In-Plane Critical Magnetic Fields in Magic-Angle Twisted Trilayer Graphene

It has recently been shown [Y. Cao, J. M. Park, K. Watanabe, T. Taniguchi, and P. Jarillo-Herrero, Pauli-limit violation and re-entrant superconductivity in moiré graphene, Nature (London) 595, 526 (2021).NATUAS0028-0836] that superconductivity in magic-angle twisted trilayer graphene survives to in-plane magnetic fields that are well in excess of the Pauli limit, and much stronger than the in-plane critical magnetic fields of magic-angle twisted bilayer graphene. The difference is surprising because twisted bilayers and trilayers both support the magic-angle flat bands thought to be the fountainhead of twisted graphene superconductivity. We show here that the difference in critical magnetic fields can be traced to a C_{2}M_{h} symmetry in trilayers that survives in-plane magnetic fields, and also relative displacements between top and bottom layers that are not under experimental control at present. An gate electric field breaks the C_{2}M_{h} symmetry and therefore limits the in-plane critical magnetic field.