Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) State in a Strongly Correlated d-wave Superconductor

TThe FFLO state is an unconventional superconducting (SC) state found under the influence of the Zeeman field. This is identified by finite center-of-mass momenta in the Cooper pairs which causes the pairing amplitude to modulate in real space. On the other hand, strong repulsion smears out spatial variations in the order parameters. We investigate the effects of strong correlation on the FFLO state in a d-wave superconductor within an integrated framework of Hartree-Fock-Bogoliubov theory and Gutzwiller approximation. Zeeman field causes a superconductor to undergo from BCS to FFLO and finally to a normal state with itinerant magnetism. We find that strong interaction enhances the phase space for the FFLO phase by shifting its boundaries significantly. With strong interaction, the density of states features a significantly sharper mid-gap peak in the FFLO phase creating strongly localized Andreev bound states. We discuss the fate of the FFLO phase in a competing ordered ground state (GS) by considering a GS with d-wave SC and antiferromagnetic (AFM) orders. Upon exposing such a GS to Zeeman field, we find that the FFLO modulation survives along with the AFM order with contrasting spatial features in the presence of strong correlation.