Electrical band flattening, valley flux, and superconductivity in twisted trilayer graphene

Twisted graphene multilayers have been demonstrated to yield a versatile playground to engineer controllable electronic states. Here, by combining first-principles calculations and low-energy models, we demonstrate that twisted graphene trilayers provide a tunable system where Van Hove singularities can be controlled electrically. In particular, it is shown that besides the band flattening, bulk valley currents appear, which can be quenched by local chemical dopants. We finally show that in the presence of electronic interactions, a nonuniform superfluid density emerges whose nonuniformity gives rise to spectroscopic signatures in dispersive higher-energy bands. Our results put forward twisted trilayers as a tunable van der Waals heterostructure displaying electrically controllable flat bands and bulk valley currents.