It is found that particle pairing is nothing else but grouping in the statistical sense and that only in the particle–hole channel does the BCS Hamiltonian have the BCS solution for an attractive interaction, whereas the interaction in the particle–particle channel is still repulsive. A generalized perturbation approach beyond the random phase approximation (RPA), based on Ward's identity, was developed by the authors to deal with both weakly and strongly coupled electronic systems. The full summation of all of the possible Feynman diagrams of two-particle interaction guarantees its validity. A phase transition in this method is determined by instability of the normal state, often referred to as the pairing instability, but better to resonance of interaction, equivalent to the pole condition in the two-particle scattering amplitude. Of more importance and interest is that superconductivity, regardless of low or high temperature, is found to originate from the Coulomb correlations. It was shown that only if interaction in the particle–particle channel is repulsive may the instability occur and the irreducible response function, hence conductivity, tends to infinity as temperature approaches T c . The transition temperature T c is found to be related to the physical, chemical and structural parameters, such as the dielectric constant, concentration of carriers and interlayer spacing. Therefore, low- and high-temperature superconductivity do not have an intrinsic distinction but their observed different properties. An application of the approach to a layered two-dimensional system immediately leads to the metal–superconductor (MS) transition with a possible high transition temperature, while the MS transition in an isotropic three-dimensional system can never exhibit a high transition temperature.
Energy gaps in high-transition-temperature cuprate superconductors
