Superconducting and correlated insulating states are observed in graphene multilayers at a magic twist angle. Tunability of the twist angle and hence the band structure realize nearly flat bands, where the intriguing phases appear. First, we theoretically study the origin of these correlated states based on a Van Hove singularity (VHS) and Fermi surface nesting [1]. Then, we introduce a high-order VHS as a possible explanation for the magic angle, at which the density of states shows a power-law divergence [2]. Finally, we discuss correlation effects at a high-order VHS [3]. We perform a renormalization-group analysis to find a nontrivial metallic state, where various divergent susceptibilities coexist but no long-range order appears. We term such a metallic state as a supermetal. Our controlled analysis shows that a supermetal at the interacting fixed point is a non-Fermi liquid.
[1] H. Isobe, N. F. Q. Yuan, and L. Fu, Phys. Rev. X 8, 041041 (2018).
[2] N. F. Q. Yuan, H. Isobe, and L. Fu, arXiv:1901.05432.
[3] H. Isobe and L. Fu, arXiv:1905.05188.