Eur. Phys. J. B 65, 29-38 (2008)
https://doi.org/10.1140/epjb/e2008-00328-1

A superconductor with 4-fermion attraction weakly perturbed by magnetic impurities

Instytut Fizyki, Uniwersytet M. Kopernika, ul. Grudziądzka 5, 87-100 Torun, Poland

Corresponding author: ^a dawid.borycki@fizyka.umk.pl

Received: 26 March 2008
Published online: 22 August 2008

Abstract

A superconductor with 4-fermion attraction, considered by Maćkowiak and Tarasewicz is modified by adding to the Hamiltonian a long-range magnetic interaction V between conduction fermions and localized distinguishable spin 1/2 magnetic impurities. V has the form of a reduced s-d interaction. An upper and lower bound to the system's free energy density is derived and the two bounds are shown to coalesce in the thermodynamic limit. The resulting mean-field equations for the gap Δ and a parameter y, characterizing the impurity subsystem are solved and the solution minimizing f is found for various values of magnetic coupling constant g and impurity concentration. The phase diagrams of the system are depicted with five distinct phases: the normal phase, unperturbed superconducting phase, perturbed superconducting phase with nonzero gap in the excitation spectrum, perturbed gapless superconducting phase and impurity phase with completely suppressed superconductivity.