaling results or the diffusion coefficient to consider the two-level correlation function $R\left(\varepsilon \right)$ for a disordered electron system in the crossover region, characterized by the appearance of a macroscopic correlation or localization length, $\xi$, that diverges at the metal-insulator transition. We show new critical statistics, characterized by a nontrivial asymptotic behavior of $R\left(\varepsilon \right)$, to emerge on both sides of the transition at higher energies, and to expand to all energies larger than mean level spacing when $\xi$ exceeds the system size.