Time-reversal symmetry breaking superconductivity in the presence of loop-current fluctuations

Loop currents have been proposed in various superconductors and recently confirmed in kagome materials, raising a fundamental question regarding their intrinsic connection to superconductivity. Here, we study a sign-problem-free bilayer $t-J_{\perp }-V$ model hosting a spontaneous interlayer loop-current parent state, and explore the interplay between loop-current fluctuations and superconductivity using unbiased projector quantum Monte Carlo simulations. Near half-filling, unbiased interlayer interactions induce spontaneous loop currents that break time-reversal symmetry. Upon hole doping, the loop-current order is suppressed, and interlayer $s$-wave superconductivity emerges where loop-current fluctuations become dominant. We establish a phase diagram revealing a transition from the loop-current parent to a superconducting state, reminiscent of the evolution from an antiferromagnetic parent to superconductivity in cuprates. Strikingly, a coexisting regime emerges near the phase boundary, yielding time-reversal-symmetry-breaking superconductivity. Our study reveals an intrinsic connection between loop currents and superconductivity, and identifies a promising mechanism for time-reversal symmetry breaking in superconductors. Furthermore, our results offer insights into unconventional superconductivity in loop-current systems and establish a minimal theoretical framework for understanding time-reversal symmetry breaking in bilayer correlated electron systems.