Emergent pairing states and tunable symmetry in the anisotropic triangular lattice

The superconducting pairing symmetry is significantly constrained by lattice symmetry, yet how this pairing symmetry evolves with changes in lattice symmetry remains unclear. In this study, through variational quantum Monte Carlo simulations on the Hubbard model, we investigate the evolution of the superconducting ground state on an anisotropic triangular lattice with smoothly tunable frustration. At half-filling, we identify a hidden ${C}_{6}$-like $s+d+id$-wave superconductivity, which breaks time-reversal symmetry, emerging for moderate frustrations. This occurs as the lattice symmetry transitions from ${C}_{4}$ to ${C}_{2}$, where the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave and $s+{d}_{xy}$-wave superconducting ground states dominate, respectively. Notably, we find an isotropic-like $d+id$-wave superconducting phase at ${t}^{\ensuremath{'}}/t\ensuremath{\approx}0.7$, much lower than the expected value ${t}^{\ensuremath{'}}/t=1$ predicted by most previous studies. At high electron doping levels, we further discover an unexpected quasi-one-dimensional ${d}_{xy}^{\ensuremath{'}}$-wave superconductivity characterized by strong pairing on the next-nearest-neighbor bond, despite the absence of direct hopping. The numerical data also reveal that pairing symmetries, belonging to distinct irreducible representations of the given point group, can mix together, beyond the conventional theories based on the linear gap equations.