Multifractality: generic property of eigenstates of 2D disordered metals.

TL;DR

This paper demonstrates that eigenstates of 2D disordered metals exhibit multifractality across all disorder levels, with non-universal amplitude distributions leading to complex spatial structures.

Contribution

It reveals the universal multifractal nature of eigenstates in 2D disordered metals and links it to supersymmetric sigma-model solutions.

Findings

Distribution of small amplitudes follows random matrix theory

Large amplitude decay is non-universal and slow

Inverse participation numbers show multifractality at all disorder levels

Abstract

The distribution function of local amplitudes of eigenstates of a two-dimensional disordered metal is calculated. Although the distribution of comparatively small amplitudes is governed by laws similar to those known from the random matrix theory, its decay at larger amplitudes is non-universal and much slower. This leads to the multifractal behavior of inverse participation numbers at any disorder. From the formal point of view, the multifractality originates from non-trivial saddle-point solutions of supersymmetric $\sigma$-model used in calculations.