LEVEL CORRELATIONS DRIVEN BY WEAK LOCALIZATION IN 2-D SYSTEMS

TL;DR

This paper investigates how weak localization influences two-level correlations in 2D disordered systems, revealing sensitivity to magnetic effects while level number variance remains largely unaffected.

Contribution

It demonstrates that in 2D systems, two-level correlations are driven by weak localization effects, which are highly sensitive to magnetic and spin interactions, unlike level number fluctuations.

Findings

Two-level correlation function is determined by weak localization effects.

Correlation decreases with magnetic field or impurities, and changes sign with spin-orbit interaction.

Level number variance is almost unaffected by weak localization effects.

Abstract

We consider the two-level correlation function in two-dimensional disordered systems. In the non-ergodic diffusive regime, at energy $\epsilon>E_{c}$ ($E_{c}$ is the Thouless energy), it is shown to be completely determined by the weak localization effects, thus being extremely sensitive to time-reversal and spin symmetry breaking: it decreases drastically in the presence of magnetic field or magnetic impurities and changes its sign in the presence of a spin-orbit interaction. In contrast to this, the variance of the levels number fluctuations is shown to be almost unaffected by the weak localization effects.