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Bandwidth and Electron Correlation-Tuned Superconductivity in Rb$_{0.8}$Fe$_{2}$(Se$_{1-z}$S$_z$)$_2$

We present a systematic angle-resolved photoemission spectroscopy study of the substitution-dependence of the electronic structure of Rb$_{0.8}$Fe$_{2}$(Se$_{1-z}$S$_z$)$_2$ (z = 0, 0.5, 1), where superconductivity is continuously suppressed into a metallic phase. Going from the non-superconducting Rb$_{0.8}$Fe$_{2}$(Se$_{1-z}$S$_z$)$_2$ to superconducting Rb$_{0.8}$Fe$_{2}$Se$_2$, we observe little change of the Fermi surface topology, but a reduction of the overall bandwidth by a factor of 2 as well as an increase of the orbital-dependent renormalization in the $d_{xy}$ orbital. Hence for these heavily electron-doped iron chalcogenides, we have identified electron correlation as explicitly manifested in the quasiparticle bandwidth to be the important tuning parameter for superconductivity, and that moderate correlation is essential to achieving high $T_C$.