Surface criticality and multifractality at localization transitions

Subramaniam AR, Gruzberg IA, Ludwig AWW, Evers F, Mildenberger A, Mirlin AD. Physical Review Letters, 96, 126802, 2006


We develop the concept of surface multifractality for localization-delocalization (LD) transitions in disordered electronic systems. We point out that the critical behavior of various observables related to wave functions near a boundary at a LD transition is different from that in the bulk. We illustrate this point with a calculation of boundary critical and multifractal behavior at the 2D spin quantum Hall transition and in a 2D metal at scales below the localization length.