Novel coupling between charge order and time-reversal-symmetry-breaking superconductivity

The interplay between charge-density waves (CDWs), which break translational symmetry, and spatially homogeneous superconductivity, which breaks global U(1) gauge symmetry, can give rise to an intriguing phenomenon: the pair-density wave, characterized by a spatial modulation of the superconducting order parameter. Yet how CDWs couple to unconventional superconducting states-particularly those with time-reversal symmetry breaking (TRSB)-remains largely unexplored. Here, using scanning tunneling microscopy on heavily hole-doped Ba$_{1-x}$K$_x$Fe$_2$As$_2$, which hosts an s $\pm$ is superconducting state, we reveal a previously unobserved coupling between a surface CDW and TRSB superconductivity. Experimentally, the TRSB superconductivity imparts "chirality" to the CDW, which manifests as commensurate domains separated by domain walls with $\pi$-phase slips-forming what we term a bipolar CDW. The domain walls delineate TRSB domains of opposite chirality, consistent with spontaneous breaking of U(1) $\times$ Z2. Supported by theoretical modelling, we construct a framework in which a hidden interfacial pair-density modulation (PDM) mediates a linear coupling between the surface CDW and interband Josephson currents of TRSB superconductivity. Crucially, the theory shows that realizing this linear coupling requires a controlled global phase difference $\delta$ $\phi$ = $\pi$/2 between the PDM and CDW states. Our results uncover a previously overlooked connection between charge ordering and TRSB superconductivity, opening a pathway to explore intertwined quantum orders in iron-based superconductors and other strongly correlated systems.