in momentum space for different ratios of majority to minority species fermions at the Fermi surfaces. 37 majority and 7 minority fermions create a 3:1 spin imbalance at the Fermi surfaces and 61 majority and 7 minority fermions create a 4:1 spin imbalance.[]{data-label="imbas"}](4_1sy "fig:"){width="\linewidth"}

### Changing spin-imbalance

Following on from our analysis of the 61 up-spin and 19 down-spin system, we now study two examples of greater spin-imbalance on a triangular lattice shown in Fig. \[imbas\]. 37 majority and 7 minority fermions were used to create a 3:1 ratio at the Fermi surfaces with $a=5.6$ and ${r_\mathrm{e}}=0$. Peaks are clearly structured in a ring between $q=\sqrt{3}G$ and $q=2G$ at 10 sample standard deviations above zero. Similarly, 61 majority and 7 minority fermions were used to create a 4:1 ratio at the Fermi surfaces with $a=6.3$ and ${r_\mathrm{e}}=0$, and the condensate fraction once again forms a ring structure peaked from $q=\sqrt{7}G$ to $q=\sqrt{12}G$ at 7 sample standard deviations above zero. Pairing FFLO peaks cannot be seen, and a BCS peak is even more strongly suppressed than in the 2:1 imbalanced case. These systems both provide further strong evidence of a spatially modulated superconducting order parameter, that is of the communal pairing 