The fate of s_± superconductivity in the bilayer nickelate La₃Ni₂O₇

摘要

该文针对双层镍酸盐La₃Ni₂O₇中高温超导的配对对称性问题，在s±与铜氧化物类d波竞争的理论背景下，构建了保留半满t-J模型完整SU(2)粒子-空穴对称性的平均场分数化方案，并将其应用于La₃Ni₂O₇的简化双层t-J模型。作者指出，常规U(1)处理未充分计入库仑排斥和禁止双占据约束，而其分数化方法会引入额外的库仑赝势限制。计算表明，该赝势抑制s±配对、有利于d波配对，从理论上说明层间耦合与局域无双重占据条件可改变La₃Ni₂O₇的配对对称性竞争；这一结论属于平均场理论预测，并非实验已确立的配对机制。

材料

• La₃Ni₂O₇

方法

• mean-field fractionalization treatment
• SU(2) particle-hole-symmetric t-J model
• Wen-Lee path-integral formulation
• Hubbard-Stratonovich decoupling
• Bogoliubov-de Gennes (BdG) mean-field theory
• self-consistent mean-field calculations
• free-energy minimization

关键词

• s± superconductivity
• d wave pairing
• pairing symmetry
• coulomb pseudopotential
• interlayer coupling
• interlayer pairing
• intralayer pairing
• coulomb repulsion
• no double occupancy constraint
• pairing susceptibility
• bilayer nickelates

亮点

• The mean-field fractionalization captures the full SU(2) particle-hole symmetry of the t-J model at half-filling.
• The additional Coulomb pseudopotential constraint on the superconducting order parameter is absent in conventional mean-field treatments.
• The correction from the Coulomb pseudopotential is positive semidefinite and reduces the eigenvalues of the susceptibility matrix, lowering T_c for s± pairing.
• Recent ARPES measurements on ambient-pressure (La,Pr,Sm)La₃Ni₂O₇ films reveal nodeless gaps on the α and β Fermi-surface pockets, challenging the d-wave state favored by the calculations and motivating phase-sensitive tests.

结论

• A systematic treatment of the full SU(2) particle-hole symmetry of the half-filled t-J model leads to an added Coulomb pseudopotential constraint that is absent in the usual U(1) treatment.
• Applying the fractionalization scheme to a simplified bilayer t-J model of La₃Ni₂O₇ shows that the Coulomb pseudopotential suppresses the existence of s± symmetry in favor of d-wave pairing.
• The Coulomb constraint does not prohibit superconductivity; strong interlayer exchange enhances interlayer pairing and can partially overcome the Coulomb suppression.
• For the parameters studied, the constraint favors d-wave superconductivity over much of the phase diagram, including the nominal doping of La₃Ni₂O₇.
• The Coulomb pseudopotential creates a positive-semidefinite correction to the pairing susceptibility, reducing T_c for s± pairing while leaving the d-wave channel unaffected by symmetry.

主要论断

• A mean-field fractionalization treatment capturing the full SU(2) particle-hole symmetry of the half-filled t-J model leads to an added Coulomb pseudopotential constraint that is absent in the usual U(1) treatment.
  • 证据: The abstract states that the proposed fractionalization treatment captures the full SU(2) particle-hole symmetry and leads to an added Coulomb pseudopotential constraint absent in the usual U(1) treatment.,Section I.2 states that the transverse constraints eliminate an on-site spinon pair amplitude and that their Lagrange multiplier acts as a self-consistent Coulomb pseudopotential.
• In the simplified bilayer t-J model of La₃Ni₂O₇, the Coulomb pseudopotential suppresses s± symmetry in favor of d-wave pairing.
  • 证据: The abstract states that applying the scheme to a simplified bilayer t-J model shows the Coulomb pseudopotential suppresses s± symmetry in favor of d-wave pairing.,Section V reports that once the Coulomb pseudopotential constraint is added, s± pairing is suppressed significantly.
• The d-wave channel is unaffected by the Coulomb pseudopotential by symmetry, while the s± pairing susceptibility is reduced by a positive-semidefinite correction.
  • 证据: Section V states that the Coulomb pseudopotential creates an effective susceptibility with a positive semidefinite correction that reduces eigenvalues and T_c for pairing.,Section V and VI state that for d-wave pairing the correction is zero because d-wave symmetry is orthogonal to the Coulomb pseudopotential.
• Strong interlayer exchange can enhance interlayer pairing and partially overcome Coulomb suppression, but the constraint still favors d-wave over much of the phase diagram, including the nominal doping of La₃Ni₂O₇.
  • 证据: Section VI states that strong interlayer exchange enhances interlayer pairing and can partially overcome Coulomb suppression.,Section VI states that for the parameters studied the constraint favors d-wave superconductivity over much of the phase diagram, including the nominal doping of La₃Ni₂O₇.
• The result is a mean-field theoretical prediction rather than an experimentally established pairing mechanism, and ARPES data on ambient-pressure films may challenge the favored d-wave state.
  • 证据: The summary_en states that the conclusion is a mean-field theoretical prediction, not an experimentally established pairing mechanism.,Section VI notes that recent ARPES measurements reveal nodeless gaps that challenge the d-wave state favored by the calculations.

研究流程

• model_construction — A minimal bilayer t-J model captures the relevant low-energy bilayer nickelate physics for studying pairing competition.
  • 材料: simplified bilayer t-J model of La₃Ni₂O₇; projected bilayer t-J model; Hubbard operators on the local three-state space
  • 方法: derive interlayer superexchange from Hund's coupling to orbitals; Fourier transform projected hopping to a Bloch Hamiltonian
  • 观察: the model qualitatively reproduces the Fermi-surface pocket features seen in ARPES
• strong_coupling_fractionalization — A mean-field fractionalization treatment preserving full SU(2) particle-hole symmetry introduces an additional Coulomb pseudopotential constraint absent in the usual U(1) treatment.
  • 材料: fermionic spinon; two-component charge boson; Wen-Lee SU(2) gauge formulation
  • 方法: slave-boson fractionalization; impose local charge and transverse constraints; symplectic Hubbard-Stratonovich decoupling
  • 观察: the constraints produce longitudinal and on-site pair Lagrange multipliers
• mean_field_saddle_point — The mean-field saddle-point equations yield a pairing instability and critical temperature for competing d-wave and s± states.
  • 材料: bilayer Bogoliubov-de Gennes Hamiltonian; intralayer and interlayer link fields
  • 方法: momentum-space link fields; Bogoliubov-de Gennes spectrum; free-energy extremization; coupled self-consistency equations
  • 观察: the pairing instability is determined by a sign change in the susceptibility determinant
• numerical_solution — The Coulomb pseudopotential suppresses s± pairing in favor of d-wave pairing over much of the studied phase diagram.
  • 材料: coupled self-consistency equations; doping sweep
  • 方法: numerically minimize the free energy; solve the coupled self-consistency equations; calculate critical temperatures
  • 观察: without the Coulomb constraint s± can exceed d-wave at larger doping; with the Coulomb constraint s± is suppressed and forced to change sign between Fermi surfaces
• interpretation — The local no-double-occupancy condition alters the competition between interlayer s± and intralayer d-wave pairing, favoring d-wave for the parameters studied.
  • 材料: pairing-symmetry phase diagram; comparison with ARPES literature
  • 方法: compare symmetry sectors; analyze the positive-semidefinite correction to the susceptibility
  • 观察: the d-wave channel is orthogonal to the Coulomb pseudopotential; the s± pairing susceptibility is reduced by the constraint; strong interlayer exchange can enhance interlayer pairing but does not eliminate the constraint