Correlated phases in spin-orbit-coupled rhombohedral trilayer graphene

Recent experiments indicate that crystalline graphene multilayers exhibit much of the richness of their twisted counterparts, including cascades of symmetry-broken states and unconventional superconductivity. Interfacing Bernal bilayer graphene with a WSe₂ monolayer was shown to dramatically enhance superconductivity—suggesting that proximity-induced spin-orbit coupling plays a key role in promoting Cooper pairing. Motivated by this observation, we study the phase diagram of spin-orbit-coupled rhombohedral trilayer graphene via self-consistent Hartree-Fock simulations, elucidating the interplay between displacement field effects, long-range Coulomb repulsion, short-range (Hund's) interactions, and substrate-induced Ising spin-orbit coupling. In addition to generalized Stoner ferromagnets, we find various flavors of intervalley coherent ground states distinguished by their transformation properties under electronic time reversal, C₃ rotations, and an effective antiunitary symmetry. We pay particular attention to broken-symmetry phases that yield Fermi surfaces compatible with zero-momentum Cooper pairing, identifying promising candidate orders that may support spin-orbit-enhanced superconductivity. ; © 2024 American Physical Society. ; We are grateful to Yiran Zhang, Alex Thomson, Cyprian Lewandowski, and Stevan Nadj-Perge for insightful discussions and collaborations on related projects. J.M.K. acknowledges support from the SURF programme at Caltech. É.L.-H. was supported by the Gordon and Betty Moore Foundation's EPiQS Initiative, Grant No. GBMF8682. The U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Science Center supported the high-performance computing as well as the symmetry analysis component of this work. Additional support was provided by the Caltech Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation through Grant No. GBMF1250, and the Walter Burke Institute for ...