Influence of spatial dispersion in the topological edge states of magnetized plasmas

Conventional Chern insulators are two-dimensional periodic structures that support unidirectional edge states at the boundary, while the wave propagation in the bulk regions is forbidden. The number of unidirectional edge states is governed by the gap Chern number, a topological invariant that depends on the global properties of the system over the entire wavevector space. This concept can also be extended to systems with a continuous translational symmetry provided they satisfy a regularization condition for large wavenumbers. Here, we discuss how the spatial dispersion, notably the high-spatial frequency behavior of the material response, critically influences the topological properties, and consequently, the net number of unidirectional edge states. In particular, we show that seemingly small perturbations of a local magnetized plasma can lead to distinct Chern phases and, consequently, markedly different edge state dispersions.