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Abstract

Recent advances in experimental techniques have helped establish unprecedented control over the electronic structure and properties of 2D materials. Moiré materials are created by producing a small lattice mismatch between two superimposed lattices by introducing a small relative twist or superimposing lattices with different lattice constants. Moiré graphene structures have been shown to host a variety of interesting phases, like superconductivity and strongly-correlated topological insulators. The quantum devices group at UBC assembled a 5-layer moiré graphene structure with a relative twist between a bilayer and a trilayer stack. They measured the Longitudinal and Hall resistivity while varying an out-of-plane electric field (D) through the stack and the electron density (n) in the layers. They showed that in the presence of a non-zero electric field and a small magnetic field, spontaneously symmetry broken correlated topological insulators are obtained at integer fillings with respect to charge neutrality. Many non-trivial metallic phases (halos) have also been observed in the vicinity of the insulators in the D vs. n phase diagram. The goal of this thesis is to gain a theoretical understanding of these insulators and phases surrounding these insulators through a mean field approach. This is achieved by starting with the phenomenological Bistritzer-MacDonald model of t2+3 and adding correlations through a Hartree-Fock decoupling of Coulomb interactions. The nature of the symmetry broken insulators is characterized through Spin-Valley order parameter calculations. In addition, layer polarization and screening in the graphene stack is accounted for self-consistently and discussed in context of the halos. All results have been contextualized with experimental parameters and assumptions of the theory.