Superconducting phase diagram of itinerant antiferromagnets

TL;DR

This paper investigates the phase diagram of the Hubbard model in the weak-coupling limit, revealing dominant $d_{x^2-y^2}$-wave superconductivity coexisting with antiferromagnetic order, influenced by spin fluctuations and interband pairing.

Contribution

It provides a detailed analysis of the superconducting pairing symmetry and the effects of spin fluctuations and interband pairing in the antiferromagnetic Hubbard model.

Findings

$d_{x^2-y^2}$-wave pairing dominates in both electron- and hole-doped regimes.

Longitudinal spin fluctuations support $p$-wave pairing, but are overshadowed by transverse fluctuations.

Interband pairing gaps have the same parity as intraband gaps and are of similar magnitude.

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 quasi-particles of the antiferromagnetic metallic state. We find a dominant $d_{x^2-y^2}$-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 $d_{x^2-y^2}$. The sub-leading 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 non-zero 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 give intraband and interband pairing gaps of $d_{x^2-y^2}$ structure and similar gap magnitude. In conclusion, the $d_{x^2-y^2}$ gap dominates for both hole and electron doping inside the spin-density-wave phase.