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, $μ{\rm dc}$, 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.

💡 Research Summary

This paper presents a comprehensive investigation of the electronic structure of the unconventional odd‑parity superconductor UTe₂, focusing on the degree of covalency, the itinerant versus localized nature of the U 5f electrons, and the dominant valence configuration. The authors combine density‑functional theory (DFT) with dynamical mean‑field theory (DMFT) and introduce a material‑specific tuning of the double‑counting correction μ_dc. The tuning is guided by the photon‑energy dependence of photo‑ionization cross‑sections measured in valence‑band photoelectron spectroscopy (PES). By adjusting μ_dc to reproduce both hard‑X‑ray (hν = 6000 eV) and soft‑X‑ray (hν ≈ 800 eV) PES spectra, they determine an optimal value of μ_dc = 4.75 eV. This value yields an excellent agreement with experimental valence‑band features (labeled A–D) and is highly sensitive: small deviations lead to noticeable mismatches in peak intensities and positions.

The DFT calculations employ the local‑density approximation with spin‑orbit coupling for the experimentally determined orthorhombic structure. A tight‑binding Hamiltonian including U 5f, 7s, 7p, 6d and Te 5s, 5p orbitals is constructed. Local Coulomb interactions on the U 5f shell are introduced with Hubbard U = 3 eV and Hund’s J = 0.59 eV, and the impurity problem is solved by continuous‑time quantum Monte Carlo (CT‑QMC) retaining only density‑density terms. After self‑consistency, the self‑energy is analytically continued via the maximum‑entropy method to obtain spectral functions.

The resulting density of states shows that the U 5f states form an extremely narrow band within ~‑0.2 eV to 0.5 eV around the Fermi level, reproducing the flat low‑energy feature observed in angle‑resolved PES (ARPES). In contrast, the strongly dispersive bands along the Γ–Z–X₁ direction up to ~1 eV are dominated by hybridized U 6d and Te 5p states, while the narrow 5f‑derived feature contributes a small but distinct weight near the Fermi level. This demonstrates that the 5f electrons are neither fully localized nor completely itinerant; they retain a narrow‑band character while being strongly hybridized with the conduction bath.

A quantitative analysis of the many‑body configuration weights reveals contributions from U 5fⁿ (n = 1–4) configurations, with the 5f² configuration being the most prevalent (~45 %). The average 5f occupation ⟨n_f⟩ ≈ 2.5 indicates a mixed‑valence ground state, consistent with earlier resonant inelastic X‑ray scattering (RIXS) observations of 5f² multiplet excitations. The mixed‑valence character is further corroborated by the successful reproduction of the U 4f core‑level spectra. By incorporating a core‑valence interaction U_fc = 5.0 eV in the impurity Hamiltonian, the calculated main line and satellite match the experimental hard‑X‑ray photoemission data, and the line shape is highly sensitive to both μ_dc and U_fc.

The authors also compute the time‑dependent charge‑correlation function C(τ), which reveals significant charge fluctuations arising from the coexistence of multiple 5f configurations. These fluctuations coexist with the coherent valence dynamics generated by hybridization, underscoring the dual nature of the 5f electrons in UTe₂.

In summary, the study (i) demonstrates that a material‑specific double‑counting correction, calibrated against photon‑energy‑dependent PES, enables DFT + DMFT to faithfully reproduce valence‑band, ARPES, and core‑level spectra of a strongly correlated actinide; (ii) establishes that UTe₂ hosts a mixed‑valence 5f shell with ⟨n_f⟩ ≈ 2.5, dominated by the 5f² configuration; (iii) shows that the 5f electrons form narrow bands that hybridize strongly with U 6d and Te 5p states, leading to both charge‑fluctuation and coherent hybridization effects; and (iv) provides a solid electronic‑structure foundation for interpreting the unconventional spin‑triplet superconductivity and its extreme upper critical fields observed in UTe₂.