Orbital and Spin Order in Graphene Multilayer Quantum Hall Systems

Graphene multilayers in a strong magnetic field have rich interaction physics. Ordered states include broken symmetry incompressible integer and fractional Quantum Hall states, including large gap states at even denominator fractions [1]. The phase diagrams of these systems depend subtly on an interplay between internal spin, valley, and sometimes additional orbital degrees of freedom present within the anomalous Landau levels at neutrality. We will explain why a correct description of orbital polarization requires the inclusion of exchange interactions with the negative energy sea, and why the filling factor dependence of orbital polarization is sensitive to particle-hole symmetry breaking. These ideas will be applied to bilayer graphene, to multilayer rhombohedral graphene stacks, and to bulk graphite.

[1] Assouline, A., Wang, T., Zhou, H., Cohen, L. A., Yang, F., Zhang, R., Taniguchi, T., Watanabe, K., Mong, R. S. K., Zaletel, M. P., & Young, A. F. "Energy gap of the even-denominator fractional quantum Hall state in bilayer graphene" arXiv:2308.05729. (2023)