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

Abstract

Superconductivity and nematicity coexist in the phase diagram of many correlated systems, including iron-based superconductors. We investigate how Hund-driven correlations reshape boson-mediated superconductivity in a multiorbital nematic metal. We find that dynamical correlation effects beyond a quasiparticle-only description are essential to capture the robustness of superconductivity in the Hund regime. In the nematic phase, Hund correlations simultaneously enhance the orbital differentiation of the superconducting gaps and inhibit the most extreme nematic-driven orbital polarization and coherence collapse that would otherwise suppress pairing at strong coupling. A controlled cutoff analysis reveals a nontrivial, orbital-dependent buildup of the gaps, indicating that different frequency windows of the correlated spectrum contribute unevenly to pairing in the nematic Hund regime. This implies that pairing mechanisms with different characteristic boson energies can lead to distinct gap structures and trends.

Figures (11)

• Figure 1: Evolution of normal-state properties across the nematic-Hund crossover. Normal-state orbital quasiparticle weights $Z_\mu$ (a) and occupations $n_\mu$ (b) as a function of $U$, for representative $\eta$ and $J_H/U$. (a) At low $J_H/U$ nematicity triggers a strongly orbital-selective coherence collapse, leading to an orbital-selective Mott (OSM) response (shaded region). At large $J_H/U$ the system remain metallic with finite $Z_\mu$ and a significant $xz/yz$ differentiation. (b) The corresponding occupations reveal that the OSM state arises from $\eta$-driven charge reorganization at low-$J_H/U$, a tendency substantially mitigated by large Hund's exchange.
• Figure 2: Spectral evolution and orbital anisotropy in the nematic Hund's metal. Orbital-resolved spectral functions $A_\mu (\omega)$ for $U=1.5$ eV at $J_H/U=0.05$ (a,c) and high $J_H/U=0.25$ (b,d). Vertical dashed lines indicate the effective Hubbard interaction $U_{\text{eff}}=U-3J_H$. (a,b) In the tetragonal case ($\eta=0$), increasing $J_H/U$ reduces the energy separation between coherent quasiparticle peaks and incoherent Hubbard bands. (c,d) In the nematic phase ($\eta=0.04$ eV), low $J_H/U$ results in a nearly rigid shift of the xz/yz spectra in opposite directions relative to the Fermi level ($E_F$). In contrast, the Hund regime (d) exhibits a strongly frequency-dependent $xz/yz$ imbalance. The $xy$ orbital is less sensitive to nematicity, while increasing $J_H/U$ suppresses its spectral weight near $E_F$. (e,f) The nematic anisotropy $R_A(\omega)$ shows a characteristic sign change at $E_F$ for low $J_H/U$, whereas the Hund regime develops complex finite-$\omega$ features, signaling a broad redistribution of the orbital imbalance.
• Figure 3: Comparison between full dynamical and the quasiparticle approximation. Orbital-resolved superconducting gaps $\Delta_\mu/g$ versus U (for $\omega_0=\infty$) for different nematicities $\eta$. Results from the full DMFT-based pairing kernel (filled symbols) are compared against the quasiparticle (QP) approximation (open symbols) for (a) low and (b) high Hund's coupling. The QP approximation systematically underestimates the gaps and artificially suppresses superconductivity at intermediate U, even while $Z_\mu$ is still finite. In contrast, the full DMFT solutions remain robust and sizable across the entire parameter range, despite the strongly suppressed $Z_\mu$ demonstrating that incoherent spectral weight is essential for pairing in the Hund regime.
• Figure 4: Hund-driven stabilization of superconductivity and enhancement of orbital differentiation in the nematic phase. Evolution of normal- and superconducting-state observables in the nematic phase, normalized to their tetragonal ($\eta=0$) values. Top row: $\eta$-sweep at fixed $U=1.0$ eV. Bottom row: $U$-sweep at fixed $\eta=0.02$ eV. (a) Normalized occupations $n_\mu(\eta)/n_\mu(0)$: at low $J_H/U$, nematic polarization of the $xz/yz$ orbitals is strongly amplified, whereas in the Hund regime, the occupations remain closer to their tetragonal values. (b) Normalized quasiparticle weights $Z_\mu(\eta)/Z_\mu(0)$: Hund's coupling enhances orbital differentiation while simultaneously preventing the transition into the OSM state. (c) Normalized gaps $\Delta_\mu(\eta)/\Delta_\mu(0)$: Hund correlations amplify the nematic differentiation of the superconducting response while inhibiting the OSM-driven collapse that quenches pairing at low $J_H/U$.
• Figure 5: Orbital-dependent gap buildup and hierarchy inversion. Frequency cutoff dependence of the superconducting gaps $\Delta_\mu(\omega_0)/g$ at $U=1.5$ eV for $J_H/U=0.05,0.25$ in the tetragonal, $\eta=0$(a) and nematic case, $\eta=0.04$ eV, case (b). Dashed lines indicate the effective interaction scale $U_{\text{eff}}=U-3J_H$. In the Hund regime, dynamical correlations not only enhance the orbital differentiation of the asymptotic gap values ($\omega_0 \rightarrow \infty$) but also induce a non-monotonic buildup. This results in a crossing of the xz and yz gap curves, showing that the gap hierarchy at low-energy cutoffs can be inverted compared to the full frequency-integrated results.