Can strong repulsive interactions be shown to give rise to pairing in a controlled way? We find that for a single flavor-polarized band, there is a small expansion parameter in the low density limit, once the Bloch wave-function form factor is taken into account. A perturbative expansion is possible, even if the interaction is much stronger than the Fermi energy ${\epsilon }_F$. As a matter of principle, our work shows analytically how strong pairing can emerge from strong repulsion. We illustrate our method with two examples: a two-dimensional Dirac model and a one-dimensional tight-binding model with two orbitals. In the latter case, using density matrix renormalization group, we show that the analytical theory indeed guided us to discover the parameter regime where $p$-wave pairing with order-1 strength is dominant.

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• Perturbation theory
• Strong interaction
• Superconductivity
• Ferromagnetic superconductors