Interactions and quantum hall effects in graphene multilayers

In a strong magnetic field, the psuedospin chirality of bilayer graphene’s low energy bands results in degenerate, zero energy n=0 and n=1 Landau or- bital states. In this thesis, we find that in addition to endowing states with energetic broadness disorder strongly mixes the zero energy orbitals of the lowest Landau level. We study the dependence of mixing and conductivity on inter-layer bias. Quantum Hall ferromagnetic states emerge when electronic interactions are included at the mean-field level. We study the character of ground states and quasiparticle excitations in the context of orbital degen- eracy and in the presence of interactions with the filled Dirac sea of states. Lastly, we study the effect of interactions in ABA-stacked trilayer graphene, and discover a metal-insulator transition and a separate propensity to break mirror symmetry in certain areas of parameter space.