Bulk-boundary correspondence in Josephson Junctions

We discuss bound states appearing at the interface between two different superconductors characterized by different nontrivial topological numbers such as one-dimensional winding numbers and Chern numbers. The one-dimensional winding number characterizes d_{xy} and p_x wave superconductors. The Chern number characterizes chiral-p, chiral-d, and chiral-f wave superconductors. The interfacial bound state appears at the zero-energy when the topological numbers of the two superconductors are different from each other. When the two superconductors are characterized by the Chern numbers n and m, for example, the number of the zero-energy bound is |n-m| independent of junction parameters such as the phase difference across the junction and the transmission probability of interface. We generalize a concept of bulk-boundary correspondence to the Josephson junctions consisting of two topological superconductors.