Superconductivity with macroscopic time-reversal symmetry breaking in the presence of loop-current fluctuations

Loop currents (LCs) have been proposed in various superconductors and recently confirmed in kagome materials, raising a fundamental question regarding their intrinsic connection to superconductivity (SC). Here, we investigate this issue using a sign-problem-free bilayer t-J_⊥-V model that hosts a spontaneous interlayer loop-current (ILC) parent state, via unbiased projector quantum Monte Carlo simulations. Near half-filling, interlayer interactions stabilize ILC order that breaks time-reversal symmetry (TRS). Upon hole doping, the ILC order is suppressed, while interlayer s-wave SC emerges with optimal doping behavior. Specifically, superconducting correlations are enhanced in the regime where ILC order is weakened, demonstrating an intimate interplay between the two phases. The resulting phase diagram reveals a transition from the half-filled ILC parent state to doped SC, reminiscent of the evolution from antiferromagnetic order to SC in cuprates, except that LCs involve orbital magnetism. Strikingly, a significant coexistence region emerges near the quantum critical regime, where SC develops with the persistence of residual ILC correlations and appreciable fluctuations, giving rise to a SC state with macroscopic TRS breaking. Our results establish a minimal theoretical framework for exploring the connection between LCs and SC, and reveal a promising route to TRS breaking in superconductors, offering important insights into the unconventional SC in LC systems.