Conductivity of defectless graphene

Conductivity of graphene, a flat monolayer of carbon atoms, as a function of doping charge shows a pronounced minimum at the neutrality, compensation point. The theory predicts for this point a universal conductivity, whereas the experimental conductivity exceeds this prediction by few times. This discrepancy persists for long time now and may justify an additional study of zero gap semiconductors, with graphene being an example. Needless to say, adequate understanding of the physical mechanisms at the compensation point is also important in some of proposed future applications of graphene in electronic devices. In my view, the problem is that a concept of non-interacting quasiparticles, well established in normal Fermi liquids, is being translated onto the graphene without careful consideration. In normal Fermi liquids the Galilean invariance makes the electronelectron interaction ineffective to relax the current and the Fermi liquid can flow as a whole. Also the rate of electron-electron scattering is relatively small ∼ T /ǫF for large Fermi surfaces. Hence, the transport at low temperature is determined by disorder. On the other hand, the neutral graphene is different. In its Brillouin zone there exist two points where the electron dispersion acquires a cone-like shape, exactly the relativistic massless Dirac dispersion. This feature is simply understood using the tight binding model on the honeycomb lattice, that may represents the band structure of the graphene. At the cone apexes the two crystal bands of graphene meet. The valence band is filled at the compensation point whereas the conduction band is empty. At low temperature the electronic excitations of two types: particles and holes, are present in the vicinity of these two apexes. This special crystal band structure transform the Galilean invariance into Lorentz one but instantaneous Coulomb interaction breaks it and the current is not conserved. Therefore, in defectless graphene at compensation point the current can relax in the process of the Coulomb interaction alone. As the Fermi circle degenerates into two points the rate of Coulomb scattering is no longer weak ∼ T . All this special features of graphene call for a study of the role of Coulomb interaction on the evolution of graphene charge carriers. One important motivation for such study is the recent success in the theory of scattering on charged impurity to explain a linear dependence of the conductivity as a function of the doping charge away from the compensation point.