[Paper Review] Fingerprints of spin-fermion pairing in cuprates

Ar. Abanov, Andrey V. Chubukov+1 more|arXiv (Cornell University)|Oct 26, 2000

Advanced Physical and Chemical Molecular Interactions4 references3 citations

TL;DR

This paper proposes that spin-fermion coupling in cuprate superconductors generates experimentally detectable singularities in electronic response functions due to propagating magnon-like quasiparticles with gap Δₛ. It demonstrates that spectral functions, density of states, tunneling conductance, and optical conductivity exhibit sharp features at ω = Δ + Δₛ and ω = 2Δ + Δₛ, providing direct fingerprints of spin-mediated d-wave pairing, with strong consistency between these signatures and neutron scattering data on Δₛ.

ABSTRACT

We demonstrate that the feedback effect from bosonic excitations on fermions, which in the past allowed one to verify the phononic mechanism of a conventional, $s-$wave superconductivity, may also allow one to experimentally detect the ``fingerprints'' of the pairing mechanism in cuprates. We argue that for spin-mediated $d-$wave superconductivity, the fermionic spectral function, the density of states, the tunneling conductance through an insulating junction, and the optical conductivity are affected by the interaction with collective spin excitations, which below $T_c$ are propagating, magnon-like quasiparticles with gap $Δ_s$. We show that the interaction with a propagating spin excitation gives rise to singularities at frequencies $Δ+ Δ_s$ for the spectral function and the density of states, and at $2Δ+ Δ_s$ for tunneling and optical conductivities, where $Δ$ is the maximum value of the $d-$wave gap. We further argue that recent optical measurements also allow one to detect subleading singularities at $4Δ$ and $2Δ+ 2Δ_s$. We consider the experimental detection of these singularities as a strong evidence in favor of the magnetic scenario for superconductivity in cuprates.

Motivation & Objective

• To identify experimentally detectable signatures of spin-mediated d-wave superconductivity in cuprates.
• To establish that feedback from collective spin excitations (magnon-like quasiparticles) modifies fermionic response functions in a measurable way.
• To link observed singularities in ARPES, tunneling, and optical conductivity to the spin resonance gap Δₛ, validating the magnetic pairing scenario.
• To reconcile theoretical predictions of singularities at Δ+Δₛ and 2Δ+Δₛ with existing experimental data across multiple probes.

Proposed method

• Uses a strong-coupling spin-fermion model to describe electron interactions via exchange of collective spin excitations with gap Δₛ.
• Analyzes the fermionic self-energy and spectral function using a self-consistent approach, incorporating the propagating spin mode below Tc.
• Calculates the density of states, SIS tunneling conductance, and optical conductivity (W(ω)) within the same framework, including vertex corrections and feedback effects.
• Derives analytical expressions for singularities in response functions, showing sharp features at ω = Δ + Δₛ (spectral function, DOS) and ω = 2Δ + Δₛ (tunneling, optical conductivity).
• Compares theoretical predictions with ARPES, tunneling, and optical conductivity data, and validates Δₛ against neutron scattering measurements.
• Considers finite-temperature effects and shows that the singularity at 2Δ + Δₛ remains sharp at T ≪ Δ.

Experimental results

Research questions

• RQ1 Can the interaction between fermions and propagating spin excitations in d-wave superconductors produce experimentally observable singularities in electronic response functions?
• RQ2 Do the predicted singularities at ω = Δ + Δₛ and ω = 2Δ + Δₛ in spectral function, density of states, tunneling conductance, and optical conductivity match existing experimental data?
• RQ3 Is the value of the spin resonance gap Δₛ extracted from multiple probes consistent with direct neutron scattering measurements?
• RQ4 Can subleading singularities at 4Δ and 2Δ + 2Δₛ in optical conductivity serve as additional evidence for the magnetic pairing mechanism?

Key findings

• The fermionic spectral function and density of states exhibit a sharp singularity at ω = Δ + Δₛ due to coupling with propagating spin excitations, with the peak located near hot spots.
• The SIS tunneling conductance and optical conductivity show a dominant singularity at ω = 2Δ + Δₛ, arising from two-fermion scattering via the spin mode.
• The value of Δₛ extracted from ARPES, tunneling, and optical conductivity data agrees well with the neutron scattering resonance energy, providing strong consistency across probes.
• Subleading singularities at 4Δ and 2Δ + 2Δₛ are predicted in optical conductivity and have been observed experimentally at the expected frequencies.
• Finite-temperature effects reduce the sharpness of the 2Δ + Δₛ peak, but the singularity remains at the same frequency for T ≪ Δ.
• The results provide strong evidence for the magnetic pairing scenario in cuprates, as the observed singularities are uniquely tied to spin-mediated pairing and not present in conventional s-wave theories.