Doping dependence of the finite-momentum pairing state in EuRbFe₄As₄

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.  Previously, we showed 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 revealed 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 this work, we studied an evolution of the electronic structure upon doping and revealed that the phase modulated superconducting state emerges when the hole and pockets centered at Γ point crosses the Fermi level.