i-Josephson Junction as Topological Superconductor

We show that the time reversal symmetry inevitably breaks in a superconducting Josephson junction formed by two superconductors with different pairing symmetries dubbed as i-Josephson junction. While the leading conventional Josephson coupling vanishes in such an i-Josephson junction, the second order coupling from tunneling always generates chiral superconductivity orders with broken time reversal symmetry. Josephson frequency in the i-junction is doubled, namely $\omega = 4eV /h$. The result provides a way to engineer topological superconductivity such as the d + id' -wave superconducting state characterized by a nonzero Chern number.