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Magnetism---in particular magnetic fluctuations---are thought thought to play a role in a variety of unconventional superconductors, including cuprates, heavy fermions, and moire graphene. I will describe a new venue for examining this interplay by tuning the chemical potential through a van Hove singularity in simple allotropes of graphene, in particular rhombohedral trilayer [1-2] and Bernal bilayer [3] graphene. In both systems, applying a perpendicular electric field gaps out a series of low-energy Dirac nodes, leading to a divergence in the density of states at densities easily accessible by the field effect. Using both transport and compressibility measurements, we find that this regime is characterized by a cascade of phase transitions between states of differing fermi surface degeneracy. These include quarter- and half-metals with only one or two occupied (out of a possible four) combined spin- and valley flavors, as well as a variety of states showing partial polarization within the spin- and valley-isospin space. Most surprisingly, superconductivity arises near a number of phase boundaries. In the trilayer, we observe two superconducting states for hole doping; one arises from a normal state that preserves the spin and valley symmetry, and is suppressed by in-plane magnetic fields in accordance with the Clogston-Chandrasekhar limit, while the other arises from a full spin polarized half metallic state and is not affected by in plane magnetic fields. In bilayer graphene, superconductivity is not observed at B=0, but emerges only above a critical field in plane field, consistent with a magnetic field induced transition into a spin polarized ferromagnetic state with a spin-triplet superconducting ground state. I will lay out the many outstanding theoretical puzzles in these systems, as well as experimental opportunities enabled by the exceptionally good reproducibility and and high sample quality.
[1] H. Zhou, T. Xie, A. Ghazaryan, T. Holder, J. R. Ehrets, E. M. Spanton,
T. Taniguchi, K. Watanabe, E. Berg, M. Serbyn, & A. F. Young. “Half and quarter metals in rhombohedral trilayer graphene.” 598: 429-433 Nature (2021).
[2] H. Zhou, T. Xie, T. Taniguchi, K. Watanabe & A. F. Young. “Superconductivity in rhombohedral trilayer graphene,” Nature 598: 434-438 (2021).
[3] H. Zhou, Y. Saito, L. Cohen, W. Huynh, C. L. Patterson, F. Yang, T. Taniguchi, K. Watanabe, "Isospin magnetism and spin-triplet superconductivity in Bernal bilayer graphene." Science, eabm8386 (2022).
Zoom link: https://bnl.zoomgov.com/j/1605020278?pwd=cHJ1bDRuK1FDNnZLSnpxVkZhcDQ3QT09