Role of electron-electron interactions in Chiral 2DEGs

In this thesis we study the effect of electron-electron interactions on Chiral two-dimensional electron gas (C2DEGs). C2DEGs are a very good description of the low-energy electronic properties of single layer and multilayer graphene systems. The low-energy properties of single layer and multilayer graphene are described by Chiral Hamiltonians whose band eigenstates have definite chirality. In this thesis we focus on the effect of electron-electron interactions on two of these systems: monolayer and bilayer graphene.;In the first half of this thesis we use the massless Dirac Fermion model and random-phase-approximation to study the effect of interactions in graphene sheets. The interplay of graphene's single particle chiral eigenstates along with electron-electron interactions lead to a peculiar suppression of spin susceptibility and compressibility, and also to an unusual velocity renormalization. We also report on a theoretical study of the influence of electron-electron interactions on ARPES spectra in graphene. We find that level repulsion between quasiparticle and plasmaron resonances gives rise to a gap-like feature near the Dirac point.;In the second half we anticipate interaction driven integer quantum Hall effects in bilayer graphene because of the near-degeneracy of the eight Landau levels which appear near the neutral system Fermi level. We predict that an intra-Landau-level cyclotron resonance signal will appear at some odd-integer filling factors, accompanied by collective modes which are nearly gapless and have approximate q3/2 dispersion. We speculate on the possibility of unusual localization physics associated with these modes.