Weak coupling theory of nickel-based 327 superconductors

Summary

This review summarizes weak-coupling theoretical studies of superconductivity in pressurized bilayer nickelate La₃Ni₂O₇, primarily employing the random phase approximation (RPA), fluctuation exchange approximation (FLEX), and functional renormalization group (FRG), based on a bilayer two-orbital Hubbard model with Ni dx²-y² and d3z²-r² orbitals. Studies show that under pressure the Fermi surface consists of an electron-like α pocket and hole-like β and γ pockets; the γ pocket, dominated by the d3z²-r² orbital, exhibits strong nesting with the other pockets, significantly enhancing antiferromagnetic spin fluctuations and mediating attractive pairing. Different methods generally predict the dominant pairing symmetry to be s±-wave: the superconducting gaps on the γ and α pockets have the same sign, whereas the β pocket has the opposite sign, and this pairing is closely related to the interlayer pairing channel dominated by the d3z²-r² orbital. RPA efficiently describes spin and charge susceptibilities, FLEX self-consistently renormalizes quasiparticles and spin fluctuations, and FRG can treat competing orders such as superconductivity, spin density wave, and charge density wave in an unbiased manner. The review concludes that weak-coupling theory can effectively connect Fermi surface geometry with the spin-fluctuation pairing mechanism, and points out that future studies should be combined with strong-coupling pictures and more accurate first-principles parameters.

Materials

• La₃Ni₂O₇

Methods

• Random phase approximation (RPA)
• Fluctuation-exchange approximation (FLEX)
• Functional renormalization group (FRG)
• DFT
• Cluster dynamical mean-field theory
• Constrained random phase approximation

Keywords

• high temperature superconductivity
• spin fluctuations
• fermi surface nesting
• s± wave pairing
• unconventional superconductivity
• interlayer pairing
• gamma pocket

Highlights

• The review systematically compares RPA, FLEX, and FRG, emphasizing their complementary strengths and their convergence on spin-fluctuation-mediated s±-wave pairing.
• The weak-coupling understanding is extended to ambient-pressure La₃Ni₂O₇ thin films, including substrate strain effects and the debated presence of the γ pocket.
• Electron-phonon coupling alone is insufficient to generate superconductivity, but interlayer electron-phonon coupling can cooperate with electronic correlations to promote interlayer d3z2-r2 pairing.

Conclusions

• Weak-coupling theories, primarily RPA, FLEX, and FRG, generally predict s±-wave pairing symmetry in the pressurized bilayer nickelate La₃Ni₂O₇.
• The superconducting pairing is mediated by spin fluctuations enhanced by Fermi surface nesting, with the γ pocket dominated by the Ni d3z2-r2 orbital playing a key role.
• Interlayer coupling between Ni 3d_z2 orbitals is dominant in the superconducting pairing, and the pairing state is sensitive to crystal field splitting and interlayer interactions.
• FRG studies of the pressure dependence of T_c in La₃Ni₂O₇ are consistent with experimental observations, supporting an itinerant weak-coupling picture.

Main claims

• Weak-coupling approaches (RPA, FLEX, and FRG) broadly predict s±-wave pairing symmetry in pressurized La₃Ni₂O₇, with the superconducting gap maintaining the same sign on the gamma and alpha pockets and the opposite sign on the beta pocket.
  • Evidence: The abstract states: 'a dominant s±-wave pairing symmetry is widely predicted across different methodologies. In this state, the superconducting gap function maintains the same sign on the γ and α pockets but reverses sign on the β pocket.',The full text conclusion states: 'Techniques such as the RPA…, fluctuation-exchange approximation (FLEX)…, and FRG… mainly agree on s±-wave symmetry.'
• The gamma pocket, predominantly derived from the Ni d3z2-r2 orbital, is central to the weak-coupling pairing mechanism because its strong nesting with other Fermi surface pockets enhances antiferromagnetic spin fluctuations that mediate attractive pairing.
  • Evidence: The abstract states: 'The γ pocket, predominantly derived from the d3z2−r2 orbital, exhibits strong nesting with the other pockets. This nesting significantly enhances antiferromagnetic spin fluctuations, which in turn mediate attractive pairing interactions.',The full text states: 'These complementary techniques collectively reinforce the conclusion that spin-fluctuation-mediated pairing, driven by the interlayer nesting between the d3z2−r2-dominated γ pocket and other Fermi surface sheets, is the primary mechanism underlying superconductivity in the bilayer nickelate system.'
• Weak-coupling theory effectively links Fermi surface geometry to spin-fluctuation-mediated superconductivity in La₃Ni₂O₇, but future work needs integration with strong-coupling pictures, more precise ab initio-derived parameters, and definitive experimental tests.
  • Evidence: The abstract states: 'Finally, we outline outstanding challenges and future directions, emphasizing the need for closer integration with strong-coupling pictures, more precise ab initio-derived model parameters, and definitive experimental tests to distinguish between competing theoretical scenarios.',The full text conclusion states: 'Theoretical research on nickel-based high-temperature superconductivity is still in its early stages and requires more precise experimental guidance. Further development of both weak-coupling and strong-coupling theories is necessary.'

Workflow

Not available in this batch.