$d$-wave superconductivity in quintuple-layer bulk superconductor La${}_6$Ni${}_5$O${}_{12}$

Abstract

The recent realization of bulk superconductivity in the quintuple-layer nickelate La${}_6$Ni${}_5$O${}_{12}$ opens new opportunities to probe the pairing symmetry of the reduced Ruddlesden--Popper (RP) nickelate family. Using an effective five-layer Hubbard model and variational Monte Carlo calculations, we find that a spin-singlet $d_{x^2-y^2}$-wave state is energetically favored, while extended-$s$-wave pairing is strongly suppressed. Based on the optimized superconducting state, we further calculate several experimentally accessible observables. The tunneling density of states exhibits a characteristic V-shaped low-energy spectrum, the superfluid density shows a linear low-temperature depletion, the Knight shift decreases below $T_c$, and the spin-lattice relaxation rate follows $1/T_{1}T\propto T^2$, together providing consistent signatures of a clean nodal superconductor. Extending the same framework to related reduced RP nickelates, we find a robust $d$-wave tendency in infinite-layer LaNiO${}_2$, while trilayer La${}_4$Ni${}_3$O${}_8$ at its nominal filling lies close to the boundary between $d$-wave superconductivity and a non-superconducting state. These results establish bulk La${}_6$Ni${}_5$O${}_{12}$ as a promising platform for determining the pairing symmetry of nickelate superconductors and suggest a common $d_{x^2-y^2}$-wave pairing tendency across the reduced RP nickelate family.

arXiv comment6+4 pages, 3+1 figures