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Critical level statistics for weakly disordered graphene.

E Amanatidis1, I Kleftogiannis, D E Katsanos

  • 1Department of Physics, University of Ioannina, Ioannina 45110, Greece.

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Summary
This summary is machine-generated.

Weakly disordered graphene with zigzag edges exhibits intermediate level statistics, not chaotic or localized. This suggests critical quantum transport via edge states in topological insulators, unlike ordinary Anderson insulators.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Quantum Mechanics

Background:

  • In two dimensions, chaotic level statistics with Wigner spacing distribution are theoretically expected for massless fermions in the Dirac region.
  • Graphene, a 2D material, exhibits unique electronic properties due to its massless Dirac fermions.

Purpose of the Study:

  • To investigate the level statistics of weakly disordered finite graphene samples with zigzag edges.
  • To understand the nature of quantum transport in graphene under varying disorder strengths.

Main Methods:

  • Analysis of level spacing distribution P(S) for finite graphene samples with zigzag edges.
  • Comparison of obtained statistics with theoretical predictions for chaotic (Wigner) and localized (Poisson) systems.

Main Results:

  • The level statistics for weakly disordered graphene with zigzag edges were neither chaotic (Wigner) nor localized (Poisson).
  • The observed statistics resemble those at the critical point of the Anderson metal-insulator transition.
  • For strong disorder, graphene behaves as an ordinary Anderson insulator with Poisson statistics.

Conclusions:

  • Weakly disordered graphene with critical level statistics exhibits quantum transport via edge states, similar to topological insulators.
  • The findings bridge the understanding between chaotic, localized, and critical phenomena in disordered 2D electron systems.