Electrically tunable frustrated lattices and magnetism in twisted bilayer graphene

Twisted graphene bilayers have become a powerful solid-state platform to realize a plethora of electronic states, stemming from the emergence of controllable moire superlattices and their electrical tunability. Here we theoretically show that twisted bilayer graphene is a versatile platform to realize tunable frustrated magnets, by realizing triangular and Kagome lattices of localized modes in two dramatically different regimes [1,2]. First, for rotation angles around 1.5 degrees, we show that the magnetic instabilities of the emergent triangular AA lattice can be electrically controlled [1]. In particular, we show that the ferromagnetic and antiferromagnetic ordering inside the AA regions can be electrically switched, giving rise to superlattice spin spirals in the emergent triangular moire superlattice. Second, we show that in the tiny angle regime of 0.2 degrees, an emergent Kagome lattice of localized modes can be electrically generated, stemming from an artificial gauge field created by the interlayer bias [2]. In particular, we show that the microscopic properties of these Kagome modes are controlled by the magnitude of the electrically generated gauge field, yielding a powerful solid-state platform to experimentally engineer a paradigmatic model of frustrated magnetism. These rich and electrically controllable frustrated lattices provide a potential route to experimentally explore frustrated magnetism and quantum spin liquid physics in twisted graphene bilayers.

[1] L. A. Gonzalez-Arraga, J. L. Lado, F. Guinea, and P. San-Jose, Phys. Rev. Lett. 119, 107201 (2017)
[2] A. Ramires and J. L. Lado, Phys. Rev. Lett. 121, 146801 (2018)