Abstract
A general theory of superconductivity is formulated within the thermodynamic Green function method for various types of pairing mediated by phonons, spin fluctuations, and strong Coulomb correlations in the Hubbard and t-J models. A rigorous Dyson equation for matrix Green functions is derived in terms of a self-energy as a many-particle Green function. By applying the noncrossing approximation for the self-energy, a closed selfconsistent system of equations is obtained, similar to the conventional Eliashberg equations. A brief discussion of superconductivity mediated by kinematic interaction with an estimation of a superconducting transition temperature in the Hubbard model is given.
Highlights
Thermodynamic, retarded and advanced Green functions (GFs) introduced by Bogoliubov and Tyablikov in a seminal work [1] was used soon afterwards in the studies of superconductivity within the Bardeen-Cooper-Schrieffer (BCS) model [2] as discussed by Zubarev in his famous review on the double-time GF in the statistical physics [3]
Zubarev formulated a theory of superconductivity for an electron-phonon system based on the equation of motion method for GFs [4]
In Zubarev formulation based on a subsequent differentiation of GFs over the same time, it is impossible to employ the skeleton diagram technique
Summary
Thermodynamic, retarded and advanced Green functions (GFs) introduced by Bogoliubov and Tyablikov in a seminal work [1] was used soon afterwards in the studies of superconductivity within the Bardeen-Cooper-Schrieffer (BCS) model [2] as discussed by Zubarev in his famous review on the double-time GF in the statistical physics [3]. By differentiating the GFs over two times, this problem can be solved and the Eliashberg type equations can be formulated in a very simple and transparent way for any model of electronboson interaction as was shown by Vujicic et al [6] This method within the Mori-type projection technique was used later in order to study superconductivity in the t-J model [7,8,9] and the Hubbard model [10]. In the present paper we give a general formulation of a theory of superconductivity by applying the equation of motion method to the thermodynamic GFs. We consider several models where superconducting pairing is mediated by electron-phonon and spin-fluctuation interactions, or by a kinematic interaction originating from strong Coulomb correlations, as in the Hubbard and t-J models.
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