Skyrmion and Tetarton Lattices in Twisted Bilayer Graphene

Abstract: Recent experiments on twisted bilayer graphene show an anomalous quantum Hall (AQH) effect at filling of $3$ electrons per moir`e unit cell. The AQH effect arises in an insulating state with both valley- and ferromagnetic order. We argue, that weak doping of such a system leads to the formation of a novel topological spin texture, a double-tetarton lattice'. The building block of this lattice, thedouble-tetarton', is a spin configuration which covers $1/4$ of the unit-sphere twice. In contrast to skyrmion lattices, the net magnetization of this magnetic texture vanishes. Only at large magnetic fields more conventional skyrmion lattices are recovered. But even for large fields the addition of a single charge to the ferromagnetic AQH state flips hundreds of spins. Our analysis is based on the investigation of an effective non-linear sigma model which includes the effects of long-ranged Coulomb interactions.