I will present weak-coupling renormalization group analyses and explain how various novel correlated phases can develop at the Van Hove singularities in graphene moiré systems. Motivated by the structures of low-energy flat bands on the moiré superlattices, I will focus on the two-orbital hexagonal lattice models at the Van Hove doping. First, I will show that a chiral 'high-Tc'-like phase diagram is hosted by an SU(4) symmetric model with conventional Van Hove singularity. Here a d-wave staggered-flux Chern insulator is flanked by the d-wave chiral superconducting domes on both sides of doping. Upon valley splitting which breaks the SU(4) symmetry, the phase diagram turns into a competition between chiral superconductivity and various spin and/or valley density waves. Second, I will demonstrate how various polarized ordered phases may occur when the Van Hove singularities become 'high-order'. These include the p-wave chiral and helical and d-wave chiral superconductivities, s-wave ferromagnetism, as well as f-wave and p-wave polar valley-polarized orders.

Reference:
[1] Y.-P. Lin and R. M. Nandkishore, Phys. Rev. B 100, 085136 (2019).
[2] Y.-P. Lin and R. M. Nandkishore, arXiv:2008.05485.