We analyze the transition into the most favorable ordered state for a system of 2D fermions with spin and valley degrees of freedom. We show that for a range of rotationally invariant dispersions, the ordering transition is highly unconventional: the associated susceptibility diverges (or almost diverges) at the transition, yet immediately below it the system jumps discontinuously into a fully polarized state. We analyze the dispersion of the longitudinal and transverse collective modes in different parameter regimes above and below the transition. Additionally, we consider ordering in a system with full $\mathrm{SU(4)}$ symmetry and show that there is a cascade of discontinuous transitions into a set of states, which includes a quarter-metal, a half-metal and a three-quarter metal. We compare our results with the data for biased bilayer and tri-layer graphene.
Topological flat bands, valley polarization, and interband superconductivity in magic-angle twisted bilayer graphene with proximitized spin-orbit couplings
Crystal-symmetry-paired spin-valley locking in a layered room-temperature antiferromagnet
Southern University of Science and Technology（南方科技大学）；The Hong Kong University of Science and Technology（香港科技大学）；Zhejiang University（浙江大学）；Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences（中国科学院上海微系统与信息技术研究所）；Shanghai Advanced Research Institute, Chinese Academy of Sciences（中国科学院上海高等研究院）；Hiroshima University（广岛大学）；University of Science and Technology of China（中国科学技术大学）；Institute of Advanced Science Facilities, Shenzhen（深圳先进科学设施研究院）
Extended s-wave superconductivity in M-point twisted bilayer SnSe2
University of Würzburg（维尔茨堡大学）；Max Planck Institute for the Structure and Dynamics of Matter（物质结构与动力学马克斯·普朗克研究所）；The Flatiron Institute（平顿研究所）；Leinweber Institute for Theoretical Physics, Stanford University（斯坦福大学莱因韦伯理论物理研究所）；Institute for Advanced Study, Tsinghua University（清华大学高等研究院）；Department of Physics, Princeton University（普林斯顿大学物理系）；ITAMP, Harvard-Smithsonian Center for Astrophysics（哈佛-史密森天体物理中心）；Harvard University
