Recently, the magnetic domain walls have been experimentally observed in antiferromagnetic topological insulators ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$. Here we study the intrinsic topological zero-line modes (ZLMs) that appear along the domain walls, and find that these ZLMs are layer dependent in ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ multilayers. We reveal the role of the spatial layer degree of freedom and magnetic domain wall configurations in determining the electronic transport properties and the distribution of the ZLMs in antiferromagnetic topological insulator systems. For antiferromagnetic domain wall with out-of-plane magnetization within each domain, we find that ZLMs are only distributed in the odd-number layers equally. For the Néel domain wall, the ZLMs are no longer distributed in the odd-number layers equally due to the mirror symmetry $\left(M_z\right)$ breaking, and can exist in the even-number layers in multilayer systems. Moreover, the ZLMs are mainly distributed in the outermost layers with increasing layer thickness. Our findings lay out a strategy in manipulating ZLMs and can be utilized to distinguish the corresponding magnetic structures.

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.