  In order to understand the material dependence of $T_c$ within the
single-layered cuprates, we study a two-orbital model that considers both
$d_{x^2-y^2}$ and $d_{z^2}$ orbitals. We reveal that a hybridization of
$d_{z^2}$ on the Fermi surface substantially affects $T_c$ in the cuprates,
where the energy difference $\Delta E$ between the $d_{x^2-y2}$ and $d_{z^2}$
orbitals is identified to be the key parameter that governs both the
hybridization and the shape of the Fermi surface. A smaller $\Delta E$ tends to
suppress $T_c$ through a larger hybridization, whose effect supersedes the
effect of diamond-shaped (better-nested) Fermi surface. The mechanism of the
suppression of d-wave superconductivity due to $d_{z^2}$ orbital mixture is
clarified from the viewpoint of the ingredients involved in the Eliashberg
equation, i.e., the Green's functions and the form of the pairing interaction
described in the orbital representation. The conclusion remains qualitatively
the same if we take a three-orbital model that incorporates Cu 4s orbital
explicitly, where the 4s orbital is shown to have an important effect of making
the Fermi surface rounded. We have then identified the origin of the material
and lattice-structure dependence of $\Delta E$, which is shown to be determined
by the energy difference $\Delta E_d$ between the two Cu3d orbitals (primarily
governed by the apical oxygen height), and the energy difference $\Delta E_p$
between the in-plane and apical oxygens (primarily governed by the interlayer
separation $d$).
