Bulk-boundary correspondence in Josephson junctions

We discuss Andreev 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 dxy and px wave superconductors. The Chern number characterizes chiral superconductors. The number of interfacial bound states at the zero-energy is equal to the difference between the topological numbers on either sides of the Josephson junction. We also discuss relation between properties of the Andreev bound states at the zero-energy and features of Josephson current at low temperature.