Towards Highly Sensitive Capacitance Measurements of a Quantum Anomalous Hall Phase in Van Der Waal Heterostructures

One of the pioneering achievements in condensed matter physics of the 20th century is the observation of the quantum Hall e↵ect (QHE) in which the Hall resistance in a two-dimensional (2D) sample takes on quantized values in the presence of a strong perpendicular magnetic field. The precise quantization of the hall resistance to one part in a billion has provided a practical, worldwide resistance standard. A long-standing goal has been to realize a similar state of matter but without the need of a strong quantizing magnetic field. The quantum anomalous Hall e↵ect (QAHE) is such a state that is predicted to exist in 2D materials with intrinsic magnetism and strong spin orbit coupling. Very few materials have these inherent properties, but new materials can be synthetically engineered by stacking and combining 2D layers into heterostructures with desired characteristics. In this thesis, we work toward combining graphene and few-layer graphene with materials that exhibit strong spin orbit coupling (molybdenum disulfide) with the goal of realizing a robust QAHE. To ascertain the presence of a zero-field gap in the electronic spectrum of the material, a benchmark of the QAHE, we implement a highly sensitive capacitance measurement technique. We present theoretical background on the quantum Hall e↵ects and capacitance measurements to begin. We then present fabrication and measurements of four devices, two incorporating single layer graphene and two with bilayer graphene. Our work opens the door to prospective devices with utility in spintronics and topological quantum computing