Speaker: Ilya Gruzberg, Physics Dept. University of Chicago
Abstract: Anderson metal-insulator transitions (MIT) caused by disorder in electronic systems exhibit many fascinating features making them quite special. In particular, electronic wave functions that are extended in the metal and localized in the insulator, appear to have intricate self-similar structure right at the transition. This structure leads to an infinite number of scaling multifractal exponents that describe the moments of the wave functions. We have recently developed the concept of multifractality of wave functions for finite samples with boundaries and corners. It appears that the critical behavior of various observables related to wave functions near a boundary at a MIT is different from that in the bulk. In two dimensions (2D), the multifractal exponents at a corner are found to be directly related to those at a straight boundary through a relation arising from conformal invariance. This provides direct evidence for conformal invariance at a 2D MIT. Moreover, the presence of boundaries modifies the multifractal spectrum of the whole sample even in the thermodynamic limit. I will illustrate all these ideas and developments with several examples of MIT's that we have studied.