Transport Properties of Topological 1D Zero-Line Mode in Graphene

When the inversion symmetry of graphene systems is broken, e.g. graphene subjected to a staggered sublattice potential or bilayer under an applied interlayer potential difference, a bulk band gap opens to support the quantum valley-Hall state. When the potential varies spatially, a topological one-dimensional conducting channel is formed along the zero-line of the potential. We find that such a state shows the property of zero bend resistance. And if two straight zero lines crosses, we show that the splitting of the zero line mode obeys a counterintuitive current partition law. We provide a theory to understand the physics behind these novel characteristics.