Superconducting phase diagram of itinerant antiferromagnets

Abstract

We study the phase diagram of the Hubbard model in the weak-coupling limit for coexisting spin-density-wave order and spin-fluctuation-mediated superconductivity. Both longitudinal and transverse spin fluctuations contribute significantly to the effective interaction potential, which creates Cooper pairs of the quasiparticles of the antiferromagnetic metallic state. We find a dominant dx2−y2-wave solution in both electron- and hole-doped cases. In the quasi-spin-triplet channel, the longitudinal fluctuations give rise to an effective attraction supporting a p-wave gap, but are overcome by repulsive contributions from the transverse fluctuations which disfavor p-wave pairing compared to dx2−y2. The subleading pair instability is found to be in the g-wave channel, but complex admixtures of d and g are not energetically favored since their nodal structures coincide. Inclusion of interband pairing, in which each fermion in the Cooper pair belongs to a different spin-density-wave band, is considered for a range of electron dopings in the regime of well-developed magnetic order. We demonstrate that these interband pairing gaps, which are nonzero in the magnetic state, must have the same parity under inversion as the normal intraband gaps. The self-consistent solution to the full system of five coupled gap equations gives intraband and interband pairing gaps of dx2−y2 structure and similar gap magnitude. In conclusion, the dx2−y2 gap dominates for both hole and electron doping inside the spin-density-wave phase.

Similar papers