Non-coplanar magnetism, topological density wave order and emergent symmetry at half-integer filling of moir? Chern bands

Twisted double-and mono-bilayer graphene are graphene-based moire materials host-ing strongly correlated fermions in a gate-tunable conduction band with a topologi-cally non-trivial character. Using unbiased exact diagonalization complemented by unre-stricted Hartree-Fock calculations, we find that the strong electron-electron interactions lead to a non-coplanar magnetic state, which has the same symmetries as the tetrahe-dral antiferromagnet on the triangular lattice and can be thought of as a skyrmion lattice commensurate with the moire scale, competing with a set of ferromagnetic, topological charge density waves featuring an approximate emergent O(3) symmetry, 'rotating' the different charge density wave states into each other. Direct comparison with exact di-agonalization reveals that the ordered phases are accurately described within the unre-stricted Hartree-Fock approximation. Exhibiting a finite charge gap and Chern number |C | = 1, the formation of charge density wave order which is intimately connected to a skyrmion lattice phase is consistent with recent experiments on these systems.