SPECTRAL CORRELATIONS IN DISORDERED ELECTRONIC SYSTEMS: CROSSOVER FROM METAL TO INSULATOR REGIME

TL;DR

This paper investigates the spectral correlations in disordered electronic systems near the metal-insulator transition, revealing new critical statistics and crossover behaviors influenced by the localization length.

Contribution

It introduces a semiclassical approach combined with scaling results to analyze the two-level correlation function across the metal-insulator transition, highlighting new critical spectral statistics.

Findings

Identification of new critical spectral statistics near transition

Demonstration of crossover behavior in spectral correlations

Expansion of critical statistics to all energies above mean level spacing

Abstract

We use the semiclassical approach combined with the scaling results for the diffusion coefficient to consider the two-level correlation function $R(\varepsilon)$ 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 $R(\varepsilon)$, 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.