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Phys. Rev. Lett. 96, 126802 (2006) [4 pages]

Surface Criticality and Multifractality at Localization Transitions

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A. R. Subramaniam1, I. A. Gruzberg1, A. W. W. Ludwig2, F. Evers3, A. Mildenberger4, and A. D. Mirlin3,5,*
1James Franck Institute, University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637, USA
2Physics Department, University of California, Santa Barbara, California 93106, USA
3Institut für Nanotechnologie, Forschungszentrum Karlsruhe, 76021 Karlsruhe, Germany
4Fakultät für Physik, Universität Karlsruhe, 76128 Karlsruhe, Germany
5Institut für Theorie der kondensierten Materie, Universität Karlsruhe, 76128 Karlsruhe, Germany

Received 2 December 2005; published 27 March 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.

© 2006 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.96.126802
DOI:
10.1103/PhysRevLett.96.126802
PACS:
73.20.Fz, 72.15.Rn, 73.43.−f

*Also at Petersburg Nuclear Physics Institute, 188350 St. Petersburg, Russia.

 
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