Fermi momentum and a system crossing the Chandrasekhar-Clogston limit [@chandrasekhar_limit; @clogston_limit] would have finite momentum density of the minority species at the majority species Fermi momentum, so it is clear that the system has not relaxed into either of those possible states. Knowing this, we can now move on to study the emergence of superconductivity by examining the condensate fraction.

[0.85]{} ![Contour plot of the condensate fraction in momentum space for the spin-imbalanced case with 61 and 19 fermions of the majority and minority species respectively on the triangular lattice and 25 and 9 on the square lattice.[]{data-label="2_1"}](2_1_alt "fig:"){width="\linewidth"}

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[0.85]{} ![Contour plot of the condensate fraction in momentum space for the spin-imbalanced case with 61 and 19 fermions of the majority and minority species respectively on the triangular lattice and 25 and 9 on the square lattice.[]{data-label="2_1"}](2_1sq "fig:"){width="\linewidth"}

### Condensate fraction

The condensate fraction for the spin-imbalanced system with 61 majority and 19 minority species fermions is shown in Fig. \[2\_1tri\]. Six major peaks in the condensate fraction are visible at the points 2 $G$ units away from the origin, where $G$ is the magnitude of the reciprocal lattice vector. This is the first observation in a first principles 