  Perovskite rhodates are characterized by intermediate strengths of both
electronic correlation as well as spin-orbit coupling (SOC) and usually behave
as moderately correlated metals. A recent publication (Phys. Rev. B 95,
245121(2017)) on epitaxial SrRhO$_3$ thin films unexpectedly reported a
bad-metallic behavior and suggested the occurrence of antiferromagnetism below
100 K. We studied this SrRhO$_3$ thin film by hard x-ray photoemission
spectroscopy and found a very small density of states (DOS) at Fermi level,
which is consistent with the reported bad-metallic behavior. However, this
negligible DOS persists up to room temperature, which contradicts with the
explanation of antiferromagnetic transition at around 100 K. We also employed
electronic structure calculations within the framework of density functional
theory and dynamical mean-field theory. In contrast to the experimental
results, our calculations indicate metallic behavior of both bulk SrRhO$_3$ and
the SrRhO$_3$ thin film. The thin film exhibits stronger correlation effects
than the bulk, but the correlation effects are not sufficient to drive a
transition to an insulating state. The calculated uniform magnetic
susceptibility is substantially larger in the thin film than that in the bulk.
The role of SOC was also investigated and only a moderate modulation of the
electronic structure was observed. Hence SOC is not expected to play an
important role for electronic correlation in SrRhO$_3$.
