The electronic entropy of superconducting cuprates includes crucial information on the metallic state. In this context the electronic entropy of cuprates is calculated for the ${\mathrm{CuO}}_2$ layer in order to clarify the features of metallic states. It is shown that the observed peculiar doping dependence of electronic entropy can be explained by the Kamimura-Suwa model without introducing the pseudogap concept, while an ordinary band structure gives too small values even in the overdoped region. It is also shown that the observed anomalous behaviors in normal-state properties of cuprates such as resistivity and the Hall effect are explained by the Kamimura-Suwa model. From these results it is suggested that the hole carriers in cuprates form a metallic state by taking the Zhang-Rice singlet and Hund’s coupling triplet alternately in the presence of the local antiferromagnetic ordering.

In 1986 Bednorz and Műller discovered high temperature superconductivity in copper oxides by chemically doping holes into La₂CuO₄ (LCO), the antiferromagnetic insulator. Despite intense experimental and theoretical research during the past 34 years, no general consensus on the electronic-spin structures and the origin of pseudogap has been obtained. In this circumstance, we performed a first-principles calculation of underdoped cuprate superconductors La_2-xSr_xCuO₄ (LSCO) within the meta-generalized gradient approximation of the density functional theory. Our calculations clarify first the important role of the anti Jahn-Teller (JT) effect, the backward deformation against the JT distortion in La₂CuO₄ by doping extra holes. The resulting electronic structure agrees with the two-component theory provided by the tight-binding model of Kamimura and Suwa (K-S), which has been also used to elucidate the d-wave superconductivity. Our first-principles calculation thus justifies the K-S model and demonstrates advanced understanding of cuprates. For example, the remarkable feature of our calculations is the appearance of the spin-polarized band with a nearly flat-band character, showing the peaky nature in the density of states at the Fermi level.