By employing a model of a two-dimensional d-wave superconductor, we investigate the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state under the influence of a Zeeman field and antiferromagnetic order. Through self-consistent solutions to the Bogoliubov–de Gennes equations, we derive the spatial distributions of the superconducting order parameter and magnetization, thereby revealing the interplay between antiferromagnetic and superconducting orders. The local density of states is computed to characterize low-energy excitations and the formation mechanism of the FFLO state. Our results show that the coexistence of antiferromagnetic and superconducting orders gives rise to a spatially modulated FFLO state, where the competition between these two orders significantly influences the spatial patterns of the order parameters and magnetic properties. These findings offer insights into the complex interplay between magnetism and superconductivity in strongly correlated systems, emphasizing the role of external fields and magnetic order in stabilizing exotic superconducting phases.
Liu et al. (Mon,) studied this question.