We study transport in twisted bilayer graphene and show that electrostatic barriers can act as valley splitters, where electrons from the $K$ ($K$) valley are transmitted only to e.g. the top (bottom) layer, leading to valley-layer locked currents. W
e show that such a valley splitter is obtained when the barrier varies slowly on the moire scale and induces a Lifshitz transition across the junction, i.e. a change in the Fermi surface topology. Furthermore, we show that for a given valley the reflected and transmitted current are transversely deflected, as time-reversal symmetry is effectively broken in each valley separately, resulting in valley-selective transverse focusing at zero magnetic field.
