Multifractality: Generic Property of Eigenstates of 2D Disordered Metals

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, in dimension d = 2, has a logarithmically normal asymptotic dependence. The inverse participation numbers calculated on the basis of the distribution function indicate a multifractal behaviour in different fundamental symmetry classes. Our calculation is based on the derivation of the non-trivial saddle-point of the reduced supersymmetric σ-model.