Near-flat-band-driven violation of Pauli limit in heavy fermion superconductors

TL;DR

This work shows that in the two-dimensional Kondo–Heisenberg model, strong correlations and Kondo hybridization enable a substantial violation of the conventional Pauli paramagnetic limit for spin-singlet superconductivity. By solving a self-consistent mean-field theory for $s$-, extended-$s$-, and $d$-wave pairings under Zeeman fields, the authors map $T_c(B)$ and $B_c$ across fillings, extract the Clogston–Chandrasekhar ratio $r_{ m CC}$, and identify a near-flat-band mechanism that enhances Pauli-limiting fields as the Fermi level approaches a weakly dispersive region of the lower hybridized band. The enhancement is strongest near half filling and remains channel-dependent due to band curvature and gap structure, providing a microscopic route to large $H_{c2}$ in heavy-fermion superconductors. The results establish a band-structure viewpoint for Pauli-limit violations and offer a baseline for incorporating additional effects such as orbital coupling or spin–orbit interactions in future studies.

Abstract

Heavy-fermion superconductors often display upper critical fields that exceed the conventional Pauli paramagnetic limit, indicating that strong correlations and hybridized quasiparticle bands play an essential role in the paramagnetic pair-breaking process. Within the two-dimensional Kondo-Heisenberg model, we perform a self-consistent mean-field analysis of spin-singlet s-, extended-s-, and d-wave pairing under Zeeman fields, and compute the critical field Bc, the transition temperature Tc, and the Clogston-Chandrasekhar ratio rCC. We find that rCC increases sharply as the conduction filling approaches half filling. This enhancement arises from the weakly dispersive region of the lower hybridized band, where the strongly reduced Fermi velocity diminishes the normal-state paramagnetic energy and stabilizes superconductivity. At fixed filling, the distinct JH dependences among the three pairing channels reflect the sensitivity of Pauli limiting to both band curvature and the structure of the order parameter. These results provide microscopic evidence that proximity to a near-flat hybridized band offers a robust route to enhanced Pauli-limiting fields in heavy-fermion superconductors.

Figures (11)

• Figure 1: (Color online) (a) Evolution of the pairing amplitudes $\Delta_{cf}$ and $\Delta_{f}$ as a function of the local AFM exchange $J_H/t$. (b) Condensation energy $E_{\rm cond}=\Omega_{\rm SC}-\Omega_{\rm N}$ (per site, in units of $t$) for the $s$-, extended-$s$-, and $d$-wave states. Model parameters: $t'/t=0.3$, $n_c=0.91$, and $J_K/t=2$. Line styles and colors follow the legend.
• Figure 2: (Color online) Zero-field superconducting ground-state phase diagram for $t'/t=0.3$ and $J_K/t=2.0$. The red curve marks the boundary between nodal and nodeless $d$-wave states, obtained from our self-consistent solutions following the standard criterion in Ref. Liu2014CPL.
• Figure 3: (Color online) Field dependence of the pairing amplitudes $\Delta_{cf}$ and $\Delta_f$ at $k_{\mathrm B}T=10^{-4}$ for representative $s$-, extended-$s$-, and $d$-wave states. Panels (a) and (b) correspond to moderately doped and near–half-filled cases, respectively. The pairing amplitudes collapse at a critical field $B_c$, signaling a quasi–first-order suppression of superconductivity.
• Figure 4: (Color online) Free-energy difference $\Delta F = F_{\mathrm N} - F_{\mathrm{SC}}$ versus $\mu_{\mathrm B}B$ at $k_{\mathrm B}T=10^{-4}$. Positive values favor superconductivity.
• Figure 5: (Color online) Temperature dependence of $\Delta_{cf}$ and $\Delta_f$ at $\mu_{\mathrm B}B=0.05$ for $s$-, extended-$s$-, and $d$-wave states. Panels (a) and (b) show moderately doped and near–half-filled cases, respectively. In each case the order parameters decrease smoothly with temperature and vanish at the corresponding $T_c(B)$.