Gate-controlled topological conducting channels in bilayer graphene

The existence of inequivalent valleys K and K' in the momentum space of two-dimensional hexagonal lattices provides a new electronic degree of freedom, the manipulation of which can potentially lead to new types of electronics, in analogy to the role played by electron spin. In materials with broken inversion symmetry, such as an electrically gated bilayer graphene, the momentum-space Berry curvature $\Omega$ carries opposite sign in the K and K' valleys. A sign reversal of $\Omega$ along an internal boundary of the sheet gives rise to counter-propagating one-dimensional conducting modes encoded with opposite valley indices. These metallic states are topologically protected against backscattering in the absence of valley-mixing scattering, and thus can carry current ballistically. In bilayer graphene, the reversal of $\Omega$ can occur at the domain wall of AB and BA stacked domains, or at the line junction of two oppositely gated regions. The latter approach can provide a scalable platform to implement valleytronic operations such as valves and waveguides, but is technically challenging to realize. Here we fabricate a dual-split-gate structure in bilayer graphene and demonstrate transport evidence of the predicted metallic states. They possess a mean free path of up to a few hundred nanometers in the absence of a magnet field. The application of perpendicular magnetic field suppresses backscattering significantly and enables a 400-nanometer-long junction to exhibit conductance close to the ballistic limit of 4 $e^2/h$ at 8 Tesla. Our experiment paves the path to the realization of gate-controlled ballistic valley transport and the development of valleytronic applications in atomically thin materials.