Topological and correlated quantum matter in twisted graphene multilayers

Two-dimensional materials, and in particular graphene, provide a powerful solid-state platform to create artificial heterostructures, lacking the conventional constraints of lattice match and alignment of bulk compounds. In particular, by controlling the rotation angle between two graphene layers, an emergent structure known as moire pattern appears, dramatically impacting the low energy electronic properties of graphene. Here we will address how the emergent moire pattern in graphene multilayers provides a versatile knob to create controllable electronic states. In particular, we will show [1,2,3] how twisted graphene bilayers allow creating artificial gauge fields [2], and tunable correlated states [1,3], and we will highlight how these different electronic states can be electrically controlled in experiments.  [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)[3] T. M. R. Wolf, J. L. Lado, G. Blatter, and O. Zilberberg, Phys. Rev. Lett. 123, 096802 (2019)