Dynamical polarization of graphene at finite doping

The polarization of graphene is calculated exactly within the random phase approximation for arbitrary frequency, wavevector and doping. At finite doping, the static susceptibility saturates to a constant value for low momenta. At q = 2kF it has a discontinuity only in the second derivative. In the presence of a charged impurity this results in Friedel oscillations which decay with the same power law as the Thomas?Fermi contribution, the latter being always dominant. The spin density oscillations in the presence of a magnetic impurity are also calculated. The dynamical polarization for low q and arbitrary ? is employed to calculate the dispersion relation and the decay rate of plasmons and acoustic phonons as a function of doping. The low screening of graphene, combined with the absence of a gap, leads to a significant stiffening of the longitudinal acoustic lattice vibrations.

[1]  P. Kim,et al.  Experimental observation of the quantum Hall effect and Berry's phase in graphene , 2005, Nature.

[2]  A. Fetter,et al.  Quantum Theory of Many-Particle Systems , 1971 .

[3]  Frank Stern,et al.  Polarizability of a Two-Dimensional Electron Gas , 1967 .

[4]  M. W. Klein,et al.  Magnetic and nonmagnetic impurities in two-dimensional metals , 1975 .

[5]  Béal-Monod Mt Ruderman-Kittel-Kasuya-Yosida indirect interaction in two dimensions. , 1987 .

[6]  T. Ando Screening Effect and Impurity Scattering in Monolayer Graphene(Condensed matter: electronic structure and electrical, magnetic, and optical properties) , 2006 .

[7]  G. Mahan Many-particle physics , 1981 .

[8]  P. Wallace The Band Theory of Graphite , 1947 .

[9]  David P. DiVincenzo,et al.  Self-consistent effective-mass theory for intralayer screening in graphite intercalation compounds , 1984 .

[10]  Local defects and ferromagnetism in graphene layers , 2005, cond-mat/0505557.

[11]  Shung Dielectric function and plasmon structure of stage-1 intercalated graphite. , 1986, Physical review. B, Condensed matter.

[12]  Shung Lifetime effects in low-stage intercalated graphite systems. , 1986, Physical review. B, Condensed matter.

[13]  Magnetic field driven metal insulator phase transition in planar systems , 2002, cond-mat/0202422.

[14]  Andre K. Geim,et al.  Electric Field Effect in Atomically Thin Carbon Films , 2004, Science.

[15]  A. Geim,et al.  Two-dimensional gas of massless Dirac fermions in graphene , 2005, Nature.

[16]  Kentaro Nomura,et al.  Quantum Hall ferromagnetism in graphene. , 2006, Physical review letters.

[17]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[18]  J. W. McClure,et al.  Band Structure of Graphite and de Haas-van Alphen Effect , 1957 .

[19]  S. Lang,et al.  An Introduction to Fourier Analysis and Generalised Functions , 1959 .

[20]  N. M. R. Peres,et al.  Electronic properties of disordered two-dimensional carbon , 2006 .

[21]  Non-Fermi liquid behavior of electrons in the half-filled honeycomb lattice (A renormalization group approach) , 1993, hep-th/9311105.