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Anderson transition in low-dimensional disordered systems driven by long-range nonrandom hopping.

A Rodríguez1, V A Malyshev, G Sierra

  • 1Departamento de Matemática Aplicada y Estadística, Universidad Politécnica, E-28040 Madrid, Spain.

Physical Review Letters
|February 7, 2003
PubMed
Summary

Delocalized states can exist in low-dimensional disordered systems, challenging the single-parameter scaling hypothesis. This finding applies to the Anderson model with specific long-range hopping, revealing extended states at band edges.

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Area of Science:

  • Condensed Matter Physics
  • Disordered Systems
  • Quantum Mechanics

Background:

  • The single-parameter scaling hypothesis posits no delocalized states in low-dimensional disordered systems for noninteracting quasiparticles.
  • Anderson localization is a key phenomenon in disordered materials, impacting electronic properties.

Purpose of the Study:

  • To investigate the occurrence of delocalized states in one- and two-dimensional disordered systems.
  • To examine the validity of the single-parameter scaling hypothesis under specific conditions.

Main Methods:

  • Analytical approach using supersymmetric methods.
  • Renormalization group analysis.
  • Numerical simulations of the Anderson model.

Main Results:

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  • Extended states were found to occur in the one- and two-dimensional Anderson model.
  • This occurs when the hopping strength decays as a power of the distance between sites.
  • Delocalization of states was observed at one of the band edges of the quasiparticle energy spectrum.

Conclusions:

  • The single-parameter scaling hypothesis may not universally apply to all low-dimensional disordered systems.
  • Long-range hopping interactions can lead to delocalization, contradicting predictions of Anderson localization.
  • The interplay between level spacing and disorder renormalization is crucial for understanding state delocalization.