Physical origin of current partition at a topological trifurcation

In gated bilayer graphene, topological zero-line modes (ZLMs) appear along lines separating regions with opposite valley Hall topologies. Although it is experimentally difficult to design the electric gates to realize ZLMs due to the extremely challenging techniques, twisted bilayer graphene provides a natural platform to produce ZLMs in the presence of a uniform electric field. In this Letter, we develop a set of wave-packet dynamics for ZLMs in monolayer graphene, which can be utilized to characterize various gapless edge modes and can quantitatively reproduce the electronic transport properties at topological intersections. To our surprise, at a topological trifurcation, we show that the counterintuitive current partition (i.e., the direct transport propagation) originates from the microscopic mechanism ``bypass jump'' which is proved to exist in both monolayer and bilayer systems. Our method can be applied to understand the microscopic pictures of the electronic transport features of all kinds of topological states.