Unconventional superconductivity in La 3 Ni 2 O 7 from the perspective of symmetry

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 phenomenological symmetry-based method to investigate the superconducting gap structure in $\mathrm{La_{3}Ni_{2}O_{7}}$. Using density-functional theory methods (DFT+$U$), together with the experimentally determined $T_c$ and structural symmetry, 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 pairing configurations are distinct. In the pressurized bulk, superconductivity is dominated by the out-of-plane pairing of the Ni-$d_{z^2}$ orbitals, while in the thin film, the 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 type, driven by the decreased ratio of inter-layer to intra-layer hoppings in the thin film. Our result sheds lights on the microscopic pairing in $\mathrm{La_{3}Ni_{2}O_{7}}$ and reveals the significance of the symmetry. This method can potentially be generalized to a broader range of unconventional superconductors.