π /2-Josephson junction as a topological superconductor

Superconducting states with broken time-reversal symmetry are rarely found in nature. Here we predict that it is inevitable that the time-reversal symmetry is broken spontaneously in a superconducting Josephson junction formed by two superconductors with different pairing symmetries dubbed as π/2-Josephson junction. While the leading conventional Josephson coupling vanishes in such an π/2-Josephson junction, the second-order coupling from tunneling always generates chiral superconductivity orders with broken time-reversal symmetry. Josephson frequency in the π/2 junction is doubled, namely ω=4eV/h. The result can not only provide a way to engineer topologically trivial or nontrivial time-reversal breaking superconducting states, but also be used to determine the pairing symmetry of unconventional superconductors.