c-axis oxygen in copper oxide superconductors

Exploration of the roles of c-axis oxygen in the copper-oxide superconductors has revealed a new type of tetragonal-orthorhombic transition in the system ${\mathit{R}}_{2\mathrm{-}\mathit{z}}$ ${\mathrm{Ce}}_{\mathit{z}}$ ${\mathrm{Ba}}_{2\mathrm{-}\mathit{y}}$ ${\mathit{L}}_{\mathit{y}}$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{8+\mathit{x}}$(R=Nd or Gd, L=La or Nd) and one probably due to cluster rotation in fluorinated ${\mathrm{La}}_{2\mathrm{-}\mathit{y}}$ ${\mathrm{Dy}}_{\mathit{y}}$ ${\mathrm{CuO}}_{4\mathrm{-}\mathit{x}}$ ${\mathrm{F}}_{2\mathit{x}}$ having the ${\mathit{T}}^{\mathrm{*}}$ structure with interstitial F ordered in the rocksalt layer. The former is due to c-axis ionic displacements that relieve a compressive stress on the (Ba,L)O rocksalt sheets, the latter a tensile stress on the LaO rocksalt sheets. In the ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6+\mathit{x}}$ structure, the c-axis oxygen participates in oxygen diffusion in the superconductively inactive layers, they act as gates for stabilizing holes in Cu(1)${\mathrm{O}}_{\mathit{x}}$ planes versus ${\mathrm{CuO}}_2$ sheets, and they modulate the width W of the ${\mathrm{\sigma }}_{\mathit{x}}^2$-${\mathit{y}}^{2\mathrm{*}}$ conduction band. These modulations are shown to be capable of changing the bandwidth from W<U to W>U and hence to provide a rationalization for the nonsuperconducting metallic copper oxides containing copper in a formal valence state greater than 2+. As modulators of bandwidth, their displacements offer electron-lattice interactions for pairing superconductive holes. In the n-type superconductors, interstitial c-axis oxygen perturbs the ${\mathrm{\sigma }}_{\mathit{x}}^2$-${\mathit{y}}^{2\mathrm{*}}$ band so as to introduce localized states at the band edges that suppress superconductivity.