  How out-of-plane disorder affects the electronic structure has been
investigated for the single-layer cuprates
Bi$_2$Sr$_{1.6}$$Ln$$_{0.4}$CuO$_{6+\delta}$ ($Ln$ = La, Nd, Gd) by
angle-resolved photoemission spectroscopy. We have observed that, with
increasing disorder, while the Fermi surface shape and band dispersions are not
affected, the quasi-particle width increases, the anti-nodal gap is enhanced
and the superconducting gap in the nodal region is depressed. The results
indicate that the superconductivity is significantly depressed by out-of-plane
disorder through the enhancement of the anti-nodal gap and the depression of
the superconducting gap in the nodal region.
