Topological superconducting transition driven by time-reversal-symmetry breaking

Three-dimensional line-nodal superconductors exhibit nontrivial topology, which is protected by the time-reversal symmetry. Here we investigate four types of short-range interaction between the gapless line-nodal fermionic quasiparticles by carrying renormalization group analysis. We find that such interactions can induce the dynamical breaking of time-reversal symmetry, which alters the topology and might lead to six possible distinct superconducting states, distinguished by the group representations. After computing the susceptibilities for all the possible phase-transition instabilities, we establish that the superconducting pairing characterized by $id_{xz}$-wave gap symmetry is the leading instability in noncentrosymmetric superconductors. Appropriate extension of this approach is promising to pick out the most favorable superconducting pairing during similar topology-changing transition in the polar phase of $^3$He.