The Electronic Compressibility of Rhombohedral Graphene Multilayers

Abstract

In condensed matter systems, energy bands with narrow dispersion frequently host correlated electronic phases that arise from strong Coulomb interactions. When these bands also have concentrated Berry curvature, the correlated phases may be topologically non-trivial. The low-energy bands of rhombohedral graphene multilayers possess both of these ingredients, making this a promising class of materials in which to search for correlated topological electronic ground states. This thesis describes our electronic compressibility measurements on rhombohedral graphene multilayers, with a particular focus on the pentalayer system (R5G). We utilize a planar capacitance technique that probes the thermodynamic density of states and enables us to extract energy gaps of incompressible phases. We observe a variety of correlated electronic phenomena including half and quarter metals, layer antiferromagnetism, correlation-driven Chern insulators, and thermodynamic signatures of potential Wigner crystallization. We also study the electronic compressibility of R5G aligned to a hexagonal boron nitride (hBN) substrate to form a moiré superlattice. Motivated by the recent discovery of the fractional quantum anomalous Hall effect in this system when the electrons are pushed away from the moiré interface by an external electric displacement field, we study the opposite moiré-proximal limit, in which the superlattice potential is considerably stronger. We observe integer and fractional Chern insulator states that persist down to low magnetic fields in addition to numerous trivial and topological charge density waves. We map out a phase diagram that is highly sensitive to both displacement and magnetic fields, establishing the R5G-hBN superlattice as a highly-tunable system for studying the interplay between intrinsic band topology and strong lattice effects.