Topological superconducting transition driven by time-reversal-symmetry breaking

Abstract

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 idxz-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.

Quantum criticality of fermion velocities and critical temperature nearby a putative quantum phase transition in the $d$-wave superconductors

“…1, we therefore ought to take discreetly into account the contributions from the interplay between the nodal QPs. On one hand, these nodal QPs themselves may mutually intertwine with each other owing to the strong fluctuations and become one of the major elements at the lowest-energy limit [65][66][67][68][69][70][71][72][73][74][75][76][77][78][79][81][82][83][84][85][86][87][88][89][90][91][92][93][94][95][96][97][98]104 . On the other hand, fermionic couplings can also impact other interaction parameters including fermion velocities v F,∆ and Yukawa coupling via participating in the coupled RG evolutions, which will be established in Sec.…”

“…However, quantum criticality would coax these nodal QPs to mutually intertwine with each other and influence fermion velocities plus Yukawa coupling. Consequently, fermion-fermion interactions may play important roles in determining critical behaviors around certain QCP [65][66][67][68][69][70][71][72][73][74][75][76][77][78][79][81][82][83][84][85][86][87][88][89][90][91][92][93][94][95][96][97][98]104 . Consequently, one can expect that uncovering the contributions from these two quantum critical ingredients may well improve our understandings on the quantum criticality of certain QCP in the d-wave superconductor.…”

Fermion-fermion interaction driven instability and criticality of quadratic band crossing systems with the breaking of time-reversal symmetry

“…In addition, the couplings ∆ c/s i and ∆ PP i serve as the strength of associated fermion-source terms, which can be regarded as order parameters accompanied by corresponding symmetry breakings. In principle, the onset of fermionic bilinear is a manifest signal for certain instability and hence implies a phase transition tied to some symmetry breaking 47,81,84,85,105,107 . Table II catalogues the primary candidates of fermion bilinears and related phase transitions for our system.…”