BCS–BEC Crossover in Two-Dimensional Attractive Hubbard Model under Magnetic Field
The Bardeen–Cooper–Schrieffer (BCS)–Bose–Einstein condensation (BEC) crossover in the two-dimensional attractive Hubbard model under the magnetic field is discussed at the half-filling at T = 0 K on the basis of the formalism of Eagles and Leggett. It is shown that the so-called Fulde–Ferrel–Larkin–Ovchinikov (FFLO)-like state with a non-zero center-of-mass wave vector q ≠ 0 is not stabilized in the weak-coupling (BCS) region, while such a state with q ≠ 0 is stabilized against that with q = 0 even in a wide strong-coupling (BEC) region where di-fermion molecules are formed. The physical implication of this surprising result is discussed.