Quantum fluctuation-induced first-order breaking of time-reversal symmetry in unconventional superconductors
Using the hole-doped square-lattice - model, this study demonstrates that quantum phase fluctuations fundamentally alter the mean-field picture of time-reversal symmetry breaking in unconventional superconductors by inducing a first-order transition and phase separation between symmetric and asymmetric phases, thereby significantly narrowing the stability region of the exotic $s+id$ state.