  Iron-chalcogenide superconductors display rich phenomena caused by
orbital-dependent band shifts and electronic correlations. Additionally, they
are potential candidates for topological superconductivity due to the band
inversion between the Fe $d$ bands and the chalcogen $p_z$ band. Here we
present a detailed study of the electronic structure of the nematic
superconductors FeSe$_{1-x}$Te$_x$ ($0<x<0.4$) using angle-resolved
photoemission spectroscopy to understand the role of orbital-dependent band
shifts, electronic correlations and the chalcogen band. We assess the changes
in the effective masses using a three-band low energy model, and the band
renormalization via comparison with DFT band structure calculations. The
effective masses decrease for all three-hole bands inside the nematic phase
followed by a strong increase for the band with $d_{xy}$ orbital character.
Interestingly, this nearly-flat $d_{xy}$ band becomes more correlated as it
shifts towards the Fermi level with increasing Te concentrations and as the
second superconducting dome emerges. Our findings suggests that the $d_{xy}$
hole band, which is very sensitive to the chalcogen height, could be involved
in promoting an additional pairing channel and increasing the density of states
to stabilize the second superconducting dome in FeSe$_{1-x}$Te$_x$. This
simultaneous shift of the $d_{xy}$ hole band and enhanced superconductivity is
in contrast with FeSe$_{1-x}$S$_x$.
