Thermodynamic Green functions in theory of superconductivity

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.

Iron-Based Superconductors

“…The iron-based superconductors (FebSc) have many different systems that greatly enlarge the family of unconventional superconductors [32]. The first FebSc system LaFePO 1Àx F x was discovered by H. Hosono et al in 2006 with Tc$4K, but it did not draw much attention until the same group substituted P by As and discovered a Tc of 26K in LaFeAsO 1Àx F x in 2008.…”

Two-time Green’s functions in superconductivity theory

“…Eliashberg-type equations can also be easily obtained in the method of two-time GFs by differentiating them with respect to the two times [8], [9]. This then leads to an exact Dyson equation for a matrix GF with the self-energy operator given by the multiparticle GF, calculating which in the approximation of noncrossing diagrams leads to the system of Eliashberg equations.…”

“…In this paper, we formulate a general superconductivity theory based on the method of the equations of motion for GFs [9]. We consider different types of the interaction leading to pairing: the electronphonon interaction, scattering on spin fluctuations, and the kinematic interaction due to strong Coulomb correlations in the Hubbard model.…”

Двухвременные Функции Грина В Теории Сверхпроводимости

“…Уравнения типа Элиашберга можно легко получить и в методе двухвременных ФГ с помощью дифференцирования их по двум временам [8], [9]. При этом возникает точное уравнение Дайсона для матричной ФГ с массовым оператором в виде многочастичной ФГ, вычисление которой в приближении непересекающихся диаграмм приводит к системе уравнений Элиашберга.…”

“…В настоящей работе на основе метода уравнений движений для ФГ формулируется общая теория сверхпроводимости [9]. Мы рассматриваем различные типы взаимодействия, приводящие к спариванию: электронно-фононное взаимодействие, рассеяние на спиновых флуктуациях или кинематическое взаимодействие, обусловленное сильными кулоновскими корреляциями в модели Хаббарда.…”