Quantum Phase Transitions And Non-Fermi Liquid Behaviors In Dirac Fermion Systems

Dirac fermions are the low energy excitations of a number of or a variety of inter-esting systems in condensed matter physics, such as high temperature cuprate super-conductors, some typical heavy fermion superconductors, graphene, and topological insulators. Once the Dirac fermions are subjected to some kind of long-range interac-tion, the system may exhibit numerous novel behaviors including non-Fermi liquids be-haviors, dynamic gap generation etc. The long-rang interactions usually include gauge interaction, long-range Coulomb interaction, and fluctuation of the order parameter at some quantum critical point. In this thesis, three subjects are studied. First, the non-Fermi liquid behaviors of Dirac fermions induced by U(1) gauge interaction. Second, the dynamic gap generation of Dirac fermions due to the long-rang Coulomb interac-tion in graphene. Third, the influence of nematic fluctuation on the Dirac fermions in the vicinity of nematic quantum critical point within the dome of the d wave supercon-ducting phase.