Visualizing the finite-momentum pairing state in EuRbFe₄As₄ via quasiparticle interference

Nonmagnetic superconductors are characterized by pairs of electrons with equal and opposite momenta. When superconductors are subjected to magnetic interactions, it has been hypothesized that they could feature pairs of electrons with nonzero total momentum, leading to a superconducting order parameter whose phase or amplitude is spatially modulated. In this work, we show evidence from Spectroscopic Imaging Scanning Tunneling Microscopy (SI-STM) that a phase-modulated superconducting order parameter exists in the magnetic (T_m ~ 15K) iron pnictide superconductor (T_c ~ 37K) EuRbFe₄As₄ (ER-1144). By utilizing the quasiparticle interference (QPI) imaging, we reveal that the magnetic superconducting state features gapless excitations of a Bogoliubov Fermi surface, which break the four-fold rotational (C₄) symmetry of the crystal lattice. In addition, temperature and field-dependent measurements reveal a recovery of the C₄ symmetry, demonstrating that the anisotropic Bogoliubov Fermi surface is closely tied to the crystal’s magnetic order. The observed anisotropy can be naturally explained by the unidirectional Doppler shift in the quasiparticle energies that is inherent to a phase-modulated superconductor.