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We study attractively interacting fermions on a square lattice withdispersion relations exhibiting strong spin-dependent anisotropy. The resultingFermi surface mismatch suppresses the s-wave BCS-type instability, clearing theway for unconventional types of order. Unbiased sampling of the Feynmandiagrammatic series using Diagrammatic Monte Carlo methods reveals a rich phasediagram in the regime of intermediate coupling strength. Instead of a proposedCooper-pair Bose metal phase [A. E. Feiguin and M. P. A. Fisher, Phys. Rev.Lett. 103, 025303 (2009)] we find an incommensurate density wave at stronganisotropy and two different p-wave superfluid states with unconventionalsymmetry at intermediate anisotropy.

p-wave Superfluidity by Spin-Nematic Fermi Surface Deformation