Nodal Orbital-Anti-Phase Superconducting State in Bilayer Nickelates

摘要

本文针对双层镍酸盐La₃Ni₂O₇中压力或压缩应变诱导的高温超导，在正常态电子结构可导致成键-反键s±波或d波配对的基础上，研究超导能隙的轨道反相声结构。作者采用有效四轨道模型，先分析单层双轨道模型中的能隙节点条件，再推广到双层体系，并利用成键/反键基矢将节点特征与层内、层间配对分量的符号及相对大小联系起来。结果表明，当参与配对的轨道间能隙符号相反时，除对称性强制的节点外，α和/或β费米面片上还会出现额外节点对；这些节点并非能隙函数对称性所要求，可通过ARPES探测。此外，轨道反相能隙会改变低温超流刚度的温度依赖，为在双层镍酸盐及相关多轨道体系中检验该超导态提供了具体实验判据。

材料

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方法

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关键词

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亮点

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结论

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主要论断

• An orbital-anti-phase superconducting gap can produce additional node pairs on the α and/or β Fermi surface sheets.
  • 证据: Abstract: 'We demonstrate that additional pairs of nodes may appear on the α and/or β Fermi surface sheets due to the sign change of the superconducting gap between the involved orbitals.',Summary: 'additional node pairs appear on the α and/or β Fermi surface sheets in addition to symmetry-enforced nodes'
• These additional nodes are accidental and carry topological charges governing their pairwise creation and annihilation.
  • 证据: Summary: 'nodes are accidental, in the sense that they are not enforced by the symmetry of the superconducting order parameter',Summary: 'they carry topological charges that govern their pairwise creation and annihilation as the relative magnitudes of the orbital pairing components are varied'
• For s±-wave pairing, the orbital-in-phase state is fully gapped, while the orbital-anti-phase state develops accidental nodes on mixed-orbital α and β sheets; the γ band remains nodeless.
  • 证据: Summary: 'For the state, we find that the orbital-in-phase configuration … is fully gapped, whereas the orbital-anti-phase configuration develops accidental nodes on the mixed-orbital and Fermi surface sheets.',Summary: 'the predominantly derived band remains nodeless due to its weak orbital mixing'
• For d-wave pairing, orbital-anti-phase structure can in principle generate additional nodes, but for the representative parameters considered no additional nodes emerge.
  • 证据: Summary: 'For the d-wave state, the orbital-anti-phase configuration can, in principle, generate additional accidental nodes … however, the orbital mixing is not sufficiently strong to produce such additional nodes.'
• The temperature dependence of superfluid stiffness is a sensitive experimental probe of accidental nodes in orbital-anti-phase bilayer nickelates.
  • 证据: Abstract: 'the orbital-anti-phase gap modifies the temperature dependence of the superfluid stiffness at low temperatures, providing a concrete experimental prediction',Summary: 'the low-temperature behavior of the superfluid stiffness is particularly sensitive to the nodal structure of the and Fermi surface sheets'
• Available ARPES data are more naturally reproduced by the orbital-in-phase state, but they do not exclude the orbital-anti-phase s± state.
  • 证据: Full text: 'the available ARPES results are more naturally reproduced by the orbital-in-phase state',Full text: 'the orbital-anti-phase -wave state is still consistent with the available ARPES data'

研究流程

• model_setup — An effective multiorbital bilayer model can capture the normal and superconducting states relevant to La₃Ni₂O₇.
  • 材料: single-layer two-orbital model; bilayer two-orbital model with effective Ni d orbitals; effective four-orbital model for La₃Ni₂O₇; tight-binding parameters from Ref. [40]
  • 方法: Bogoliubov-de Gennes Hamiltonian formulation; bonding/antibonding basis transformation; Nambu spinor representation
  • 观察: Low-energy physics is governed by multiorbital and bilayer effects with hybridization between Ni and O orbitals.
• nodal_condition_derivation — Orbital-anti-phase pairing can generate accidental point nodes whose creation and annihilation are governed by topological charges.
  • 材料: normal-state Fermi surfaces; orbital gap functions; orbital hybridization
  • 方法: derive nodal conditions from BdG eigenvalues; intersection-number and topological-charge analysis
  • 观察: Opposite orbital phases allow additional non-trivial nodes beyond symmetry-enforced nodes.
• bilayer_classification — A general classification links the orbital-layer structure of the order parameter to the presence or absence of accidental nodes.
  • 材料: bonding and antibonding sectors; intralayer and interlayer pairing components; orbital and layer degrees of freedom
  • 方法: project pairing onto bonding and antibonding bands; classify sign-and-magnitude configurations; define P and related sign parameters
  • 观察: The nodal character of bonding and antibonding sectors is controlled by the signs and relative magnitudes of intra- and interlayer pairing.
• gap_parametrization — Representative s±-wave and d-wave parameter sets allow comparison of orbital-in-phase and orbital-anti-phase nodal structures against ARPES constraints.
  • 材料: ARPES-reported gap scales; α, β, and γ Fermi surface sheets; s±-wave and d-wave gap states
  • 方法: fit projected gaps using a tight-binding description; model isotropic intraorbital s±-wave gaps; model predominantly intralayer d-wave pairing
  • 观察: The orbital-in-phase s± model reproduces ARPES gap magnitudes near the diagonal, while the orbital-anti-phase s± state is also compatible with available data.
• numerical_calculation — Numerical results show that accidental nodes in orbital-anti-phase states leave measurable signatures in gap evolution and superfluid stiffness.
  • 材料: bonding β and antibonding α Fermi surface sheets; γ band; superfluid stiffness; current-current correlation function
  • 方法: compute evolution of accidental nodes with P; calculate superfluid stiffness from current-current correlation function; Peierls substitution; Matsubara Green's function eigen-decomposition
  • 观察: Accidental nodes are stable and can merge or annihilate as parameters vary; the γ band remains nodeless due to weak orbital mixing; orbital-anti-phase s± pairing gives a more concave low-temperature superfluid stiffness.
• interpretation_and_prediction — The orbital-anti-phase state makes concrete experimental predictions for bilayer nickelates and related multiorbital systems.
  • 材料: ARPES experiments; superfluid stiffness and London penetration depth
  • 方法: compare orbital-in-phase and orbital-anti-phase signatures; propose experimental tests
  • 观察: ARPES can test whether nodal positions correlate with orbital-character changes; superfluid stiffness can distinguish fully gapped and accidentally nodal pairing.