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 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.Comment: 14 pages, 9 figure

Pairing symmetry of the one-band Hubbard model in the paramagnetic weak-coupling limit: A numerical RPA study

“…35,36 In contrast to previous studies of the paramagnetic phase, our main emphasis was to study the gap structure for a large range of next-nearest neighbor hopping integrals, t , and doping levels away from half-filling, which could be potentially relevant for future systems including new classes of unconventional superconductors as well as optical lattices loaded with interacting fermions. We discussed the details of the gap structure and related this directly to the spin susceptibility at all filling levels.…”

Thermal and electrical transport in metals and superconductors across antiferromagnetic and topological quantum transitions

“…We choose the superconducting gap to have d-wave symmetry, as appropriate for cuprate superconductors and theoretical models of antiferromagnetism coexisting with superconductivity [23,24,[29][30][31][32][33][34][35][36][37][38][39][40][41]. The dispersion in Eq.…”

Cooper Pairing in A Doped 2D Antiferromagnet with Spin-Orbit Coupling

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“…To quantitatively study the effect exerted by SOC on the AFM order, we employ the foregoing definitions of ground state to obtain the self-consistent equation of the sublattice magnetization S : where, 3 , 8 . We show the relationship between S and the Hubbard interaction U / t in Fig.…”

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