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We explore the Floquet band-structure and electronic transport in laser-illuminated bilayer graphene. By using a bias voltage perpendicular to the graphene bilayer we show how to get one-way charge and valley transport among two unbiased leads. In contrast to quantum pumping, our proposal uses a different mechanism based on generating a non-reciprocal bandstructure with a built-in directionality. The Floquet states at one edge of a graphene layer become hybridized with the continuum on the other layer, and so the resulting bandstructure allows for one-way transport as in an . Our proof-of-concept may serve as a building block for devices exploiting one-way states.

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