Electronic States and Excitation Spectra of Copper Oxides with Ladder and/or Chain

Recently the superconductivity has been reported in the copper oxides (Sr,Ca)$_{14}$Cu$_{24}$O$_{41}$ with ladders and edge-sharing chains under pressure. In order to understand the mechanism of the superconductivity, it is crucial to clarify the distribution of self-doped holes. From the analysis of the optical conductivity by ionic model and exact diagonalization method, we confirm that with substituting Ca for Sr, the self-doped holes are transferred from the chains to the ladders. We also examine the electronic states of edge-sharing chain in a variety of copper oxides, and derive the effective Hamiltonian. The dependences of the magnetic interactions between Cu ions and of the hopping energies of the Zhang-Rice singlet on the bond angle of Cu-O-Cu are discussed.