Time reversal invariant topological superconductivity in correlated non-centrosymmetric systems

Using functional renormalization group method, we study the favorable condition for electronic correlation driven time reversal invariant topological superconductivity in symmetry class DIII. For non-centrosymmetric systems we argue that the proximity to ferromagnetic (or small wavevector magnetic) instability can be used as a guideline for the search of this type of superconductivity. This is analogous to the appearance of singlet unconventional superconductivity in the neighborhood of antiferromagnetic instability. We show three concrete examples where ferromagnetic-like fluctuation leads to topological pairing.