Surface criticality and multifractality at localization transitions

TL;DR

This paper introduces the concept of surface multifractality at localization-delocalization transitions, highlighting boundary effects on wave function behavior in disordered systems, with specific calculations for 2D quantum Hall and metallic systems.

Contribution

It develops the theory of surface multifractality at LD transitions and demonstrates boundary critical behavior through specific model calculations.

Findings

Boundary critical behavior differs from bulk at LD transitions.

Surface multifractality is a distinct phenomenon from bulk multifractality.

Calculated boundary multifractal spectra for 2D quantum Hall and metallic systems.

Abstract

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.