  A comprehensive angle resolved photoemission spectroscopy study of the band
structure in single layer cuprates is presented with the aim of uncovering
universal trends across different materials. Five different hole- and
electron-doped cuprate superconductors
(La$_{1.59}$Eu$_{0.2}$Sr$_{0.21}$CuO$_4$, La$_{1.77}$Sr$_{0.23}$CuO$_4$,
Bi$_{1.74}$Pb$_{0.38}$Sr$_{1.88}$CuO$_{6+\delta}$,
Tl$_{2}$Ba$_{2}$CuO$_{6+\delta}$, and
Pr$_{1.15}$La$_{0.7}$Ce$_{0.15}$CuO$_{4}$) have been studied with special focus
on the bands with predominately $d$-orbital character. Using light polarization
analysis, the $e_g$ and $t_{2g}$ bands are identified across these materials. A
clear correlation between the $d_{3z^2-r^2}$ band energy and the apical oxygen
distance $d_\mathrm{A}$ is demonstrated. Moreover, the compound dependence of
the $d_{x^2-y^2}$ band bottom and the $t_{2g}$ band top is revealed. Direct
comparison to density functional theory (DFT) calculations employing hybrid
exchange-correlation functionals demonstrates excellent agreement. We thus
conclude that the DFT methodology can be used to describe the global band
structure of overdoped single layer cuprates on both the hole and electron
doped side.
