[Paper Review] Possible Pairing Mechanisms of PuCoGa$_5$ Superconductor

Yunkyu Bang, Alexander V. Balatsky+2 more|arXiv (Cornell University)|Feb 27, 2004

Metallurgical and Alloy Processes4 citations

TL;DR

This paper investigates spin fluctuations and phonons as pairing mechanisms in the unconventional superconductor PuCoGa₅, finding that spin fluctuations with a characteristic energy of ~150 K best explain the resistivity data and superconducting transition temperature (Tc = 18.5 K). The analysis suggests that the large residual resistivity (~20 μΩ·cm) implies an intrinsic Tc₀ of ~39 K, supporting unconventional (e.g., d-wave) pairing and ruling out phonon-mediated pairing as the primary mechanism.

ABSTRACT

We examine possible pairing mechanisms of superconductivity in PuCoGa$_5$ based on spin-fluctuations or phonons as mediating bosons. We consider experimental data of specific heat C(T) and resistivity $ρ(T)$ as input to determine a consistent scattering boson with the superconducting transition temperature of 18.5K in PuCoGa$_5$. Irrespective to the type of boson, the characteristic boson frequency is found to be $\sim 150 K$ from the resistivity fitting. The spin fluctuation model is most consistent with the experimental resistivity, successfully explaining the anomalous temperature dependence ($\sim \frac{T^2}{150 K +T}$) at low temperatures as well as the saturation behavior at high temperatures. Assuming that the pairing state is non s-wave, the large residual resistivity $ρ_{imp} \sim 20 μΩcm \sim 120 K$ suggests that an ideally pure sample of PuCoGa$_5$ would have a maximum T$_c$ of 39 K.

Motivation & Objective

• To determine whether spin fluctuations or phonons mediate superconductivity in PuCoGa₅, given its unusually high Tc of 18.5 K for an f-electron system.
• To reconcile experimental resistivity ρ(T) with superconducting pairing by identifying a consistent scattering boson.
• To assess the impact of strong electron-boson coupling and impurity scattering on Tc, particularly given the large residual resistivity (~20 μΩ·cm).
• To evaluate whether phonon-mediated s-wave pairing or spin-fluctuation-mediated unconventional pairing better fits the data.

Proposed method

• Uses the Kubo formula and Matsubara frequency summation to calculate conductivity σ(T) from the self-energy Σ(k,ω) in the Born approximation.
• Models electron-boson coupling via a spectral function B(q,ω′) for both spin fluctuations and phonons, with coupling strength g and characteristic energy scale ω₀.
• Fits the measured resistivity ρ(T) using the resulting spectral function, extracting λ (dimensionless coupling) and ω₀ from the temperature dependence.
• Applies the Allen-Dynes formula to estimate Tc from ω₀ and λ, comparing predictions with the observed Tc = 18.5 K.
• Evaluates the effect of impurity scattering on Tc using a modified Abrikosov-Gor'kov formula, assuming Z ≈ 5 and Γ_imp ≈ 2 K.
• Compares theoretical resistivity curves (T⁴/³ at low T, saturation at high T) with experimental data to assess model consistency.

Experimental results

Research questions

• RQ1 Can spin fluctuations or phonons consistently explain the resistivity ρ(T) and superconducting Tc = 18.5 K in PuCoGa₅?
• RQ2 What is the characteristic energy scale of the dominant scattering boson that fits the resistivity data?
• RQ3 Why does the resistivity exhibit a T⁴/³ dependence at low temperatures, and can this be explained by phonon or spin-fluctuation scattering?
• RQ4 How does the large residual resistivity (~20 μΩ·cm) affect the intrinsic Tc₀, and what does this imply for pairing symmetry?
• RQ5 Why is UCoGa₅ not superconducting despite structural similarity, if phonons are the pairing mechanism?

Key findings

• The characteristic energy scale of the scattering boson is ~150 K, extracted from fitting the resistivity ρ(T) across all temperatures.
• The spin fluctuation model successfully reproduces the anomalous T⁴/³ dependence at low T and saturation at high T, matching experimental ρ(T) data.
• Phonon-mediated pairing is inconsistent with the T⁴/³ resistivity behavior and requires an unphysical ω₀ = 150 K, conflicting with the Debye temperature θD = 240 K from specific heat.
• The large residual resistivity ρ_imp ≈ 20 μΩ·cm implies an intrinsic Tc₀ ≈ 39 K, suggesting that the observed Tc = 18.5 K is suppressed by pair-breaking effects.
• The observed Tc degradation over time due to radiation damage is consistent with unconventional pairing, but also possible with s-wave pairing if displaced Pu ions act as magnetic impurities.
• The spin-fluctuation model is the most consistent with all experimental data, supporting unconventional (e.g., d-wave) pairing in PuCoGa₅.