dx2−y2-wave Bose metal induced by next-nearest-neighbor hopping anisotropy

Superconductivity arises when electrons form Cooper pairs with phase coherence. In contrast, a lack of phase coherence in Cooper pairs can lead to an uncondensed metallic ground state known as the Bose metal state. In this paper, we investigate an attractively interacting fermionic system with nearest-neighbor hopping (t) and next-nearest-neighbor hopping (${t}^{\ensuremath{'}}$) anisotropy between two species of spins in a two-dimensional lattice. Utilizing the constrained path quantum Monte Carlo method, we demonstrate the existence of a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave Cooper pair Bose metal (CPBM) phase with ${t}^{\ensuremath{'}}/t>0.7$. The CPBM phase exhibits a domelike structure in the phase diagram of filling $n\ensuremath{\sim}0.65$, with the maximal region around an optimal ${t}^{\ensuremath{'}}/t\ensuremath{\sim}0.2$, suggesting that an appropriate value of ${t}^{\ensuremath{'}}$ facilitates the formation of the Bose metal. Furthermore, we find that a Bose metal formed by fermions with a closed Fermi surface confirms that the crucial condition for this exotic phenomenon is primarily the anisotropy of the Fermi surface rather than its topology. Our finding of the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave CPBM demonstrates the same pairing symmetry as the pseudogap behavior in cuprates, and its experimental realization in ultracold atom systems is also feasible.