%0 Journal Article %T Orbital mixture effect on the Fermi surface-$T_c$ correlation in the cuprate superconductors --- bilayer vs single layer %A Hirofumi Sakakibara %A Katsuhiro Suzuki %A Hidetomo Usui %A Satoaki Miyao %A Isao Maruyama %A Koichi Kusakabe %A Ryotaro Arita %A Hideo Aoki %A Kazuhiko Kuroki %J Physics %D 2014 %I arXiv %R 10.1103/PhysRevB.89.224505 %X By constructing $d_{x^2-y^2}-d_{z^2}$ two-orbital models from first principles, we have obtained a systematic correlation between the Fermi surface warping and the evaluated $T_c$ for various bilayer as well as single-layer cuprates. This reveals that smaller mixture of the $d_{z^2}$ orbital component on the Fermi surface leads to both of larger Fermi surface warping and higher $T_c$. The theoretical correlation strikingly resembles a systematic plot for the experimentally observed $T_c$ against the Fermi surface warping due to Pavarini {\it et al.} [Phys. Rev. Lett. {\bf 87}, 047003 (2001)], and the present result unambiguously indicates that the $d_{z^2}$ mixture is a key factor that determines $T_c$ in the cuprates. %U http://arxiv.org/abs/1403.2497v3