Two-dimensional honeycomb lattices are characterized by a unique electronic degree of freedom, namely, valley, in the momentum space. Analogous to spin, the existence of the valley degree of freedom enriches the physics of gapless and gapped two-dimensional materials such as graphene, bilayer graphene and transition metal dichalcogenides. The manipulation of the valley degree of freedom may lead to a new type of electronics called valleytronics, the realization of which remains difficult so far. In this talk, I will first give a brief overview of phenomena arising from the valley degree of freedom in honeycomb lattices. Then I would like to discuss our effort of creating topological conducting channels in bilayer graphene, which are valley-momentum locked helical one-dimensional edge states (aka kink states). I will describe the fabrication process and the experimental evidences and properties of the kink states. They are entirely created and controlled electrically and thus may allow a pathway to achieve on-chip valve and waveguide designs by controlling the valley degree of freedom.
