Phase diagrams for two-component D-wave fermion superfluids with density imbalance

Abstract

Abstract Finite-temperature phase structures for asymmetric two-component D-wave fermion superfluids in the weak coupling BCS regime are investigated. The Fulde–Ferrell–Larkin-Ovchinnikov (FFLO) state becomes non-degenerate with the orientation of Cooper pair momentum due to the anisotropic pairing gap for D-wave pairing. The new parameter θ 0, corresponding to the orientation of Cooper pair momentum, greatly enriches the phase structures. Especially, the phase separation (PS) region in the phase diagram is significantly reduced comparing to that for S-wave pairing. Theoretically, the stability condition of solutions is equivalent to the positive definite Hessian matrix of free energy in the hyperplane defined by the number density constraints in the parameter space spanned by the average chemical potential μ, relative chemical potential h, paring gap Δ, pair momentum q, and θ 0. In addition, the stability condition of the superfluid density is essentially included in the positive definite Hessian matrix. Moreover, the positiveness of imbalance number susceptibility D δ ρ / D h is always equivalent to the positiveness of the smaller eigenvalue λ − of the number susceptibility matrix. While the criteria ∂2Ω/∂Δ2 and ∂ 2 Ω ∂ Δ 2 ∂ 2 Ω ∂ q 2 − ∂ 2 Ω ∂ Δ ∂ q 2 against PS in previous studies are equivalent to λ − only under the prerequisite that the solution is a local minimum in the corresponding hyperplane.