Spectral Correlations from the Metal to the Mobility Edge

D. Braun; G. Montambaux

doi:10.1103/PhysRevB.52.13903

paper

Spectral Correlations from the Metal to the Mobility Edge

arXiv:cond-mat/9506063 · doi:10.1103/PhysRevB.52.13903

Abstract

We have studied numerically the spectral correlations in a metallic phase and at the metal-insulator transition. We have calculated directly the two-point correlation function of the density of states $R (s, s^{'})$ . In the metallic phase, it is well described by the Random Matrix Theory (RMT). For the first time, we also find numerically the diffusive corrections for the number variance $< δ n^{2} (s) >$ predicted by Al'tshuler and Shklovski\uı. At the transition, at small energy scales, $R (s - s^{'})$ starts linearly, with a slope larger than in a metal. At large separations $∣ s - s^{'} ∣ ≫ 1$ , it is found to decrease as a power law $R (s, s^{'}) \sim - c /∣ s - s^{'} ∣^{2 - γ}$ with $c \sim 0.041$ and $γ \sim 0.83$ , in good agreement with recent microscopic predictions. At the transition, we have also calculated the form factor $K ~ (t)$ , Fourier transform of $R (s - s^{'})$ . At large $s$ , the number variance contains two terms $< δ n^{2} (s) >= B < n >^{γ} + 2 π K ~ (0) < n > w h er e$ \tilde{K}(0) $i s t h e l imi t o f t h e f or m f a c t or f or$ t \to 0$.

7 RevTex-pages, 10 figures. Submitted to PRB

Spectral Correlations from the Metal to the Mobility Edge

Abstract

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