The β decay of the semimagic Sn isotopes 136,137,138 Sn has been studied at the Radioactive Isotope Beam Factory at the RIKEN Nishina Center. The first experimental information on excited states was obtained for 137 Sb while, in the case of 136 Sb, the established excitation scheme could be extended by ten previously unidentified levels. In the decay of the most-neutron-rich isotope 138 Sn, two γ rays were observed for the first time. The new experimental results, in combination with state-of-the-art shell-model calculations, provide the first information with respect to the evolution of the 0g 7/2 and 1d 5/2 proton single-particle states with increasing neutron number beyond N = 84.