In materials systems with flat energy bands and limited disorder, interactions among electrons dominate and can dramatically alter physical behavior. Traditionally, two-dimensional electron gases (2DEGs) have offered excellent platforms to study these effects because the kinetic energy of the electrons is effectively quenched by a perpendicular magnetic field. The recent discovery of graphene, a two-dimensional form of carbon, has opened the door for further exploration into many-body phenomena. Graphene, unlike conventional 2DEGs, has fourfold degenerate electronic states due to its spin and valley degrees of freedom. This thesis describes several experiments that show how these underlying symmetries combine with electron-electron interactions to produce novel and tunable correlated electronic phases of matter.Physic
