Layer-dependent zero-line modes in antiferromagnetic topological insulators

Recently, the magnetic domain walls have been experimentally observed in antiferromagnetic topological insulators MnBi$_2$Te$_4$, where we find that the topological zero-line modes (ZLMs) appear along the domain walls. Here, we theoretically demonstrate that these ZLMs are layer-dependent in MnBi$_2$Te$_4$ multilayers. For domain walls with out-of-plane ferromagnetism, we find that ZLMs are equally distributed in the odd-number layers. When domain walls possess in-plane magnetization, the ZLMs can also exist in even-number layers due to in-plane mirror-symmetry breaking. Moreover, the conductive channels are mainly distributed in the outermost layers with increasing layer thickness. Our findings lay out a strategy in manipulating ZLMs and also can be utilized to distinguish the corresponding magnetic structures.