Quantitative Measurement of Valley Polarization in a Multicomponent Fractional Quantum Hall System

In bilayer graphene, the electronic structure at high magnetic fields are enhanced by spin, valley and orbital degrees of freedom. In particular, the valley quantum number can be directly mapped onto layer polarization, allowing for direct capacitive probes. In this talk, I will present quantitative measurements of valley polarization in high quality bilayer graphene quantum Hall system. The valley polarization is obtained by measuring anti-symmetric combinations of top- and bottom- gate capacitances to the graphene bilayer. We improve on past approaches by using a multilayer heterostructure in which the bilayer is encapsulated in successive layers of hexagonal boron nitride (hBN), monolayer graphene, hBN, and graphite, allowing full control of density and layer polarization in both the bilayer and in the monolayer graphene gates. Our layer resolved measurements provide new quantitative insight into the ground states and excitations of both integer and fractional quantum Hall phases in bilayer graphene.