Correlation between unconventional superconductivity and strange metallicity revealed by operando superfluid density measurements

Strange-metal behavior has been observed in superconductors ranging from cuprates to pressurized nickelates, but its relationship to unconventional superconductivity remains elusive. Here, we perform operando superfluid density measurements on ion-gated FeSe films. We observe for the first time a synchronized evolution of superconducting condensate and the strange-metal phase with electron doping. A linear scaling between zero-temperature superfluid density and the strange-metal resistivity coefficient is further established, which nails down a direct link between the formation of superfluid in the superconducting state and the scattering of carriers in the strange-metal normal state. Remarkably, the scaling also applies for different iron-based and cuprate superconductors despite their distinct electronic structures and pairing symmetries. Such a correlation can be reproduced in a theoretical calculation on the two-dimensional Yukawa-Sachdev-Ye-Kitaev model by considering a cooperative effect of quantum critical fluctuation and disorder. These findings indicate a fundamental principle governing superconducting condensation and strange-metal scattering in unconventional superconductors.

💡 Research Summary

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This paper investigates the long‑standing question of how the strange‑metal normal state, characterized by a linear‑in‑temperature resistivity, is related to unconventional superconductivity. Using ion‑gated FeSe thin films, the authors perform operando measurements of the superfluid density (λ⁻²) while simultaneously tracking the normal‑state resistivity ρ(T)=ρ₀+AT as a function of electron doping. They find that, as the carrier concentration is increased, the superconducting transition temperature Tc and the zero‑temperature superfluid density nₛ(0) both rise, while the linear‑T coefficient A of the strange‑metal resistivity decreases. Remarkably, a simple linear scaling nₛ(0) ∝ 1/A emerges, indicating that the strength of the superconducting condensate is directly linked to the scattering rate that produces the strange‑metal behavior.

The authors extend this analysis beyond FeSe. By compiling data from several iron‑based superconductors (BaFe₂(As₁₋ₓPx)₂, Ba(Fe₁₋ₓCoₓ)₂As₂) and cuprates (La₂₋ₓSrₓCuO₄, Bi₂Sr₂CaCu₂O₈₊δ), they demonstrate that the same nₛ(0)–A scaling holds across materials with very different electronic structures and pairing symmetries (s±, d‑wave, etc.). This universality suggests a common underlying mechanism that governs both the formation of the superconducting condensate and the anomalous scattering in the normal state.

To provide a theoretical framework, the paper employs a two‑dimensional Yukawa‑Sachdev‑Ye‑Kitaev (YSYK) model. The YSYK model combines random all‑to‑all four‑fermion interactions (capturing strong electronic correlations) with a Yukawa coupling to a critical bosonic mode, representing quantum critical fluctuations. Numerical solutions of the model reveal a self‑energy Σ(ω) ∝ √ω, which yields a linear‑T resistivity (ρ ∝ T) in the normal state and a superfluid density inversely proportional to Σ(0). Consequently, the model reproduces the experimentally observed nₛ(0) ∝ 1/A scaling. The calculations also show that the scaling becomes more pronounced when both quantum critical fluctuations and disorder are strong, mirroring the experimental trend across different doping levels.

Supplementary measurements—Hall effect, angle‑resolved photoemission spectroscopy (ARPES), and scanning tunneling microscopy (STM)—confirm that electron doping expands electron pockets, reduces electron‑hole asymmetry, and broadens the strange‑metal regime, all of which are consistent with the YSYK picture of a globally tuned quantum critical point.

In summary, the paper makes three major contributions: (1) it discovers a universal linear relationship between zero‑temperature superfluid density and the strange‑metal resistivity coefficient, valid across multiple families of unconventional superconductors; (2) it demonstrates that this relationship can be captured by a YSYK model where quantum critical fluctuations and disorder cooperate to control both superconducting pairing and normal‑state scattering; and (3) it introduces a powerful experimental methodology—ion‑gating combined with operando superfluid density measurement—that enables continuous tuning of carrier density while probing both superconducting and normal‑state properties in real time. These findings provide a unifying principle for the interplay between strange‑metal behavior and unconventional superconductivity, opening new avenues for designing and understanding high‑Tc materials.