Triangular antiferromagnetism on the honeycomb lattice of twisted bilayer graphene

Understand

We present the electronic band structures of states with the same symmetry as the three-sublattice planar antiferromagnetic order of the triangular lattice.

• Such states can also be defined on the honeycomb lattice provided the spin density waves lie on the bonds.
• We identify cases which are consistent with observations on twisted bilayer graphene: a correlated insulator with an energy gap, yielding a single doubly-degenerate Fermi surface upon hole doping.
• We also discuss extensions to metallic states which preserve spin rotation invariance, with fluctuating spin density waves and bulk $\mathbb{Z}_2$ topological order.