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

TL;DR

This paper revisits the Dirac equation for graphene's quasi-particles, explores its symmetry properties, and develops a quantum field theory of Coulomb interactions, analyzing their effects on physical parameters like coupling and Fermi velocity.

Contribution

It provides a detailed derivation of the Dirac equation in (1+2) dimensions for graphene and develops a quantum field theory of Coulomb interactions with implications for renormalization.

Findings

Dirac equation for graphene quasi-particles is derived with parity considerations.

Quantum field theory of Coulomb interaction is formulated and applied.

Renormalization effects on coupling constant and Fermi velocity are analyzed.

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}.