On Bogoliubov's method in superconductivity

Abstract

The Frolich Hamiltonian, with the addition of the electron-boson interaction of the fourth degree in fermion operators, is studied. The Hamiltonian takes into account the exchange interactions of the magnetic moments of the conduction electrons. The boson spectrum consists of the normal modes of coupled phonon-magnon oscillations. Using the Bogobliubov method in the theory of superconductivity and a generalized canonic transformation, a system of equations describing the mutual compensation of “dangerous” (i.e., leading to divergences) dingrams corresponding to the creation of two (bivertexes) and of four (tetravertexes) electron excitations from vacuum is obtained. The bivertex compensation equation, modified by a four-fermion interaction, indicates the possibility of an effective increase in the electron-boson coupling constant and an increase in the superconductive energy gap. Numerical investigation of the obtained system of equations was carried out. The considerable increase in the energy gap was revealed in comparison with the Frolich model.