d-wave superconductivity in quintuple-layer bulk superconductor La₆Ni₅O₁₂

Summary

This study investigates the pairing symmetry of the five-layer bulk superconductor La₆Ni₅O₁₂ by employing an effective five-layer Hubbard model constructed within density functional theory and variational Monte Carlo methods. Calculations indicate that the spin-singlet d_x²-y²-wave superconducting state is energetically dominant, whereas extended s-wave pairing is strongly suppressed. Based on the optimized state, the tunneling density of states is predicted to exhibit a V-shape, the superfluid density shows a linear low-temperature depletion, the Knight shift decreases, and the spin-lattice relaxation rate follows 1/T₁T\propto T², characteristics that collectively point to a clean nodal superconductor. Furthermore, this framework reveals that infinite-layer LaNiO₂ possesses a robust d-wave tendency, while three-layer La₄Ni₃O₈ lies near the boundary between d-wave superconductivity and a non-superconducting state at nominal filling. These results establish La₆Ni₅O₁₂ as a platform for probing pairing symmetry in nickelates and suggest a prevalent d_x²-y²-wave pairing trend within the reduced Ruddlesden-Popper nickelate family.

Materials

• La₆Ni₅O₁₂
• La₄Ni₃O₈
• LaNiO₂

Methods

• Variational Monte Carlo
• DFT
• Hubbard model

Keywords

• d wave superconductivity
• pairing symmetry
• nodal superconductor
• ruddlesden popper nickelates
• spin singlet pairing
• superfluid density
• knight shift
• spin lattice relaxation rate

Highlights

• The study utilizes a realistic five-layer Hubbard model with variational Monte Carlo calculations to specifically address the pairing symmetry in bulk quintuple-layer nickelates, overcoming limitations of thin-film-only studies.
• The framework predicts specific bulk-sensitive experimental signatures such as penetration depth and NMR responses that can directly test the predicted nodal state in La₆Ni₅O₁₂.
• The analysis suggests that electron doping could be a promising route to stabilize d-wave superconductivity in trilayer La₄Ni₃O₈ by moving it away from the non-superconducting boundary.

Conclusions

• A spin-singlet d-wave state is energetically favored in the quintuple-layer nickelate La₆Ni₅O₁₂, while extended-s-wave pairing is strongly suppressed.
• The calculated observables, including a V-shaped tunneling density of states, linear low-temperature depletion of superfluid density, decreasing Knight shift, and 1/T1T proportional to T², provide consistent signatures of a clean nodal superconductor.
• Infinite-layer LaNiO₂ exhibits a robust d-wave pairing tendency, whereas trilayer La₄Ni₃O₈ at its nominal filling lies close to the boundary between d-wave superconductivity and a non-superconducting state.
• Bulk La₆Ni₅O₁₂ is established as a promising platform for determining the pairing symmetry of nickelate superconductors, suggesting a common d-wave pairing tendency across the reduced Ruddlesden-Popper nickelate family.

Main claims

• A spin-singlet d-wave superconducting state is energetically favored in quintuple-layer La₆Ni₅O₁₂.
  • Evidence: VMC calculations show the d-wave state has lower energy than non-superconducting and extended s-wave ansatzes.,Extended s-wave pairing amplitudes are roughly two orders of magnitude weaker than d-wave amplitudes.
• The superconducting state in La₆Ni₅O₁₂ is a clean nodal superconductor.
  • Evidence: Calculated tunneling density of states exhibits a V-shaped low-energy spectrum.,Superfluid density shows linear low-temperature depletion.,Knight shift decreases below T_c.,Spin-lattice relaxation rate follows 1/T1T proportional to T².
• There is a common d-wave pairing tendency across the reduced Ruddlesden-Popper nickelate family.
  • Evidence: VMC calculations for infinite-layer LaNiO₂ find a robust d-wave tendency.,VMC calculations for trilayer La₄Ni₃O₈ show it lies near the boundary of d-wave superconductivity.

Workflow

• model_construction — A realistic five-band tight-binding model is constructed for La₆Ni₅O₁₂, with analogous models for related nickelates.
  • Materials: La₆Ni₅O₁₂; La₄Ni₃O₈; LaNiO₂
  • Methods: Density Functional Theory (DFT); Wannierization; Five-band tight-binding model construction
  • Observations: Five bands predominantly derived from Ni orbitals cross the Fermi level; Fermi surfaces resemble cuprate-like tight-binding bands
• ground_state_calculation — The ground state of the quintuple-layer La₆Ni₅O₁₂ is a spin-singlet d-wave superconducting state.
  • Materials: Multilayer Hubbard model
  • Methods: Variational Monte Carlo (VMC); Gutzwiller-projected wave function; Stochastic reconfiguration method
  • Observations: Spin-singlet d-wave state is energetically favored; Extended s-wave pairing is strongly suppressed; Layer-resolved electron density remains nearly uniform
• observable_calculation — The calculated observables exhibit consistent signatures of a clean nodal superconductor.
  • Materials: VMC-optimized variational state
  • Methods: Gutzwiller approximation; Slave-boson renormalization; Calculation of quasiparticle density of states, superfluid density, Knight shift, and spin-lattice relaxation rate
  • Observations: V-shaped tunneling density of states; Linear low-temperature depletion of superfluid density; Decrease in Knight shift below T_c; Spin-lattice relaxation rate follows 1/T1T proportional to T²
• comparative_analysis — There is a common d-wave pairing tendency across the reduced Ruddlesden-Popper nickelate family, with strength controlled by carrier concentration and layer structure.
  • Materials: Trilayer La₄Ni₃O₈; Infinite-layer LaNiO₂
  • Methods: VMC calculations on three-layer and single-layer Hubbard models
  • Observations: La₄Ni₃O₈ lies close to the boundary between d-wave superconductivity and a non-superconducting state; LaNiO₂ exhibits a robust d-wave pairing tendency