In terms of the generalized Bardeen-Cooper-Schrieffer model for a superconductor with degenerate orbital electron states, we derive a Ginzburg-Landau energy functional with a microscopic deciphering of the coefficients involved. The superconducting order parameter is separated out by expanding the wave function of a Cooper pair in the basis functions of crystal point group irreducible representations. It is shown that a many-component superconducting order parameter may arise from the degeneracy of the electron states on the Fermi surface—either owing to the degeneracy of the orbital states or owing to the degeneracy over the arms of the star, or as a result of both degeneracies simultaneously. Allowance for the orbital degeneracy extends the physical basis on which superconducting modes are realized and perturbs the classification of singlet and triplet states according to even and odd point group representations. It is also shown that allowance for the orbital degeneracy may alter the conditions for the superconducting gap to go to zero in individual Fermi surface points or lines as compared with the conditions that follow from arm degeneracy alone.
An overview of the theoretical work on the problem of the influence of the antiferromagnetic ordering of localized spins on the superconducting state is provided. Effects of the exchange interaction of electrons with localized spins, are investigated. Separate treatment is given to the electron-magnon part of this interaction. The electron-magnon contribution is shown to affect both the singlet and triplet pairings. For different antiferromagnets — a collinear antiferromagnetic structure and a simple spiral structure — we investigate in detail the effect of the electron spectrum exchange readjustment due to the magnetic structure and analyse the relation of this effect to superconductivity. The influence of nonmagnetic impurities on the superconducting transition temperature in antiferromagnets is also noted. The entire treatment is carried out in terms of a unified approach of strong-coupling theory, by invoking the use of Eliashberg equations.
Many real systems possess a hidden degree of freedom /1 to 4/, which can be described as the nonfluctuating parameter in the vicinity of phase transition. Fisher /5/ stressed the importance of the constraint upon the hidden degree of freedom. Further it was found that the tricritical behaviour coincides with the critical behaviour of the ideal system provided 01 > 0 ( oc is the critical exponent of the specific heat) and with the renormalized one provided CY < 0 / 6 / . Recently there appeared some papers devoted to renormalization group consideration /7/ of systems with constrained nonfluctuating parameter /2, 4, 8/. The new tricritical behaviour was shown to be connected with the hidden variable instability, which appeared with the hidden variable susceptibility below zero.We consider the influence of disordering upon a system with hidden degree of freedom critical behaviour. Such disordering can be caused, e. g., by the presence of "frozen" impurities.is coupled with the scalar nonfluctuating order parameter y( 2) can be described in the momentum space by the effective Hamiltonian The disordered system in which an n-component vector order parameter $( 3 ) P Following the method of Lubensky /9/ the recursion relations for the potential averages over the probability distribution function can be constructed by averaging
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