Valley-polarized tunneling currents in bilayer graphene tunneling transistors

We study theoretically the electron current across a monolayer graphene/hexagonal boron nitride/bilayer graphene tunneling junction in an external magnetic field perpendicular to the layers. We show that change in effective tunneling barrier width for electrons on different graphene layers of bilayer graphene, coupled with the fact that its Landau level wave functions are not equally distributed amongst the layers with a distribution that is reversed between the two valleys, lead to valley polarization of the tunneling current. We estimate that valley polarization ∼ 70% can be achieved in high quality devices at B=1T. Moreover, we demonstrate that strong valley polarization can be obtained both in the limit of strong-momentum-conserving tunneling and in lower quality devices where this constraint is lifted.