Robust $s_\pm$-wave pairing in a bilayer two-orbital model of pressurized La$_3$Ni$_2$O$_7$ without the $γ$ Fermi surface

TL;DR

The paper investigates superconducting pairing in a newly constructed bilayer two-orbital tight-binding model for La$_3$Ni$_2$O$_7$ under pressure, where the $\gamma$ band sinks below the Fermi level and does not form a Fermi surface. Using a multiband Hubbard interaction and spin-fluctuation–mediated pairing, the authors solve the full linearized Eliashberg equation and find robust $s_\pm$ pairing, with the $\alpha$ and $\beta$ Fermi surfaces showing sign changes across $\mathbf{Q}_3$, while the $\gamma$ and $\delta$ bands, though off-Fermi level, carry sizable paired amplitudes that contribute constructively to $\lambda$ due to near 500 meV energy separation and nesting. They also show that approximations restricting to Fermi-surface states or neglecting frequency dependence can mispredict the pairing symmetry, highlighting the need to include away-from-Fermi-surface bands in multiband superconductors. Overall, the work demonstrates that $s_\pm$ pairing remains robust in this model and that full multiband treatment is crucial for accurately capturing superconducting tendencies in pressurized La$_3$Ni$_2$O$_7$.

Abstract

We studied the superconducting pairing symmetry based on a newly constructed tight-binding model of La$_3$Ni$_2$O$_7$ under pressure, where the $γ$ band sinks below the Fermi level and does not form the Fermi surface. The superconducting pairing symmetry is $s_\pm$-wave and is robust against the variation of the interaction strength. In this model, although the $γ$ and $δ$ bands are away from the Fermi level, the superconducting pairing function on them is not tiny. Instead, since the top of the $γ$ band and bottom of the $δ$ band are both located at $\sim$500 meV away from the Fermi level, and they are almost nested by the peak structure in the spin fluctuation, thus by forming an anti-phase pairing function on them, these two bands act constructively to superconductivity. Finally with detailed derivation and numerical calculation, we demonstrate that the Fermi surface approximated Eliashberg equation may lead to deviation of the pairing symmetry.

Figures (9)

• Figure 1: (a) The eigenvalues of Eq. (\ref{['h0']}) along the high-symmetry directions. (b) The corresponding Fermi surface. The gray dotted lines in (a) and (b) are the band structure and Fermi surfaces of the model in Ref. bilayermodel.
• Figure 2: $\rho_0(\mathbf{q})$, defined as the largest eigenvalue of the matrix $\chi_0(\mathbf{q},i\omega_n=0)$, for the present model (a) and the model in Ref. bilayermodel (b).
• Figure 3: $\rho_s(\mathbf{q})$, defined as the largest eigenvalue of the matrix $\chi_s(\mathbf{q},i\omega_n=0)$, for different values of $U$ at $J_H=U/6$.
• Figure 4: (a) The spin stoner factor $\alpha_s$ as a function of $U$. (b) The largest positive eigenvalue $\lambda$ of Eq. (\ref{['Eliashberg']}) as a function of $U$. Here $J_H=U/6$.
• Figure 5: $\Delta^{bb}(\mathbf{k}_F^{b},i\pi T)$ with $b=\alpha,\beta$ at $U=1.7$ (a), $U=1.8$ (b) and $U=1.9$ (c). Here $J_H=U/6$.