Spin-Orbit Coupling and Magnetism in Multilayer Graphene

The topics covered in this work are - spin-density-wave instabilities in monolayer graphene doped to the van Hove singularity. Nesting of the Fermi surface and a diverging density of states are often ingredients for charge and/or magnetic instabilities. For highly doped monolayer graphene these conditions are satisfied. In this thesis a path integral approach is used to show that a spin-density-wave is the leading instability. -spin-orbit interactions in bilayer graphene with next-nearest neighbor interactions. Intrinsic spin-orbit interactions open a gap in the spectrum of monolayer graphene. It is shown that this is also true for bilayers. However, the Rashba spin-orbit coupling has a surprising effect in bilayer graphene. One of the parabolic bands becomes conical. This conical behavior persists when next-nearest-hopping parameters are included in the theory. -ferromagnetic instabilities due to the exchange mechanism in both ABA-stacked trilayer and ABC-stacked trilayer graphene systems. Electrons gain exchange energy by aligning their spins. Due to the Pauli exclusion principle an increase in kinetic energy is accompanying this spin alignment. A variational approach is used to show that ferromagnetic and band-ferromagnetic configurations exist in ABA-stacked trilayers. For ABC-stacked trilayers the ferromagnetic phase space is increased a factor of 25 compared with bilayer graphene, even when a simplified model of screening is taken into account. For the ABC-stacked multilayer screening is important, since the density of states diverges at the Dirac point as the number of layers equals three or more. A chapter is dedicated to calculate the polarization and screened Coulomb potentials in ABC-stacked multilayer graphene. An effective two-band model is used for the small momentum behavior, but the linear dependence of the polarization for large momenta is confirmed in the full-band model for ABC-stacked trilayer graphene.