Unconventional Superconductivity in $\mathrm{La_{3}Ni_{2}O_{7}}$ from the Perspective of Symmetry

Abstract

The recently discovered superconductor $\mathrm{La_{3}Ni_{2}O_{7}}$ has attracted significant attention due to its remarkably high transition temperature ($T_{c}$) under high pressure. Shortly after this discovery, thin-film $\mathrm{La_{3}Ni_{2}O_{7}}$ was demonstrated to exhibit ambient-pressure superconductivity; however, the corresponding $T_c$ is only about half that of the pressurized bulk material. This striking difference raises questions about the underlying mechanisms governing superconductivity in these two structures. To address this issue, we develop a symmetry-based method that investigates superconducting pairings solely based on experimentally determined symmetry and $T_c$, without assuming any specific superconducting parameters. Applying this approach, we find that both pressurized bulk and thin-film $\mathrm{La_{3}Ni_{2}O_{7}}$ exhibit $s_{\pm}$-wave pairing symmetry and two-gap superconductivity, yet their dominant microscopic origins are distinct. In the pressurized bulk, superconductivity is dominated by out-of-plane pairing of the Ni-$d_{z^2}$ orbitals, while in the thin film, in-plane pairing of the Ni-$d_{x^2-y^2}$ orbitals prevails. Furthermore, the observed reduction in $T_c$ can be attributed to this transition of the dominant pairing types, driven by the decreased ratio of inter-layer to intra-layer hoppings in the thin film. Our result sheds lights on the microscopic pairings in $\mathrm{La_{3}Ni_{2}O_{7}}$ and reveal the significance of the symmetry. This method can potentially be generalized to a broader range of unconventional superconductors.

Figures (3)

• Figure 1: (a) Schematic of the hopping terms in the tight-binding model (Eq. \ref{['eq:1']}). The two purple lines highlight the pairings $\Delta_1$ and $\Delta_{12}$, identified as $\Delta_{\perp}^{z}$ ($s_{\pm}$-wave) and $\Delta_{\parallel}^{x}$ ($s_{\pm}$-wave), respectively, which are ultimately stabilized in our calculations. (b) Normal-state band structures of $\mathrm{La_{3}Ni_{2}O_{7}}$ for pressurized bulk (solid lines) and thin film (dashed lines). The inset shows the Fermi surfaces, with purple lines indicating the momentum path used for the spectra.
• Figure 2: (a) BCS condensation energy $\mathcal{F}_{\mathrm{BdG}}^{T_c=80~\mathrm{K}}$ and $V_{i}^{T_c=80~\mathrm{K}}$ of the feasible pairings for pressurized bulk. (b) Temperature dependence of each $\Delta_{i}^{T_c=80~\mathrm{K}}$. (c) Superconducting transition temperature $T_c$ as a function of $V_{1}$ and $V_{12}$ with both interactions present. The white region indicates where $T_c \approx 80~\mathrm{K}$; the color scale shows $T_c$. The inset displays the temperature dependence of $\Delta_{1}$ and $\Delta_{12}$ for the parameter set marked by a yellow star. (d) Schematic of the momentum path and corresponding energy spectrum, with $\{\Delta_{1},\Delta_{12}\}=\{12.8,5.8\}$ meV fixed to the values from the yellow star in (c), identified as $\Delta_{\perp}^{z}$ ($s_{\pm}$-wave) and $\Delta_{\parallel}^{x}$ ($s_{\pm}$-wave), respectively. A superconducting gap of $\sim 11.3~\mathrm{meV}$ is observed at the $\beta$ pocket and $\sim 12.8~\mathrm{meV}$ at the $\gamma$ pocket along the $(0,0)-(\pi,\pi)$ direction.
• Figure 3: (a) BCS condensation energy $\mathcal{F}_{\mathrm{BdG}}^{T_c=40~\mathrm{K}}$ and interaction strength $V_{i}^{T_c=40~\mathrm{K}}$ for the feasible pairing channels in the thin film. (b) Transition temperature $T_c$ as a function of $V_{1}$ and $V_{12}$. White regions indicate parameter regimes with $T_c \approx 40~\mathrm{K}$; the color scale depicts $T_c$. The inset shows the temperature dependence of $\Delta_{1}$ and $\Delta_{12}$ for the parameter set marked by the yellow star. (c) Energy spectrum along the momentum path shown in the inset, with $\Delta_{1}$ and $\Delta_{12}$ fixed to the values from the yellow star in (b), i.e., $\{\Delta_{1},\Delta_{12}\} = \{5.1, 3.5\}$ meV. The energy gap at the $\beta$ band is $\sim 7.2$ meV, and $\sim 5.3$ meV at the $\gamma$ band. This path facilitates direct comparison with experimental results from Ref. shen2025nodelesssuperconductinggapelectronboson. (d) Normalized density of states (DOS), for which the integral over the entire energy range is unity, enabling direct comparison with the experimental results reported in Ref. fan2025superconductinggapsrevealedstm. The black and red dashed lines denote $\{\Delta_{1},\Delta_{12}\}$ obtained in our calculations, respectively.