Abstract.
We investigate Friedel Oscillations (FO) surrounding a point scatterer in graphene. We find that the long-distance decay of FO depends on the symmetry of the scatterer. In particular, the FO of the charge density around a Coulomb impurity show a faster, δρ∼1/ r3, decay than in conventional 2D electron systems. In contrast, the FO of the exchange field which surrounds atomically sharp defects breaking the hexagonal symmetry of the honeycomb lattice decay according to the 1/r2 law. We discuss the consequences of these findings for the temperature dependence of the resistivity of the material and the RKKY interaction between magnetic impurities.
Similar content being viewed by others
References
J. Friedel, Phil. Mag. 43, 153 (1952)
K.H. Lau, W. Kohn, Surf. Sci. 75, 69 (1978)
G. Zala, B.N. Narozhny, I.L. Aleiner, Phys. Rev. B 64, 214204 (2001); ibid. 64, 201201 (2001); ibid. B 65, 020201 (2002)
S.D. Sarma, E.H. Hwang, Phys. Rev. Lett. 83, 164 (1999); Phys. Rev. B 69, 195305 (2004)
A.M. Rudin, I.L. Aleiner, L.I. Glazman, Phys. Rev. B 55, 9322 (1997)
F. Stern, Phys. Rev. Lett. 44, 1469 (1980); A. Gold, V.T. Dolgopolov, Phys. Rev. B 33, 1076 (1986)
Y.Y. Proskuryakov et al., Phys. Rev. Lett. 89, 076406 (2002); Z.D. Kvon et al., Phys. Rev. B 65, 161304 (2002); A.A. Shashkin et al., Phys. Rev. B 66, 073303 (2002); V.M. Pudalov et al., Phys. Rev. Lett. 91, 126403 (2003); S.A. Vitkalov et al., Phys. Rev. B 67, 113310 (2003)
M.A. Ruderman, C. Kittel, Phys. Rev. 96, 99 (1954); T. Kasuya, Prog. Theor. Phys. 16, 45 (1956); K. Yosida, Phys. Rev. 106, 893 (1957)
K.S. Novoselov et al., Science 306, 666 (2004); K.S. Novoselov et al., Nature 438, 197 (2005)
Y. Zhang et al., Nature 438, 201 (2005); Y. Zhang et al., Phys. Rev. Lett. 94, 176803 (2005)
K. Nomura, A.H. MacDonald, Phys. Rev. Lett. 96, 256602 (2006); T. Ando, J. Phys. Soc. Jpn. 75, 074716 (2006)
E. McCann, K. Kechedzhi, V.I. Fal'ko, H. Suzuura, T. Ando, B.L. Altshuler, Phys. Rev. Lett. 97, 146805 (2006)
I.L. Aleiner, K.B. Efetov, cond-mat/0607200
Corners of the hexagonal Brilloin zone are \(\mathbf{K} _{\xi }=\xi ({\textstyle\frac{4}{3}}\pi a^{-1},0)\), where ξ=± 1 and a is the lattice constant. In the basis [ φ $K_+,A$ , φ $K_+,B$ , φ $K_-,B$ , φ $K_-,A$ , time reversal, T(W) of an operator W is described by \(T(\hat{W })=(\mathrm{\Pi}_{x}\otimes \sigma _{x}){W}^{\ast }(\mathrm{\Pi}_{x}\otimes \sigma _{x})\). This can be used to show that T(Σs)=-Σs, T(Λl)=-Λl, and T(ΣsΛ l)=ΣsΛl
E. Fradkin, Phys. Rev. B 33, 3257 (1986); E. McCann, V.I. Fal'ko, Phys. Rev. B 71, 085415 (2005); M. Foster, A. Ludwig, Phys. Rev. B 73, 155104 (2006)
S.V. Morozov et al., Phys. Rev. Lett. 97, 016801 (2006)
T. Ando, T. Nakanishi, R. Saito, J. Phys. Soc. Jpn. 67, 2857 (1998)
V. Cheianov, V.I. Fal'ko, Phys. Rev. B 74, 041403 (2006)
T. Ando, A. Fowler, F. Stern, Rev. Mod. Phys. 54, 437 (1982)
The 1/r2 FO in a gas of relativistic 2D fermions vanish in the massless limit. See D.H. Lin, Phys. Rev. A 73, 044701 (2006)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Cheianov, V. Impurity scattering, Friedel oscillations and RKKY interaction in graphene. Eur. Phys. J. Spec. Top. 148, 55–61 (2007). https://doi.org/10.1140/epjst/e2007-00225-5
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2007-00225-5