UTe$_2$: a narrow band superconductor

We investigate the nature of the 5$f$ electrons in the unconventional odd-parity superconductor UTe$_2$, focusing on the degree of covalency, localization versus itinerancy, and dominant electronic configuration. This is achieved using density functional theory (DFT) in combination with dynamical mean-field theory (DMFT) calculations. A key aspect of our approach is the material-specific tuning of the double-counting correction parameter, $\mu_{\rm dc}$, within the DFT+DMFT part. This tuning is guided by the energy dependence of photo-ionization cross-sections in valence band photoelectron spectroscopy. The reliability of the parameters is confirmed by the accurate reproduction of the angle-resolved valence-band photoemission spectra and the U 4$f$ core-level data. The DFT+DMFT model reveals that in UTe$_2$ U 5$f^n$ configurations with n=1 to 4 contribute to the ground state, with the 5$f^2$ configuration being most prevalent and an average 5$f$ shell fillings close to 2.5. The model further suggests that the 5$f$ electrons form narrow bands and that charge fluctuations due to degeneracy play a role in addition to coherent valence dynamics arising from hybridization with the conduction bath. Additionally, the significance of the U 6$d$ states in UTe$_2$ is discussed.