Superconductivity above 90 K in the square-planar compound system A${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6+\mathrm{x}}$ with A=Y, La, Nd, Sm, Eu, Gd, Ho, Er and Lu

We have found superconductivity in the 90-K range in A${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6+\mathrm{x}}$ with A=La, Nd, Sm, Eu, Gd, Ho, Er, and Lu in addition to Y. The results suggest that the unique square planar Cu atoms, each surrounded by four or six oxygen atoms, are crucial to the superconductivity of oxides in general. In particular, the high ${\mathrm{T}}_{\mathrm{c}}$ in A${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6+\mathrm{x}}$ is attributed mainly to the quasi two-dimensional assembly of the ${\mathrm{CuO}}_2$-Ba-${\mathrm{CuO}}_{2+\mathrm{x}}$-Ba-${\mathrm{CuO}}_2$ layers sandwiched between two A layers, with particular emphasis in the ${\mathrm{CuO}}_{2+\mathrm{x}}$ layers. Higher-${\mathrm{T}}_{\mathrm{c}}$ oxides are predicted for compounds with bigger assemblies of ${\mathrm{CuO}}_2$ layers coupled by Ba-layers.