The spin-imbalanced attractive Hubbard model in [formula omitted]: Phase diagrams and BCS–BEC crossover at low filling

Abstract

We study the superconducting properties of the spin-imbalanced attractive Hubbard model (AHM) in the presence of a Zeeman magnetic field, using the broken symmetry Hartree approximation, mostly in the low density case. The evolution from the weak coupling (BCS-like limit) to the strong coupling limit of tightly bound local pairs (LP) with increasing attraction, at T=0 is investigated for d=3, both for the case of a fixed chemical potential and for a fixed number of particles. Also the influence of the spin-dependent Hartree term on the phase diagrams at T≠0 at weak coupling is studied and reentrant transition is found, which is demonstrated in the temperature characteristics of the order parameter and magnetization. The BCS–BEC crossover diagrams in the presence of a Zeeman magnetic field in three dimensions for simple cubic (sc) lattice are investigated and the results are compared with those obtained in the other lattice geometries. For strong attraction and in the dilute limit, the homogeneous magnetized superconducting phase (SCM) and the tricritical point are found in the (h−μ) and (h−n) diagrams. Next, we construct the finite temperature phase diagrams at weak and strong couplings in d=3 and for symmetric hopping parameters (t↑=t↓), going beyond the standard mean field approximation. The critical temperatures of the superconducting transition are determined within the self-consistent T-matrix approach. We perform a comparison of the results obtained from the (GG0)G0 and (GG)G0 T-matrix schemes, both for the AHM at fixed low electron concentration on an sc lattice and for the 3D continuum model of a dilute gas of fermions with contact attraction. A generalization of the Tc equations for the AHM in non-zero Zeeman magnetic field case is discussed and detailed numerical solutions to these generalized equations are shown. An interesting result is that a spin polarized superfluid state with a gapless region for the majority spin species can be stable in the strong coupling regime. The influence of spin dependent hopping integrals (mass imbalance) (t↑≠t↓) on the stability of the SCM phase is also studied. We also analyze the influence of the Hartree term on the BCS–BEC crossover diagrams in magnetic field and show that the presence of such a term restricts the range of the occurrence of the SCM phase.