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Delafossite PdCrO$_2$ is an intriguing material which displays nearly-freeelectron and Mott insulating behaviour in different layers. Both angle-resolvedphotoemission spectroscopy (ARPES) and Compton scattering measurements haveestablished a hexagonal Fermi surface in the material's paramagnetic phase.However, the Compton experiment detected an additional structure in theprojected occupancy which was originally interpreted as an additional Fermisurface feature not seen by ARPES. Here, we revisit this interpretation of theCompton data. State-of-the-art density functional theory (DFT) with dynamicalmean field theory (DMFT), the so-called DFT+DMFT method, predicts the Mottinsulating state along with a single hexagonal Fermi surface in excellentagreement with ARPES and Compton. However, DFT+DMFT fails to predict theintensity of the additional spectral weight feature observed in the Comptondata. We infer that this discrepancy may arise from the DFT+DMFT not being ableto correctly predict certain features in the shape and dispersion of theunoccupied quasiparticle band near the Fermi level. Therefore, a theoreticaldescription beyond our DFT+DMFT model is needed to incorporate vital electroninteractions, such as inter-layer electron coupling interactions which forPdCrO$_2$ gives rise to the Kondo-like so-called intertwined excitation.

Impact of electron correlations on the $\mathbf{k}$-resolved electronic structure of PdCrO$_{2}$ revealed by Compton scattering