Intrinsic Flat Bands and Magnetic Proximity in Two-Dimensional Materials

van der Waals materials offer a new paradigm in controlling the properties of materials. The ability to combine materials into heterostructures and precisely control the arrangement of atoms along the stacking axis allows researchers to engineer topological properties via proximity effects, or create energetically at bands that encourage many-body effects. This work represents progress towards both engineering topological properties in materials and observing exotic correlated states in  at bands. In chapter 4, I discuss experiments towards realizing a magnetic proximity effect in a van der Waals  heterostructure, a critical ingredient to break time-reversal symmetry and realize topological phenomena such as the quantum anomalous Hall effect. To achieve this, I create heterostructures of graphene and several different 2D magnetic materials, including CrI3, CrBr₃ and a-RuC_l3. I demonstrate that the chemical instability of both CrI₃ and CrBr₃ are detrimental to graphene electronic quality and induce a massive effective doping which prohibits their use as proximity ferromagnetic materials despite their extensive optical studies. In a-RuC_l3/graphene heterostructures, I demonstrate the absence of a proposed ferromagnetic state, instead observing an anti-ferromagnetic transition at an elevated temperature that is tunable in gate voltage. 

In addition, I study intrinsic  at surface bands in rhombohedral graphite using scanning tunneling microscopy and spectroscopy, which may hold interested correlated physics including superconductivity. A thickness-dependent measurement of  at surface states is performed, demonstrating the increasing density of states of the sharp central van Hove singularity as thickness is increased for the first time experimentally. In the thickest sample, an exploration of the rhombohedral/hexagonal phase boundary illuminates how changes in stacking order as the boundary is approached have a measureable effect on the surface density of states. A search for correlated states is performed in the thickest sample, however doping due to surface contamination and a strong electric field screening prevent observation of these states. Altogether, this work is a small step forward toward engineering topological properties and exotic many body effects in 2D heterostructures.