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Paper   IPM / Physic / 8497
School of Physics
  Title:   Roughness of Undoped Graphene and Its Short-Range Induced Gauge Field
1.  N. Abed-Pour
2.  M. Neek-Amal
3.  R. Asgari
4.  F. Shahbazi
5.  N. Nafari
6.  M. R. Rahimi Tabar
  Status:   Published
  Journal: Phys. Rev. B
  Vol.:  76
  Year:  2007
  Pages:   195407
  Supported by:  IPM
We present both numerical and analytical study of graphene roughness with a crystal structure including 500 ×500 atoms. The roughness can effectively result in a random gauge field and has important consequences for its electronic structure. Our results show that its height fluctuations in small scales have scaling behavior with a temperature dependent roughness exponent in the interval of 0.6 < χ < 0.7 . The correlation function of height fluctuations depends upon temperature with characteristic length scale of ≈ 90 Å (at room temperature). We show that the correlation function of the induced gauge field has a short-range nature with correlation length of about ≅ 2−3Å. We also treat the problem analytically by using the Martin-Siggia-Rose method. The renormalization group flows did not yield any delocalized-localized transition arising from the graphene roughness. Our results are in good agreement with recent experimental observations.

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