Multifractality of wave functions and wave packets at the metal-insulator transition in the Anderson model of localization

The spatial behaviour of electronic wave functions at the metal-insulator transition in disordered systems is investigated with respect to the multifractal properties. The singularity spectrum and the generalized dimensions at the critical disorder in the band centre are determined. It is shown that a wave packet constructed by linear combination of several eigenstates shows the same multifractality. Consequently, it is expected that transport properties for wave packets can be derived from the multifractal properties of a single eigenstate.