When computing edge dispersion curves and associated edge states, it is common to impose periodic boundary conditions in one direction and Dirichlet boundary conditions in the other. This setup is naturally called the ribbon geometry, and the resulting structure has two parallel edges. It may be desirable to compute instead in a semi-infinite geometry with a single edge. In this setup, a Dirichlet boundary condition is imposed to create the edge, and periodic boundary conditions are imposed in the direction parallel to the edge. In contrast to the ribbon however, the structure is not truncated away from the edge, so no second edge is created. I will discuss how edge states can be computed in this geometry as long as the structure is eventually periodic in the direction orthogonal to the edge, and explain how our method extends to continuum PDE models and domain wall edges. Joint work with Kyle Thicke (TUM) and Jianfeng Lu (Duke).
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