  We present an angle-resolved photoemission spectroscopy study of the
single-layer T*-type structured cuprate SmLa$_{1-x}$Sr$_x$CuO$_4$ with unique
five-fold pyramidal oxygen coordination. Upon varying oxygen content,
T*-SmLa$_{1-x}$Sr$_x$CuO$_4$ evolved from a Mott-insulating to a metallic state
where the Luttinger sum rule breaks down under the assumption of a large
hole-like Fermi surface. This is in contrast with the known doping evolution of
the structural isomer La$_{2-x}$Sr$_x$CuO$_4$ with six-fold octahedral
coordination. In addition, quantitatively characterized Fermi surface suggests
that the empirical $T_\mathrm{c}$ rule for octahedral oxygen-coordination
systems does not apply to T*-SmLa$_{1-x}$Sr$_x$CuO$_4$. The present results
highlight unique properties of the T*-type cuprates possibly rooted in its
oxygen coordination, and necessitate thorough investigation with careful
evaluation of disorder effects.
