ELECTRON-ELECTRON INTERACTIONS IN DIRAC FERMIONS

Abstract

In this research, we investigate the effects of electron-electron interactions on Dirac fermions at half-filling. First, using a spinful Gross-Neveu theory, we find that the critical interaction for monolayer graphene to undergo a Fermi-liquid-to-Mott-insulator phase transition increases with the long-range component of the Coulomb potential. In the Fermi liquid phase, we map out the Fermi velocity renormalization for the whole range of interaction strength, and build a phenomenological theory to describe such renormalization in the strong interacting regime where no analytical theory is previously available. Next, we turn to the anisotropic Dirac system to study the effects of interactions on the Fermi surface anisotropy. Using several analytical and numerical tools, we find a ubiquitous simple relation for the Fermi surface anisotropy renormalization. In the third part, we examine the argument that the Dirac fermion is dynamically generated in the parabolic band of bilayer graphene to stabilize the Fermi liquid phase.