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Surface criticality and multifractality at localization transitions.

A R Subramaniam1, I A Gruzberg, A W W Ludwig

  • 1James Franck Institute, University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637, USA.

Physical Review Letters
|April 12, 2006
PubMed
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We introduce surface multifractality to study electronic systems near a localization-delocalization transition. Boundary effects on wave functions differ from bulk behavior, impacting critical properties.

Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Statistical Physics

Background:

  • Disordered electronic systems exhibit localization-delocalization (LD) transitions.
  • Wave function behavior near boundaries can differ from bulk properties.

Purpose of the Study:

  • Develop the concept of surface multifractality for LD transitions.
  • Investigate the distinct critical behavior of wave functions at boundaries versus in the bulk.

Main Methods:

  • Theoretical development of surface multifractality.
  • Calculation of boundary critical and multifractal behavior.
  • Analysis of 2D spin quantum Hall transition and 2D metal.

Main Results:

  • Surface multifractality provides a new framework for LD transitions.

Related Experiment Videos

  • Critical behavior of observables near boundaries differs from bulk behavior.
  • Demonstrated distinct boundary multifractal properties at the 2D spin quantum Hall transition.

    • Conclusions:

    • The concept of surface multifractality is crucial for understanding LD transitions.
    • Boundary effects significantly alter critical phenomena in disordered electronic systems.
    • This work highlights the importance of spatial dimensionality and boundaries in electronic phase transitions.