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Abstract:
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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 Hamiltoninans 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 supression 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 q[superscrit 3 /2] dispersion . We speculate on the possibility of unusual localization physics associated with these modes . |