Quench of chiral superconductivity by quantum phase fluctuations in twisted cuprate bilayers

Following theoretical proposals of chiral $d+i{d}^{\mathrm{\prime }}$ superconductivity in twisted cuprate bilayers, experimental signatures of time-reversal symmetry breaking (TRSB) remain highly controversial. Here we demonstrate that quantum phase fluctuations fundamentally reshape the phase diagram of this proposed chiral state. Unlike regular superconducting orders, the chiral $d+i{d}^{\mathrm{\prime }}$ state requires long-range coherence of an interlayer phase degree of freedom and is therefore intrinsically vulnerable to phase fluctuations. Incorporating these fluctuations nearly eliminates the chiral phase over most parts of the phase diagram, restricting it to a narrow twist-angle window and ultra-low temperatures. The fluctuation-driven destruction of chirality produces a first-order transition into the $d$-wave state, giving rise to coexistence and metastability. Meanwhile, Josephson phase locking is strongly weakened at the TRSB quantum critical point, which sits well within the superconducting regime. More broadly, our work establishes quantum phase fluctuations as a fundamental constraint on the emergence of TRSB phases in low-dimensional layered quantum materials.