Superconductivity at Magnetic Phase Transitions in Crystalline Graphene Allotropes

The interplay between superconductivity and magnetism is thought to play a role in a variety of unconventional superconductors, including cuprates, heavy fermions, and moire graphene. Here, 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. In both systems, applying a perpendicular electric field gaps out a series of low-energy Dirac nodes, leading to large divergences in the density of states at low densities. 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 superconducting ground state. I will lay out the many outstanding theoretical puzzles in these systems, as well as experimental opportunities enabled by the exceptionally high sample quality.<br/>References<br/>[1] Haoxin Zhou, Tian Xie, Areg Ghazaryan, Tobias Holder, James R. Ehrets, Eric M. Spanton,<br/>Takashi Taniguchi, Kenji Watanabe, Erez Berg, Maksym Serbyn, & Andrea F. Young. “Half and quarter metals in rhombohedral trilayer graphene.” <i>Nature</i> (2021).<br/>[2] Haoxin Zhou, Tian Xie, Takashi Taniguchi, Kenji Watanabe & Andrea F. Young. “Superconductivity in rhombohedral trilayer graphene,” <i>Nature</i> (2021).<br/>[3] Haoxin Zhou, Yu Saito, Liam Cohen, William Huynh, Caitlin L. Patterson, Fangyuan Yang, Takashi Taniguchi, Kenji Watanabe, Andrea F. Young. “Isospin magnetism and spin-triplet superconductivity in Bernal bilayer graphene.” arXiv:2110.11317.