Dynamical diffusion and renormalization group equation for the Fermi velocity in doped graphene

Abstract

The aim of this work is to study the electron transport in graphene with impurities by introducing a generalization of linear response theory for linear dispersion relations and spinor wave functions. Current response and density response functions are derived and computed in the Boltzmann limit showing that in the former case a minimum conductivity appears in the no-disorder limit. In turn, from the generalization of both functions, an exact relation can be obtained that relates both. Combining this result with the relation given by the continuity equation, is possible to obtain general functional behavior of the the diffusion pole. Finally, a dynamical diffusion is computed in the quasistatic limit using the definition of relaxation function. A lower cutoff must be introduce to regularize infrared divergences which allows to obtain a full renormalization group equation for the Fermi velocity, which is solved up to order O( 2 ).

Fractional statistical potential in graphene

“…and k F and f dimensionless constants [23]. Similar results are shown in [24,25] where the change in Fermi velocity is obtained for weakly doped graphene in those cases in which the concentration of impurities is lower than the critical concentration at which the spectrum of the system is rearranged [26]. Better approximations would imply to consider ripples in graphene which introduce random gauge fields, but treated perturbatively, lead to a renormalization of the Fermi velocity, which decreases at lower energies opposing the upward renormalization induced by the long-range Coulomb interaction.…”

Formation of localized magnetic states in graphene in hollow-site adsorbed adatoms

“…These impurities in graphene can be considered in various types of forms: substitutional, where the site energy is different from those of carbon atoms, which generates resonances [5] and as adsorbates, that can be placed on various points in graphene: six-fold hollow site of a honeycomb lattice, two-fold bridge site of the two neighboring carbons or top site of a carbon atom [6]. Theoretical as well as experimental studies have indicated that substitutional doping of carbon materials can be used to tailor their physical and/or chemical properties ( [7], [8]). In particular, theoretical studies on carbon vacancies in graphene ( [9] and [10]), adsorbed hydrogen atoms [11], and several other types of disorder have been done ( [12], [13], [14] and [15]).…”