Correlation-driven enhancement of pairing in a nematic Hund's metal

The gist: Dynamical correlation effects beyond a quasiparticle-only description are essential to capture the robustness of superconductivity in the Hund regime

Normal-state coherence in the tetragonal and nematic phase

The study begins by characterizing the correlated nematic normal state from which superconductivity emerges The evolution of normal-state orbital quasiparticle weights Zµ across the interaction range shows that at low JH/U, nematicity triggers a strongly orbital-selective coherence collapse, leading to an orbital-selective Mott (OSM) response At large JH/U, in contrast, Hund’s exchange strongly supports metallic behavior across orbitals: even in the presence of η > 0 the orbital-selective coherence collapse is strongly softened, and metallicity is retained in all orbitals, with a sizable orbital differentiation of the Zµ The corresponding occupations reveal that at low JH/U this nematic-driven charge reorganization is strongly amplified as U increases, driving two of the three orbitals toward (near) half filling while the other becomes correspondingly depleted or filled; this reorganization results in the OSM regime observed for the QP weights in Fig. 1(a)

Spectral evolution and orbital anisotropy in the nematic Hund’s metal

The spectral functions show that at low JH/U, panel (c), the nematic perturbation predominantly produces a relatively rigid differentiation of the xz/yz spectra around the Fermi level In contrast, in the Hund regime, panel (d), the nematic differentiation becomes strongly frequency dependent: the xz–yz imbalance evolves non-trivially with ω, with a frequency-modulated orbital redistribution of the nematic spectral weight This is already visible in the xz/yz line shapes and is emphasized by the spectral asymmetry ratio R∆(ω) In contrast to the low-JH/U case, panel (d), the nematic differentiation becomes strongly frequency dependent: the xz–yz imbalance evolves non-trivially with ω, with a frequency-modulated orbital redistribution of the nematic spectral weight

Superconductivity in the correlated nematic state

The robustness of the DMFT SC solution is not controlled by coherent quasiparticles Zµ In the Hund regime, the gaps remain finite and sizable even when the corresponding quasiparticle weights are strongly suppressed Specifically at large U and sizable η, the xy orbital can become essentially incoherent (Zxy → 0) while the SC solution still yields a finite ∆xy across the whole explored nematic range This phenomenology persists across the full nematic range η and directly extends to the nematic Hund metal beyond-Z robustness of the SC solution previously identified in the tetragonal case in [15]

Cutoff dependence: spectral filtering in the nematic Hund metal

The cutoff acts as a genuinely orbital-selective spectral filter, admitting distinct combinations of coherent and incoherent spectral contributions depending on its value In Fig. 5, the buildup with ω0 is nontrivial and orbital dependent: the finite-ω0 evolution need not follow a simple monotonic approach to the ω0 → ∞ plateaus, and the hierarchy at small cutoff can differ from the asymptotic hierarchy Diagnostics based on the nematic gap anisotropy R∆(ω0) and the spectral-window anisotropy RW (ω0) show that Hund correlations reorganize the energy distribution of the xz/yz imbalance for ω < ω0, yielding a reduced and strongly cutoff-dependent nematic gap anisotropy

Conclusions

Hund physics protects superconductivity in the nematic state by suppressing extreme nematic-driven charge polarization and coherence collapse at large U The pairing window matters, as varying the pairing cutoff ω0 provides a controlled probe of which frequency sectors of the dressed spectrum effectively enter the Cooper kernel This result provides a simple lens to interpret why different materials, or different tuning parameters within the same family, can exhibit distinct nematic gap structures despite sharing a similar Hund-correlated normal state

How it works

1. Dynamical correlation effects beyond a quasiparticle-only description are essential to capture the robustness of superconductivity in the Hund regime.

2. Hund correlations play a dual role in the nematic superconductor: they amplify the nematic orbital differentiation of pairing while preventing the extreme orbital-selective coherence collapse that would suppress superconductivity.

3. The cutoff evolution of the orbital gaps is nontrivial and orbital-dependent in the nematic Hund regime, consistent with a pairing kernel sensitive to the frequency distribution of incoherent spectral weight rather than to coherent QPs alone.

4. In the Hund regime, dynamical correlations not only enhance the orbital differentiation of the asymptotic gap values (ω0 → ∞) but also induce a non-monotonic buildup.

5. The maximum of RW (ω0) occurs near the cutoff where R∆(ω0) changes sign, pointing to high-energy dynamical correlations as a key ingredient behind the inversion of the gap hierarchy.

The paper investigates how Hund-driven correlations reshape boson-mediated superconductivity in a multiorbital nematic metal by combining DMFT with BCS treatment It is important because it demonstrates that dynamical correlation effects beyond a quasiparticle-only description are essential to capture the robustness of superconductivity in the Hund regime. The findings reveal that Hund correlations play a dual role in the nematic superconductor: they amplify the nematic orbital differentiation of pairing while preventing the extreme orbital-selective coherence collapse that would otherwise suppress superconductivity. Furthermore, the analysis shows that pairing mechanisms with different characteristic boson energies can realize distinct gap structures and nematic responses even when acting on the same underlying Hund-correlated metal. The study concludes that nematicity and Hund correlations combine to make the pairing problem intrinsically frequency selective and orbitally structured.

How it works

The study combines a DMFT description of a correlated nematic three-orbital model with a mean-field BCS treatment The total Hamiltonian includes kinetic, nematic, and Hund terms. Local electronic interactions are included by considering the multiorbital Kanamori Hamiltonian which parametrizes the electron–electron interactions in terms of a Hubbard-like repulsion U and an exchange coupling JH. The pairing Hamiltonians are solved using a diagrammatic approach, where the BCS equations are coupled via the interorbital components of the particle-particle propagator. The analysis shows that while intraorbital pairing is assumed, both Gˆ−1 0 and its inverse Gˆ 0 are not block diagonal matrices due to the presence of finite interorbital hybridization term. These coupled equations are then dressed with DMFT self-energies obtained by the full frequency-dependent DMFT self-energies. The analysis shows that the QP treatment yields systematically smaller gaps than the full DMFT solution, and that this discrepancy becomes particularly pronounced at large JH, where the QP solution collapses to ∆µ = 0 already at intermediate U, while the DMFT solution remains finite. The results confirm that incoherent spectral weight is essential for pairing in the Hund regime.

1. Bold spectral filtering analysis: The AI can perform a controlled cutoff analysis to reveal how different frequency windows of the correlated spectrum contribute unevenly to pairing in the nematic Hund regime, leading to distinct gap structures based on characteristic boson energies.

2. Robustness assessment of superconductivity: The system can determine that dynamical correlation effects beyond a quasiparticle-only description are essential to capture the robustness of superconductivity in the Hund regime, confirming that pairing is sensitive to the redistribution of low-energy incoherent spectral weight encoded in the dynamical self-energies.

3. Orbital differentiation mapping: The AI can map how nematicity reshapes orbital differentiation by identifying that "Hund correlations play a dual role in the nematic superconductor: they amplify nematic orbital differentiation of pairing while preventing the extreme orbital-selective coherence collapse that would suppress superconductivity."

4. Cutoff-driven hierarchy inversion: The system can analyze the buildup with ω0 is nontrivial and orbital dependent, specifically noting that the order of the gaps at small cutoffs need not coincide with the ordering of the plateau values and identifying how this is driven by dynamical correlations, such as a crossing of the xz and yz gap curves.

5. Correlation regime prediction: The AI can predict material behavior based on Hund's coupling strength, noting that At low JH/U, nematicity can strongly polarize the xz/yz sector and trigger an orbital-selective loss of coherence, while at large JH/U, it predicts that Hund exchange suppresses this extreme nematic-driven charge polarization and coherence collapse.