Unconventional Superconductivity in $\mathrm{L}{\mathrm{a}}_3\mathrm{N}{\mathrm{i}}_2{\mathrm{O}}_7$ from the Perspective of Symmetry

Abstract

The recently discovered superconductor $\mathrm{L}{\mathrm{a}}_3\mathrm{N}{\mathrm{i}}_2{\mathrm{O}}_7$ has attracted significant attention due to its remarkably high transition temperature ($T_c$) under high pressure. Shortly after this discovery, thin-film $\mathrm{L}{\mathrm{a}}_3\mathrm{N}{\mathrm{i}}_2{\mathrm{O}}_7$ 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 $\mathrm{L}{\mathrm{a}}_3\mathrm{N}{\mathrm{i}}_2{\mathrm{O}}_7$. 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 $\mathrm{L}{\mathrm{a}}_3\mathrm{N}{\mathrm{i}}_2{\mathrm{O}}_7$ 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 $\mathrm{L}{\mathrm{a}}_3\mathrm{N}{\mathrm{i}}_2{\mathrm{O}}_7$ and reveals the significance of the symmetry. This method can potentially be generalized to a broader range of unconventional superconductors.