The purpose of this paper is to investigate the propagation of topological currents along magnetic interfaces (also known as magnetic walls) of a two-dimensional material. We consider tight-binding magnetic models associated to generic magnetic multi-interfaces and describe the \(K\)-theoretical setting in which a bulk-interface duality can be derived. Then, the (trivial) case of a localized magnetic field and the (non trivial) case of the Iwatsuka magnetic field are considered in full detail. This is a pedagogical preparatory work that aims to anticipate the study of more complicated multi-interface magnetic systems.

中文翻译：

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沿磁性界面的边缘电流量化：AK $K$ - 理论方法

本文的目的是研究拓扑电流沿二维材料的磁界面（也称为磁壁）的传播。我们考虑与通用磁性多界面相关的紧束缚磁性模型，并描述了\(K\)理论设置，其中可以导出体界面对偶性。然后，详细考虑局部磁场的（平凡）情况和岩冢磁场的（非平凡）情况。这是一项教学准备工作，旨在预测更复杂的多界面磁系统的研究。