BCS-BEC Crossover in Two-Dimensional Attractive Hubbard Model under Magnetic Field

TL;DR

This paper investigates the BCS-BEC crossover in a two-dimensional attractive Hubbard model under magnetic field at zero temperature, revealing the stability conditions of FFLO-like states across coupling regimes.

Contribution

It demonstrates that FFLO-like states with non-zero momentum are not stabilized in weak coupling but are stabilized in strong coupling, which is a novel insight.

Findings

FFLO-like states are not stabilized in weak-coupling (BCS) region.

FFLO-like states are stabilized in strong-coupling (BEC) region.

Surprising stability of non-zero momentum states in strong coupling.

Abstract

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-like state with a non-zero center-of-mass wave vector ${\bf q}\not=0$ is not stabilized in the weak-coupling (BCS) region, while such a state with ${\bf q}\not=0$ is stabilized against that with ${\bf q}=0$ even in a wide strong-coupling (BEC) region where di-fermion molecules are formed. The physical implication of this surprising result is discussed.