Valley separation via trigonal warping

Abstract: Monolayer Graphene contains two inequivalent local minimum, valleys, located at $K$ and $K'$ in the Brillouin zone. There has been considerable interest in the use of these two valleys as a doublet for information processing. Herein I propose a method to resolve valley currents spatially, using only a weak magnetic field. Due to the trigonal warping of the valleys, a spatial offset appears in the guiding centre co-ordinate, and is strongly enhanced due to collimation. This can be exploited to spatially separate valley states. Based on current experimental devices, spatial separation is possible for densities well within current experimental limits. Using numerical simulations, I demonstrate the spatial separation of the valley states.