Smectic Pair Density Wave in a magnetic iron based superconductor.*

Most known superconductors are characterized in equilibrium by a complex order parameter that is uniform in space, i.e., Δ_s~|Δ₀|e^iΦ. Yet, under specific conditions, exotic Cooper pairing state can emerge with a non-uniform equilibrium order parameter, possessing a finite center-of-mass momentum. Such spatially dependent order parameters (Δ_p(r)) can generically feature variations in either their amplitude or phase — or a combination of both. Utilizing Spectroscopic Imaging Scanning Tunneling Microscopy (SI-STM), we've identified two primary PDW states in the iron pnictide superconductor, EuRbFe₄As₄ (ER-1144), a material that features co-existing superconductivity (T_c ≈ 37 kelvin) and magnetism (T_m ≈ 15 kelvin). In the ferromagnetic superconducting phase, the first type is characterized by a superconducting gap that has a long-range, unidirectional spatial modulation (Δ_p1(r)~|Δ₀|cos(Q*r)) in the absence of any other translational symmetry breaking density-wave orders. The second type features an anisotropic Doppler energy shift in reciprocal space due to the phase winding (Δ_p2(r)~|Δ₀|e^iQ*r). In contrast, all the striking features are completely suppressed crossing the magnetic transition. Additionally, both PDW states are also impacted by an out-of-plane external magnetic field, evidenced by the Bogoliubov quasiparticle spectrum imaging. Our findings provide valuable insights into the intricate nature of the PDW states and the interplay between magnetism and superconducting order.