Direct comparison of ARPES, STM, and quantum oscillation data for band structure determination in Sr$_2$RhO$_4$

Discrepancies in the low-energy quasiparticle dispersion extracted from angle resolved photoemission, scanning tunneling spectroscopy and quantum oscillation data are common and have long haunted the field of quantum matter physics. Here, we directly test the consistency of results from these three techniques by comparing data from the correlated metal Sr$_2$RhO$_4$. Using established schemes for the interpretation of the experimental data, we find good agreement for the Fermi surface topography and carrier effective masses. Hence, the apparent absence of such an agreement in other quantum materials, including the cuprates, suggests that the electronic states in these materials are of different, non-Fermi liquid like nature. Finally, we discuss the potential and challenges in extracting carrier lifetimes from photoemission and quasiparticle interference data.