Electronic structure of La_{4}BaCu_{5}O_{13-x}

Although ${\mathrm{La}}_4$ ${\mathrm{BaCu}}_5$ ${\mathrm{O}}_{13\mathrm{-}\mathrm{x}}$ is metallic and chemically and structurally similar to known high-$T_c$ copper-oxide superconductors, it is not superconducting above 5 K, at least for the observed values of x slightly above and below 0. In order to explore possible reasons why this material is not a high-$T_c$ superconductor, we carried out detailed energy-band calculations. Even though the Cu-O network of ${\mathrm{La}}_4$ ${\mathrm{BaCu}}_5$ ${\mathrm{O}}_{13\mathrm{-}\mathrm{x}}$ may be regarded as an array of one-dimensional (1D) strands, we find that the interstrand coupling is actually sufficiently strong to make the band structure more nearly 3D than 1D in the neighborhood of the Fermi level. Since the band structures of known high-$T_c$ copper-oxide superconductors have features which are distinctly 1D and/or 2D, the absence of superconductivity in ${\mathrm{La}}_4$ ${\mathrm{BaCu}}_5$ ${\mathrm{O}}_{13\mathrm{-}\mathrm{x}}$ might be due to the predominantly 3D band structure of samples studied so far, for which x≠0. Our studies suggest that nested 1D bands separated by a reduced wave vector can be introduced on the Fermi surface by using samples with x=0. If low dimensionality is indeed a significant factor, there is a chance that stoichiometric ${\mathrm{La}}_4$ ${\mathrm{BaCu}}_5$ ${\mathrm{O}}_{13}$ could also be a high-$T_c$ superconductor.