We analyze the possible interaction-induced superconducting instabilities in noncentrosymmetric systems based on symmetries of the normal state. It is proven that pure electron-phonon coupling will always lead to a fully gapped superconductor that does not break time-reversal symmetry and is topologically trivial. We show that topologically nontrivial behavior can be induced by magnetic doping without gapping out the resulting Kramers pair of Majorana edge modes. In the case of superconductivity arising from the particle-hole fluctuations associated with a competing instability, the properties of the condensate crucially depend on the time-reversal behavior of the order parameter of the competing instability. When the order parameter preserves time-reversal symmetry, we obtain exactly the same properties as in the case of phonons. If it is odd under time reversal, the Cooper channel of the interaction will be fully repulsive leading to sign changes of the gap and making spontaneous time-reversal-symmetry breaking possible. To discuss topological properties, we focus on fully gapped time-reversal-symmetric superconductors and derive constraints on possible pairing states that yield necessary conditions for the emergence of topologically nontrivial superconductivity. These conditions might serve as a tool in the search for topological superconductors. We also discuss implications for oxide heterostructures and single-layer FeSe.

• Received 26 January 2016
• Revised 14 April 2016

DOI:https://doi.org/10.1103/PhysRevB.93.174509