Chiral Anomaly and Strength of the Electron-Electron Interaction in Graphene

Abstract

The long standing controversy concerning the effect of electron -electron interaction on the electrical conductivity of an ideal graphene sheet is settled. Performing the calculation directly in the tight binding approach without the usual prior reduction to the massless Dirac (Weyl) theory, it is found that, to leading order in the interaction strength α = e 2 / v0, the DC conductivity σ/σ0 = 1 + Cα + O α 2 is significantly enhanced with respect to the independent-electrons result σ0, i.e. with the value C = 0.26. The ambiguity characterizing the various existing approaches is nontrivial and related to the chiral anomaly in the system. In order to separate the energy scales in a model with massless fermions, contributions from regions of the Brillouin zone away from the Dirac points have to be accounted for. Experimental consequences of the relatively strong interaction effect are briefly discussed.

Universal collisionless transport of graphene

“…(2). We explain why previous lattice based attempts [14] failed to reach the correct conclusion and show how to obtain Eq. (2) even in case of the dimensional regularization scheme used in Ref.…”

“…Given this success, it is remarkable that there exists a rather long-standing controversy in the theoretical description of Coulomb interaction corrections to the optical absorption of graphene [10][11][12][13][14][15][16][17][18]. Experiments report an optical transmission close to 97.7% [19], a value that corresponds to non-interacting Dirac electrons.…”

“…Examples are the minimal conductivity in disordered samples [2], the odd-integer quantum Hall effect at high magnetic fields [3], and the observation of Klein tunneling through potential barriers [4]. These observations are explained in terms of non-interacting Dirac fermions, while the electron-electron Coulomb interaction clearly affects other experimental results such as the fractional quantum Hall effect [5, 6], and the logarithmically enhanced velocity, as seen in magneto-oscillation [7], angular resolved photoemission spectroscopy [8] and capacitance measurements of the density of states [9].Given this success, it is remarkable that there exists a rather long-standing controversy in the theoretical description of Coulomb interaction corrections to the optical absorption of graphene [10][11][12][13][14][15][16][17][18]. Experiments report an optical transmission close to 97.7% [19], a value that corresponds to non-interacting Dirac electrons.…”

“…The authors of Ref. [14] concluded that the source of the error was the linearized spectrum and concluded that a proper treatment of the spectrum in the entire Brillouin zone (BZ) is needed to determine the optical conductivity. It was added that this unexpected behavior is related to a chiral anomaly or due to non-local optical effects [24].…”

“…[12] was that, while different results can be obtained within the NA (as found in earlier work [10]), this ambiguity is eliminated when the Ward identity is enforced. However, subsequent investigations [13,14] led to an Carbon-carbon distance is a and two electron pz orbitals of typical width λ are illustrated.…”