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The European Physical Journal Special Topics

, Volume 148, Issue 1, pp 39–54 | Cite as

Weak localization in monolayer and bilayer graphene

  • K. Kechedzhi
  • E. McCann
  • V. I. Fal'ko
  • H. Suzuura
  • T. Ando
  • B. L. Altshuler
Article

Abstract.

We describe the weak localization correction to conductivity in ultra-thin graphene films, taking into account disorder scattering and the influence of trigonal warping of the Fermi surface. A possible manifestation of the chiral nature of electrons in the localization properties is hampered by trigonal warping, resulting in a suppression of the weak anti-localization effect in monolayer graphene and of weak localization in bilayer graphene. Intervalley scattering due to atomically sharp scatterers in a realistic graphene sheet or by edges in a narrow wire tends to restore weak localization resulting in negative magnetoresistance in both materials.

Keywords

European Physical Journal Special Topic Monolayer Graphene Berry Phase Weak Localization Bilayer Graphene 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. D. DiVincenzo, E. Mele, Phys. Rev. B 29, 1685 (1984) Google Scholar
  2. G.W. Semenoff, Phys. Rev. Lett. 53, 2449 (1984) Google Scholar
  3. F.D.M. Haldane, Phys. Rev. Lett. 61, 2015 (1988); Y. Zheng, T. Ando, Phys. Rev. B 65, 245420 (2002); V.P. Gusynin, S.G. Sharapov, Phys. Rev. Lett. 95, 146801 (2005); N.M.R. Peres, F. Guinea, A.H. Castro Neto, Phys. Rev. B 73, 125411 (2006); A.H. Castro Neto, F. Guinea, N.M.R. Peres, Phys. Rev. B 73, 205408 (2006) Google Scholar
  4. T. Ando, T. Nakanishi, R. Saito, J. Phys. Soc. Jpn. 67, 2857 (1998) Google Scholar
  5. E. McCann, V.I. Fal'ko, Phys. Rev. Lett. 96, 086805 (2006); J. Nilsson et al., Phys. Rev. B 73, 214418 (2006); F. Guinea, A.H. Castro Neto, N.M.R. Peres, ibid. 73, 245426 (2006); M. Koshino, T. Ando, ibid. 73, 245403 (2006); B. Partoens, F.M. Peeters, ibid. 74, 075404 (2006) Google Scholar
  6. K.S. Novoselov et al., Science 306, 666 (2004) Google Scholar
  7. K.S. Novoselov et al., Nature 438, 197 (2005) Google Scholar
  8. Y. Zhang et al., Phys. Rev. Lett. 94, 176803 (2005); Nature 438, 201 (2005) Google Scholar
  9. K.S. Novoselov et al., Nat. Phys. 2, 177 (2006) Google Scholar
  10. H. Suzuura, T. Ando, Phys. Rev. Lett. 89, 266603 (2002) Google Scholar
  11. B.L. Altshuler, D. Khmel'nitzkii, A.I. Larkin, P.A. Lee, Phys. Rev. B 22, 5142 (1980) Google Scholar
  12. S. Hikami, A.I. Larkin, Y. Nagaoka, Prog. Theor. Phys. 63, 707 (1980); B.L. Al'tshuler et al., Sov. Phys. JETP 54, 411 (1981); Zh. Eksp. Teor. Fiz. 81, 768 (1981) Google Scholar
  13. D.V. Khveshchenko, Phys. Rev. Lett. 97, 036802 (2006) Google Scholar
  14. A.F. Morpurgo, F. Guinea, Phys. Rev. Lett. 97, 196804 (2006) Google Scholar
  15. E. McCann, K. Kechedzhi, V.I. Fal'ko, H. Suzuura, T. Ando, B.L. Altshuler, Phys. Rev. Lett. 97, 146805 (2006) Google Scholar
  16. K. Kechedzhi et al., cond-mat/0701690 Google Scholar
  17. S.V. Morozov et al., Phys. Rev. Lett. 97, 016801 (2006) Google Scholar
  18. R.V. Gorbachev et al., cond-mat/0701686 Google Scholar
  19. X. Wu et al., cond-mat/0611339 Google Scholar
  20. V. Cheianov, V.I. Fal'ko, Phys. Rev. B 74, 041403 (2006) Google Scholar
  21. P.D. Dresselhaus et al., Phys. Rev. Lett. 68, 106 (1992); G.L. Chen et al., Phys. Rev. B 47, 4084 (1993); J.B. Miller et al., Phys. Rev. Lett. 90, 076807 (2003); A.L. Shelankov, Solid State Commun. 53, 465 (1985) Google Scholar
  22. H. Fukuyama, J. Phys. Soc. Jpn. 49, 649 (1980); Prog. Theor. Phys. Suppl. 69, 220 (1980) Google Scholar
  23. D.J. Bishop, D.C. Tsui, R.C. Dynes, Phys. Rev. Lett. 44, 1153 (1980); Y. Kawaguchi, S. Kawaji, J. Phys. Soc. Jpn. 48, 699 (1980); R.G. Wheeler, Phys. Rev. B 24, 4645 (1981); R.A. Davies, M.J. Uren, M. Pepper, J. Phys. C 14, L531 (1981) Google Scholar
  24. R.S. Prasad et al., Semicond. Sci. Technol. 10, 1084 (1995); A. Prinz et al., Thin Solid Films 294, 179 (1997) Google Scholar
  25. In this calculation we take into account double spin degeneracy of carriers Google Scholar
  26. G. Bergmann, Phys. Rep. 107, 1 (1984) Google Scholar
  27. A. Goldenblum et al., Phys. Rev. B 60, 5832 (1999) Google Scholar
  28. P.R. Wallace, Phys. Rev. 71, 622 (1947); J.C. Slonczewski, P.R. Weiss, Phys. Rev. 109, 272 (1958) Google Scholar
  29. N.H. Shon, T. Ando, J. Phys. Soc. Jpn. 67, 2421 (1998) Google Scholar
  30. For the monolayer, time reversal of an operator \(\hat{W}\) is described by \(({\rm \Pi} _{x}\otimes \sigma _{x}){\hat{W}}^{\ast }({\rm \Pi} _{x}\otimes \sigma _{x})\). For the bilayer, time reversal is given by \({\rm \Pi}_{x}\otimes\sigma_{x}{\hat{W}}^{\ast} {\rm \Pi}_{x} \otimes \sigma _{x}\) Google Scholar
  31. The group U4 can be described using 16 generators I,Σ slsΛ l, s,l=x,y,x Google Scholar
  32. E. McCann, V.I. Fal'ko, Phys. Rev. B 71, 085415 (2005); N. Peres, F. Guinea, A.H. Castro Neto, Phys. Rev. B 73, 125411 (2006); M. Foster, A. Ludwig, Phys. Rev. B 73, 155104 (2006) Google Scholar
  33. Corners of the hexagonal Brilloin zone are \(\mathbf{K}_{\pm }=\pm ({\textstyle\frac{2}{3}}{\rm ha}^{-1},0)\) Google Scholar
  34. V.I. Fal'ko, T. Jungwirth, Phys. Rev. B 65, 081306 (2002); D. Zumbuhl et al., Phys. Rev. B 69, 121305 (2004) Google Scholar
  35. M.S. Dresselhaus, G. Dresselhaus, Adv. Phys. 51, 1 (2002); R.C. Tatar, S. Rabii, Phys. Rev. B 25, 4126 (1982); J.-C. Charlier, X. Gonze, J.-P. Michenaud, Phys. Rev. B 43, 4579 (1991) Google Scholar
  36. E. McCann, V.I. Fal'ko, J. Phys. Cond. Matt. 16, 2371 (2004) Google Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  • K. Kechedzhi
    • 1
  • E. McCann
    • 1
  • V. I. Fal'ko
    • 1
  • H. Suzuura
    • 2
  • T. Ando
    • 3
  • B. L. Altshuler
    • 4
  1. 1.Department of PhysicsLancaster UniversityYB LancasterUK
  2. 2.Division of Applied PhysicsGraduate School of Engineering, Hokkaido UniversitySapporoJapan
  3. 3.Department of PhysicsTokyo Institute of TechnologyTokyoJapan
  4. 4.Physics DepartmentColumbia UniversityNew YorkUSA

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