Phase Transition in the Fulde–Ferrell–Larkin–Ovchinnikov States for the d-Wave Superconductor in the Two-Dimensional Orthorhombic Lattice

The Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state of a two-dimensional (2D) orthorhombic lattice superconductor is studied based on the Bogoliubov–de-Gennes equations. It is illustrated that the 2D FFLO state is suppressed and only the one-dimensional (1D) stripe state is stable. Our numerical results also reveal a phase transition with the stripe changing its orientation upon increasing the Zeeman field. A phase coexistence region exists with some local 2D features. The free energy is studied to elucidate the appearance of the FFLO state and the possible phase transition. The local density of states is calculated, which can be checked and compared with experiments in future.