Theory of Superconductivity of Electron System Containing Singlet and Triplet Pairs

Abstract

AbstractThe general case of a superconductor with singlet and triplet pairs is investigated. The method uses the B‐operators for creation and annihilation of singlet and triplet pairs, and A‐operators for interchange of multiplicity of these pairs [1, 2]. The theory utilises the properties resulting from the symmetry type of the electron‐pair wave function which do not involve the conventional assumptions regarding the dependence of the matrix element Vχ, χ on the vectors χ and χ′. A more general form of electron‐pair Hamiltonian is proposed which includes both the previously discussed [7] exchange terms and those due to the alternation of electron‐pair multiplicity. The variational problem for the coexistence of singlet and triplet pairs is solved. The trial wave functions are established both from the properties of the B‐operator and the generalized unitary Yosida operator [6] for singlet and triplet pairs. The physical significance of the limitations imposed in [8, 9] on the solutions of the super‐conductive problem with triplet pairs is clarified. The distribution functions are established for the different types of pairs and it is shown that the solutions for an isotropic gap may correspond to an anisotropic distribution of these pairs. The properties of a superconductor at non‐zero temperature are investigated using both the method of double‐time Green's functions and the method of variation of the thermodynamic potential with the interaction parameter. Some modifications are considered which allow an analysis of the problem by quantum‐field techniques.