Realization of Time Reversal Breaking Topological d + id′ Superconductivity by Proximity Effect

We show that it is inevitable that time reversal symmetry breaks in a superconducting tunneling junction formed by two superconductors with different pairing symmetries. While the leading conventional Jospheson coupling vanishes in such a junction, the forth order in tunneling always generate chiral superconductivity (SC) orders with broken time reversal symmetry. The topology of all possible TRB SC orders are analyzed and only the d + id′ order has a nonzero Chern number. The self-consistent mean field calculation is deployed on two layered t − J model to justify our viewpoints. A robust d ± id′ order appears in our setup.