Fermi surface and superconducting gap in superstructure-free ${\mathrm{Bi}}_{1.80}{\mathrm{Pb}}_{0.38}{\mathrm{Sr}}_{2.01}{\mathrm{CuO}}_{6-\delta }$

We report an ultrahigh-resolution angle-resolved photoemission spectroscopy on superstructure-free ${\mathrm{Bi}}_{1.80}{\mathrm{Pb}}_{0.38}{\mathrm{Sr}}_{2.01}{\mathrm{CuO}}_{6-\delta }$ with various hole concentrations. The Fermi surface retains a holelike character centered at (π, π) from under- to overdoping. The superconducting gap exhibits a $d_{x^2-y^2}$-like anisotropy with a typical gap value of 10–15 meV near (π, 0). Comparison with ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_8$ shows that the size of the superconducting gap and the energy of the hump structure near $E_F$ are well scaled with the maximum $T_c{(T}_c^{\max }).\mathrm{}$ This suggests that the superconducting properties are essentially characterized by $T_c^{\max }$ irrespective of the number of ${\mathrm{CuO}}_2$ layers or the BiO superstructure.