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In order to explore the reason why the single-layered cuprates,La$_{2-x}$(Sr/Ba)$_x$CuO$_4$ ($T_c\simeq$ 40K) and HgBa$_2$CuO$_{4+\delta}$($T_c\simeq$ 90K), have such a significant difference in $T_c$, we study atwo-orbital model that incorporates the $d_{z^2}$ orbital on top of the$d_{x^2-y^2}$ orbital. It is found, with the fluctuation exchangeapproximation, that the $d_{z^2}$ orbital contribution to the Fermi surface,which is stronger in the La system, works against d-wave superconductivity,thereby dominating over the effect of the Fermi surface shape. The resultresolves the long-standing contradiction between the theoretical results onHubbard-type models and the experimental material dependence of $T_c$ in thecuprates.

physical review letters

Two-Orbital Model Explains the Higher Transition Temperature of the  Single-Layer Hg-Cuprate Superconductor Compared to That of the La-Cuprate  Superconductor