Gate-controlled topological conducting channels in bilayer graphene

Understand

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.