Variation of the Bose surface by filling a Cooper-pair Bose metal

The Cooper pair Bose metal (CPBM) is a nonsuperfluid quantum phase in which uncondensed fermion pairs form a ``Bose surface'' in momentum space. We investigate the CPBM in the two-dimensional spin-anisotropic attractive Hubbard model by tuning the next-nearest-neighbor (NNN) hopping ${t}^{\ensuremath{'}}$, carrier filling $n$, and spin anisotropy $\ensuremath{\alpha}$, using large-scale constrained-path quantum Monte Carlo simulations. A moderate NNN hopping ${t}^{\ensuremath{'}}/t=0.2$ substantially enlarges the CPBM region: the phase extends into weaker anisotropy regimes and coexists with a commensurate charge-density wave (CDW) near half-filling $(n>0.95)$, where CDW order would otherwise dominate at ${t}^{\ensuremath{'}}=0$. Interestingly, ${t}^{\ensuremath{'}}$ suppresses the overall CDW peak amplitude and introduces a geometric correlation between the orientations of the Fermi and Bose surfaces: for weak Fermi-surface rotations, the Bose surface remains aligned with the lattice axes, while larger distortions drive both surfaces to rotate in tandem. Momentum-resolved pairing distributions reveal that the bosonic pairing channels are jointly controlled by ${t}^{\ensuremath{'}}$ and carrier filling $n$. For small ${t}^{\ensuremath{'}}$, ${d}_{xy}$-wave correlations dominate across the entire filling range. In contrast, for larger ${t}^{\ensuremath{'}}$, the dominant pairing symmetry varies with $n$, reflecting a nontrivial interplay between frustration and density. These findings establish carrier filling and NNN hopping as complementary levers for manipulating CPBM stability and provide concrete criteria for identifying nonsuperfluid bosonic matter in cold-atom and correlated-electron systems.