d-wave superconductivity in quintuple-layer bulk superconductor La₆Ni₅O₁₂

摘要

本研究针对五层块体超导体La₆Ni₅O₁₂，利用基于密度泛函理论构建的有效五层Hubbard模型及变分蒙特卡洛方法，探究其配对对称性。计算表明，自旋单重态d_x²-y²波超导态在能量上占优，而扩展s波配对被强烈抑制。基于优化态，作者预测了隧道态密度呈V形、超流密度低温线性耗竭、奈特位移下降及自旋晶格弛豫率遵循1/T₁T\propto T²，这些特征共同指向洁净节点超导体。此外，该框架显示无限层LaNiO₂具有稳健的d波倾向，而三层La₄Ni₃O₈在名义填充下处于d波超导与非超导态的边界附近。这些结果确立了La₆Ni₅O₁₂作为探测镍氧化物配对对称性的平台，并暗示了缩减Ruddlesden-Popper镍氧化物家族中普遍存在的d_x²-y²波配对趋势。

材料

• La₆Ni₅O₁₂
• La₄Ni₃O₈
• LaNiO₂

方法

• Variational Monte Carlo
• DFT
• Hubbard model

关键词

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

亮点

• 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.

结论

• 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.

主要论断

• A spin-singlet d-wave superconducting state is energetically favored in quintuple-layer La₆Ni₅O₁₂.
  • 证据: 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.
  • 证据: 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.
  • 证据: 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.

研究流程

• model_construction — A realistic five-band tight-binding model is constructed for La₆Ni₅O₁₂, with analogous models for related nickelates.
  • 材料: La₆Ni₅O₁₂; La₄Ni₃O₈; LaNiO₂
  • 方法: Density Functional Theory (DFT); Wannierization; Five-band tight-binding model construction
  • 观察: 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.
  • 材料: Multilayer Hubbard model
  • 方法: Variational Monte Carlo (VMC); Gutzwiller-projected wave function; Stochastic reconfiguration method
  • 观察: 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.
  • 材料: VMC-optimized variational state
  • 方法: Gutzwiller approximation; Slave-boson renormalization; Calculation of quasiparticle density of states, superfluid density, Knight shift, and spin-lattice relaxation rate
  • 观察: 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.
  • 材料: Trilayer La₄Ni₃O₈; Infinite-layer LaNiO₂
  • 方法: VMC calculations on three-layer and single-layer Hubbard models
  • 观察: La₄Ni₃O₈ lies close to the boundary between d-wave superconductivity and a non-superconducting state; LaNiO₂ exhibits a robust d-wave pairing tendency