Discriminating Gap Symmetries of Superconducting La$_3$Ni$_2$O$_7$

Abstract

The discovery of high-T$_c$ superconductor in Ruddlesden-Popper nickelate materials represented by La$_3$Ni$_2$O$_7$ has opened new directions in the quest for unconventional superconductivity. A central unresolved issue concerns the pairing symmetry of the superconducting order. In this paper, we model the superconducting order of La$_3$Ni$_2$O$_7$ using the established Fermi surface structure together with phenomenological pairing functions belonging to $s_\pm$ and $d$-wave symmetry classes, which are the leading possibilities in the current debate. We compute several experimentally accessible observables-including tunneling density of states, point contact spectroscopy, superfluid density, and Raman spectroscopy-each of which exhibits distinct characteristics for different gap symmetries. These quantities provide a concrete and experimentally testable route for identifying the pairing symmetry of La$_3$Ni$_2$O$_7$ and for clarifying the microscopic nature of nickelate superconductivity.