Dirac equation for quasi-particles in graphene and quantum field theory of their Coulomb interaction

Abstract

There is evidence for existence of massless Dirac quasi-particles in graphene, which satisfy Dirac equation in (1+2) dimensions near the so called Dirac points which lie at the corners at the graphene's brilluoin zone. We revisit the derivation of Dirac equation in (1+2) dimensions obeyed by quasiparticles in graphene near the Dirac points. It is shown that parity operator in (1+2) dimensions play an interesting role and can be used for defining "conserved" currents resulting from the underlying Lagrangian for Dirac quasi-particles in graphene which is shown to have U_{A}(1)*U_{B}(1) symmetry. Further the quantum field theory (QFT) of Coulomb interaction of 2D graphene is developed and applied to vacuum polarization and electron self energy and the renormalization of the effective coupling g of this interaction and Fermi velocity $v_f$ which has important implications in the renormalization group analysis of g and v_{f}.

10 pages, some typos have been corrected, some references have been added

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• The electronic properties of graphene
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Cited by in corpus (1)

• Parity anomaly in Dirac equation in (1+2) dimensions, quantum electrodynamics and pair production