Anomalously localised electronic states in three-dimensional disordered systems

We study the Anderson model of localisation at the metal-insulator transition in the band centre of three-dimensional disordered samples. For the critical disorder we determine a large number of wave functions of the model and study the distribution of the wave function amplitudes. Deviations from scaling of multifractal correlation functions allow us to discriminate anomalously localised states from the usual critical states. The thus identified anomalously localised states lead to deviations of the critical properties and should be eliminated from the ensemble average for a characterisation of criticality.