Theory of high temperature superconductivity based on Fermi liquid theory

Abstract

Starting with the Fermi liquid state, we explain the superconductivity in strongly correlated electron systems. For the overdoped cuprates we adopt the perturbation theory with respect to Coulomb repulsion U and obtain superconducting states of sufficiently strong correlation. For the optimally doped cuprates we use the fluctuation-exchange approximation (FLEX) describing the spin fluctuation and calculate the transition temperature to the superconductivity. For the underdoped ones we take into account the self-energy correction due to the strong superconducting fluctuations and successfully explain the pseudogap phenomena. In the underdoped case the imaginary part of the self-energy has a peak at the Fermi energy and its real part has a positive slope in the frequency dependence. These behaviors are opposite to those of the Fermi liquid and explain the reduced T-linear term of the specific heat. By including the self-energy correction, we obtain the reduced superconducting transition temperature. In this case also the renormalized quasi-particles play an essential role in realizing superconductivity. Even in the pseudogap region, there exist the quasi-particles at the Fermi energy, which give rise to the superconductivity through the gap equation.