Justification of the effective fractional Coulomb energy and the extended Brinkman-Rice picture

Abstract

In order to calculate the effective mass of quasiparticles for a strongly correlated metallic system in which the number of carriers, n, is less than that of atoms (or lattices), l, the metallic system is averaged by one effective charge per atom over all atomc sites. The effective charge of carriers, <e>=(n/l)e={rho}e, and the on-site Coulomb repulsion, U={rho}^2<e^2/r>={rho}^2kU_c, are defined and are justified by means of measurement. {rho} is band filling and k is the correlation strength. The effective mass, m^*/m=1/(1-k^2{rho}^4), calculated by the Gutzwiller variational theory, is regarded as the average of the true effective mass in the Brinkman-Rice (BR) picture and is the effect of measurement. The true effective mass has the same value irrespective of {rho}, and is not measured experimentally. The true correlation strength of the BR picture is evaluated as 0.90<k_{BR}<1 for Sr_{1-x}La_xTiO_3 and 0.92<k_{BR}<1 for YBCO. High-Tc superconductivity for YBCO is attributed to the true effective mass caused by the large k_{BR} value. The effective mass explains the metal-insulator transition of the first order on band filling. Furthermore, the pseudogap is predicted in this system.