Quasilocalized States in Disordered Metals and Nonanalyticity of the Level Curvature Distribution Function

Abstract

It is shown that the quasilocalized states in weakly disordered systems can lead to the nonanalytical distribution of level curvatures. In 2D systems the distribution function $P(K)$ has a branching point at $K\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$, while in quasi-1D systems the nonanalyticity is very weak and in 3D metals it is absent. It was shown earlier within the similar saddle-point method that for weak disorder the wave functions possess a (weak) multifractality only in 2D systems. This allows us to conjecture that the branching in $P(K)$ at $K\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ is a generic feature of all critical eigenstates with multifractal statistics. A relationship between the branching power and the fractal dimensionality ${D}_{2}$ is suggested.