Fractal dimensionality of wave functions at the mobility edge: Quantum fractal in the Landau levels.

Abstract

Wave functions at the critical energy separating localized and extended states in disordered electron systems are shown to have fractal structure. We present results for the fractal dimensionality numerically calculated for a two-dimensional system with Landau quantization in strong magnetic fields together with a turbulent structure when the phase of the wave function is considered. Implications for transport properties are discussed.