Thermodynamic Functions of Fermi Gas with Quadruple BCS-Type Binding Potential with d_{x^2 - y^2 } -Wave-Pairing Symmetry

A gas of spin 1/2 fermions with an interaction V+W = -|Λ|^-1 ∑_k,k′ g _k,k′χ(k)χ(k′) $b_{\text{k}}^{\text{*}} b_{ - {\text{k}}}^{\text{*}}$ b _k′ b _-k′ - 2γ ∑_kχ(k)n _k+ n _k-, where n _k± = $a_{{\text{k}} \pm }^{\text{*}}$ a _k±, b _k = a _k+ a _k- and a _kσ, $a_{{\text{k'}}\sigma '}^{\text{*}}$ satisfy Fermi anticommutation relations, is investigated in the $d_{x^2 - y^2}$ -pairing case. W+V₄ is nonzero only within a thin layer of one-fermion energies around the chemical potential μ, and χ(k) denotes the characteristic function of the corresponding range of momenta. Two cases are studied: 1⁰ γ = 0, 2⁰ γ = 0.10025 eV. In the first case the system exhibits a first order transition, in the second, the transition is second order. Temperature dependence of the system's thermodynamic functions is examined and compared with that of the s-pairing case.