The low energy electronic band structure of bilayer graphene

Abstract.We employ the tight binding model to describe the electronic band structure of bilayer graphene and we explain how the optical absorption coefficient of a bilayer is influenced by the presence and dispersion of the electronic bands, in contrast to the featureless absorption coefficient of monolayer graphene. We show that the effective low energy Hamiltonian is dominated by chiral quasiparticles with a parabolic dispersion and Berry phase 2π. Layer asymmetry produces a gap in the spectrum but, by comparing the charging energy with the single particle energy, we demonstrate that an undoped, gapless bilayer is stable with respect to the spontaneous opening of a gap. Then, we describe the control of a gap in the presence of an external gate voltage. Finally, we take into account the influence of trigonal warping which produces a Lifshitz transition at very low energy, breaking the isoenergetic line about each valley into four pockets.

[1]  M. Inoue.  LANDAU LEVELS AND CYCLOTRON RESONANCE IN GRAPHITE , 1962 .

[2]  Jerry Tersoff,et al.  Dielectric response of semiconducting carbon nanotubes , 2002 .

[3]  Luc Henrard,et al.  Charge carriers in few-layer graphene films. , 2006, Physical review letters.

[4]  Charlier,et al.  First-principles study of the electronic properties of graphite. , 1991, Physical review. B, Condensed matter.

[5]  J. Slonczewski,et al.  Band Structure of Graphite , 1958 .

[6]  S. Rabii,et al.  Electronic properties of graphite: A unified theoretical study , 1982 .

[7]  Electron-electron interactions and the phase diagram of a graphene bilayer , 2005, cond-mat/0512360.

[8]  G. Dresselhaus.  Graphite Landau Levels in the Presence of Trigonal Warping , 1974 .

[9]  Rong-Bin Chen,et al.  Influence of an electric field on the optical properties of few-layer graphene with AB stacking , 2006 .

[10]  M. Dresselhaus,et al.  Intercalation compounds of graphite , 1981 .

[11]  François M. Peeters,et al.  From graphene to graphite : Electronic structure around the K point , 2006 .

[12]  Tsuneya Ando,et al.  Hall conductivity of a two-dimensional graphite system , 2002 .

[13]  Vadim V Cheianov,et al.  Friedel oscillations, impurity scattering, and temperature dependence of resistivity in graphene. , 2006, Physical review letters.

[14]  Edward McCann.  Asymmetry gap in the electronic band structure of bilayer graphene , 2006 .

[15]  Electronic states and Landau levels in graphene stacks , 2006, cond-mat/0604396.

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

[17]  Johan Nilsson,et al.  Electronic properties of graphene multilayers. , 2006, Physical review letters.

[18]  V P Gusynin,et al.  Unusual microwave response of dirac quasiparticles in graphene. , 2006, Physical review letters.

[19]  Transport in bilayer graphene: Calculations within a self-consistent Born approximation , 2006, cond-mat/0606166.

[20]  K. Yoshizawa,et al.  Interlayer interactions in two‐dimensional systems: Second‐order effects causing ABAB stacking of layers in graphite , 1996 .

[21]  V P Gusynin,et al.  Unconventional integer quantum Hall effect in graphene. , 2005, Physical review letters.

[22]  G. Semenoff,et al.  Condensed-Matter Simulation of a Three-Dimensional Anomaly , 1984 .

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

[24]  A. Geim,et al.  Unconventional quantum Hall effect and Berry’s phase of 2π in bilayer graphene , 2006, cond-mat/0602565.

[25]  K. Yoshizawa,et al.  Second-order perturbational analysis of the interaction between graphite sheets , 2002 .

[26]  F. Guinea,et al.  Edge and surface states in the quantum Hall effect in graphene , 2005, cond-mat/0509709.

[27]  Vladimir I Fal'ko,et al.  Landau-level degeneracy and quantum Hall effect in a graphite bilayer. , 2006, Physical review letters.

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

[29]  Haldane,et al.  Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the "parity anomaly" , 1988, Physical review letters.

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

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

[32]  Boettger,et al.  Interplanar binding and lattice relaxation in a graphite dilayer. , 1992, Physical review. B, Condensed matter.

[33]  K. Nakao.  Landau Level Structure and Magnetic Breakthrough in Graphite , 1976 .

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

[35]  T. Ohta,et al.  Controlling the Electronic Structure of Bilayer Graphene , 2006, Science.

[36]  Riichiro Saito,et al.  Berry's Phase and Absence of Back Scattering in Carbon Nanotubes. , 1998 .

[37]  H. Philipp,et al.  Optical Properties of Graphite , 1965 .

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

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

[40]  V. P. Gusynin,et al.  Transport of Dirac quasiparticles in graphene: Hall and optical conductivities , 2006 .

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

[42]  O. P. Gupta,et al.  Effect of Trigonal Warping on Landau Levels of Graphite , 1972 .