Pseudospin magnetism and superconductivity in rhombohedral trilayer graphene

Rhombohedral (ABC) graphene trilayers consist of three layers of graphene stacked on top of each other with a relative shift.  A low-energy description of the system involves 4 flavors of fermions, corresponding to valley and spin degrees of freedom (pseudospins). Recent experiments [1,2]  performed in this system without a moir\'e potential uncovered a cascade of phase transitions as a function of carrier doping and an external displacement field. I will explain how these transitions can be understood as generalized magnetic phase transitions in the 4-dimensional pseudospin space, and focus on the valley-XY ordered phase. Using a simple phenomenological model supported by microscopic mean-field calculations, we show that a strongly trigonal warped Fermi-surface like those in ABC trilayer graphene is unstable towards valley-XY formation at even weak Coulomb interactions. I will discuss superconductivity mediated by valley-XY paramagnons and comment on similarities and differences between  ABC-trilayers and AB-bilayers.

[1] Zhou, H., Xie, T., Ghazaryan, A., Holder, T., Ehrets, J. R., Spanton, E. M., ... & Young, A. F. (2021). Half and quarter metals in rhombohedral trilayer graphene. arXiv preprint arXiv:2104.00653.

[2] Zhou, H., Xie, T., Taniguchi, T., Watanabe, K., & Young, A. F. (2021). Superconductivity in rhombohedral trilayer graphene. arXiv preprint arXiv:2106.07640.