The Quantum Hall Effect from Graphene Multilayers to Bulk Graphite

The quantum Hall effect is the paradigmatic example of the interplay of interactions and topology in a two-dimensional (2D) system. Recent experimental progress has highlighted graphene multilayers as a promising platform for realizing a rich variety of states including superconductors, and fractional quantum anomalous Hall states. It is natural to consider what happens as one keeps stacking more layers, and to consider in particular when and how the bulk graphite limit is reached. Here we address these questions by casting the multilayer problem as one of weakly coupled two dimensional systems. We show that it is possible to realize even-denominator quantum Hall states with non-Abelian fractionalized quasiparticles out to surprisingly large film thicknesses and address long standing puzzles concerning the properties of bulk graphite in the strong magnetic field quantum limit.