Smectic pair-density-wave order in EuRbFe₄As₄

The pair density wave (PDW) is a superconducting state in which Cooper pairs carry centre-of-mass momentum in equilibrium, leading to the breaking of translational symmetry^1-4. Experimental evidence for such a state exists in high magnetic field^5-8 and in some materials that feature density-wave orders that explicitly break translational symmetry^9-13. However, evidence for a zero-field PDW state that exists independent of other spatially ordered states has so far been elusive. Here we show that such a state exists in the iron pnictide superconductor EuRbFe₄As₄, a material that features co-existing superconductivity (superconducting transition temperature (T_c) ≈ 37 kelvin) and magnetism (magnetic transition temperature (T_m) ≈ 15 kelvin)^14,15. Using spectroscopic imaging scanning tunnelling microscopy (SI-STM) measurements, we show that the superconducting gap at low temperature has long-range, unidirectional spatial modulations with an incommensurate period of about eight unit cells. Upon increasing the temperature above T_m, the modulated superconductor disappears, but a uniform superconducting gap survives to T_c. When an external magnetic field is applied, gap modulations disappear inside the vortex halo. The SI-STM and bulk measurements show the absence of other density-wave orders, indicating that the PDW state is a primary, zero-field superconducting state in this compound. Both four-fold rotational symmetry and translation symmetry are recovered above T_m, indicating that the PDW is a smectic order.