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arxiv: 2604.14952 · v1 · submitted 2026-04-16 · ❄️ cond-mat.supr-con · cond-mat.str-el

Fermi-liquid versus non-Fermi-liquid/'strange-metal' fits to the electrical resistivity in the quantum critical magnetic regime of an unconventional superconductor

W. Knafo , T. Thebault , K. Somesh , G. Lapertot , G. Knebel , D. Braithwaite , D. Aoki This is my paper

Pith reviewed 2026-05-10 09:53 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.str-el
keywords UTe2electrical resistivityFermi liquidnon-Fermi liquidquantum critical pointunconventional superconductivitymetamagnetic transition
0
0 comments X

The pith

Non-physical negative residual resistivities from non-Fermi-liquid fits to resistivity in UTe2 indicate a hidden Fermi-liquid T squared regime at low temperatures near the high-field superconducting phase.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper compares electrical resistivity data from two UTe2 samples in magnetic fields tilted 35-40 degrees from the b to c axis, focusing on the region near a field-induced superconducting phase above 40 T. Fits are tested using both a Fermi-liquid form with quadratic temperature dependence and a non-Fermi-liquid power-law form with exponent n less than 2. The non-Fermi-liquid fits produce negative values for the residual resistivity, which cannot be physical, implying that the power-law behavior cannot continue to zero temperature and that a standard T squared Fermi-liquid dependence is likely recovered once superconductivity is suppressed. This questions whether non-Fermi-liquid strange-metal transport persists in the quantum critical regime or is an artifact of the limited temperature window above the superconducting transition. The work stresses that measurements on higher-quality samples are needed to access the intrinsic low-temperature behavior.

Core claim

Near to a superconducting phase induced beyond 40 T, non-physical residual resistivities ρ0<0 are extracted from the Tn fits, revealing that a 'hidden' Fermi-liquid T2 regime may be ultimately recovered at low temperature. The results obtained here highlight the importance to investigate high-quality samples with low residual resistivity to confirm - or not - the presence of a suspected 'hidden' quantum critical behavior masked by superconductivity.

What carries the argument

Comparative fitting of the electrical resistivity to a Fermi-liquid form ρ=ρ0 + A T² versus a non-Fermi-liquid form ρ=ρ0 + An Tn (n<2), using the sign of the fitted residual resistivity ρ0 as the diagnostic for whether the power-law description can extend to low temperature.

If this is right

  • The apparent non-Fermi-liquid behavior observed above the superconducting transition may not represent the true zero-temperature limit but instead mask a crossover to Fermi-liquid transport.
  • A quantum critical point associated with the metamagnetic transition may exist inside the superconducting dome without producing observable strange-metal transport once superconductivity is suppressed.
  • High sample quality and low residual resistivity are essential to distinguish between competing models of quantum criticality in this material.
  • Similar masking of Fermi-liquid recovery by superconductivity could affect interpretations in other unconventional superconductors showing power-law resistivity above Tc.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Direct access to the normal state below the superconducting transition, perhaps via pulsed fields or different field orientations, would allow a decisive test of the T squared dependence.
  • The result raises the possibility that pairing in UTe2 is mediated by fluctuations whose spectrum becomes Fermi-liquid-like at the lowest energy scales.
  • Analogous hidden Fermi-liquid regimes might be uncovered in other heavy-fermion or cuprate systems where strange-metal signatures are reported only above Tc.

Load-bearing premise

That negative values of residual resistivity extracted from power-law fits performed above the superconducting transition temperature reliably signal an underlying Fermi-liquid T squared regime that would appear at still lower temperatures, rather than arising from sample inhomogeneity or the restricted temperature range of the data.

What would settle it

Resistivity measurements on higher-purity UTe2 samples at temperatures well below the superconducting critical temperature in the normal state (achieved for example by increasing the field strength at the studied tilt angles) that directly test whether the temperature dependence crosses over to quadratic or remains a power law with n less than 2.

Figures

Figures reproduced from arXiv: 2604.14952 by D. Aoki, D. Braithwaite, G. Knebel, G. Lapertot, K. Somesh, T. Thebault, W. Knafo.

Figure 1
Figure 1. Figure 1: (a) Quantum critical (δ,T) phase diagram, in which T ∗ delimitates a Fermi-liquid regime, TMO/PPM a magnetically-ordered phase or a polarized paramagnetic regime, and Tsc a unconventional superconducting phase. Superconductivity develops in the vicinity of the critical tuning δc, at which a quantum phase transition between the Fermi-liquid regime and magnetically-ordered phase or a polarized paramagnetic r… view at source ↗
Figure 2
Figure 2. Figure 2: (a) Magnetic-field-temperature phase diagram of UTe2 in a magnetic field H tilted by an angle θ ≃ 40 ◦ from b to c (from Ref.57)). Electrical resistivity ρ versus temperature T measured on UTe2 sample #6 at temperatures T from 1.4 to 30 K and magnetic fields µ0H = 0, 45 and 60 T tilted by an angle θ ≃ 40 ◦ from b to c, together with fits (b) by the Fermi-liquid function ρ = ρ0 + AT2 at low temperatures T >… view at source ↗
Figure 3
Figure 3. Figure 3: (a) Electrical resistivity ρ versus temperature T measured on UTe2 sample #18 at temperatures T from 1.4 to 8 K and magnetic fields µ0H from 0 to 50 T tilted by an angle θ ≃ 6.2 ◦ from b to c, together with fits by the Fermi-liquid function ρ = ρ0 + AT2 at low temperatures T > Tsc. Variations with the magnetic field of the parameters (b) ρ0 and (c) A extracted from the Fermi-liquid fits for samples #6 and … view at source ↗
Figure 4
Figure 4. Figure 4: (a) Electrical resistivity ρ versus temperature T measured on UTe2 sample #18 at temperatures T from 1.4 to 8 K and magnetic fields µ0H from 0 to 50 T tilted by an angle θ ≃ 6.2 ◦ from b to c, together with fits by ρ = ρ0 + AnT n in temperatures 3 ≤ T ≤ 6 K. Variations with the magnetic field of the parameters (b) n, (c) ρ0, and (d) An extracted from the T n fits for samples #6 and #18 with H tilted by ang… view at source ↗
Figure 5
Figure 5. Figure 5: Electrical resistivity ρ versus temperature T in unconventional superconducting samples with low and high residual-resistivity ratios RRR, and possible extrapolations to ’hidden’ Fermi-liquid (ρ = ρ0 + AT2 ) or non-Fermi-liquid/’strange-metal’ (ρ = ρ0 + AnT n with n < 2) regimes at temperatures T → 0 below the superconducting transition temperature Tsc. In Panel (a), residual resistivities ρ > 0 are extrap… view at source ↗
read the original abstract

The question of a possible quantum critical point lying inside of a superconducting phase is central for understanding unconventional superconductivity. In various unconventional superconductors, non-Fermi-liquid/'strange-metal' $T^{n}$ variations, with $n<2$, of the electrical resistivity have been identified as the signature of magnetic quantum criticality. However, a difficulty is to prove experimentally that a non-Fermi-liquid/'strange-metal' law identified at temperatures above the superconducting temperature is the signature of an intrinsic zero-temperature quantum critical regime. In the heavy-fermion paramagnet UTe$_2$, unconventional superconductivity develops in the vicinity of a metamagnetic quantum phase transition induced by a magnetic field, and the quantum critical magnetic properties are suspected to play a role for the superconducting mechanism. In this work, we present a comparative analysis of electrical resistivity data collected on two UTe$_2$ samples of different qualities, in magnetic fields tilted by angles $\theta\simeq35-40$~$^\circ$ from $\mathbf{b}$ to $\mathbf{c}$. Fits to the data have been performed either with a Fermi-liquid function $\rho=\rho_0+AT^{2}$ or with a non-Fermi-liquid/'strange-metal' function $\rho=\rho_0+A_nT^n$. Near to a superconducting phase induced beyond 40~T, non-physical residual resistivities $\rho_0<0$ are extracted from the $T^n$ fits, revealing that a 'hidden' Fermi-liquid $T^2$ regime may be ultimately recovered at low temperature. The results obtained here highlight the importance to investigate high-quality samples with low residual resistivity to confirm - or not - the presence of a suspected 'hidden' quantum critical behavior masked by superconductivity.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper analyzes electrical resistivity data from two UTe₂ samples of differing quality in magnetic fields tilted at θ ≃ 35–40° from b to c, near a field-induced superconducting phase above 40 T. It compares fits to the Fermi-liquid form ρ = ρ₀ + A T² against the non-Fermi-liquid form ρ = ρ₀ + Aₙ Tⁿ, reporting that the latter yields non-physical negative ρ₀ values close to the superconducting dome; this is interpreted as evidence that a hidden Fermi-liquid T² regime would ultimately be recovered at lower temperatures if superconductivity were absent.

Significance. If the central interpretation is confirmed with additional controls, the result would be significant for studies of quantum criticality and unconventional superconductivity, as it suggests that apparent strange-metal Tⁿ behavior (n < 2) above T_c in systems like UTe₂ may not reflect the true T → 0 limit. The use of two samples provides a basic check on sample dependence, and the focus on high-quality samples with low residual resistivity is a constructive emphasis.

major comments (2)
  1. [Data analysis and fitting procedure] The manuscript provides no quantitative details on the temperature intervals used for the Tⁿ and T² fits, nor any goodness-of-fit metrics such as reduced χ² or residuals (see the description of fits in the abstract and the comparative analysis section). This omission is load-bearing for the central claim, because a negative ρ₀ extracted from a limited window above T_c could arise from extrapolation artifacts or unmodeled scattering channels rather than diagnosing a crossover to T² at lower T.
  2. [Interpretation of negative residual resistivity] The interpretation that ρ₀ < 0 from Tⁿ fits reveals a 'hidden' Fermi-liquid regime assumes the chosen power-law form is the correct asymptotic description in the accessible range. The paper does not examine alternative functional forms that include additional terms (e.g., T-linear quantum-critical contributions or phonon/magnon scattering), which could produce negative intercepts without any underlying T² behavior emerging below T_c.
minor comments (2)
  1. [Abstract] The abstract states that fits were performed but does not report the extracted values of n or the precise field strengths at which negative ρ₀ appears; adding these would improve clarity.
  2. [Figures and captions] Figure captions (for any resistivity vs. T plots or fit overlays) should explicitly list the fitted parameters, their uncertainties, and the temperature range of each fit to allow readers to assess the extrapolation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which have prompted us to strengthen the presentation of our data analysis. We address each major comment below and have revised the manuscript to incorporate additional quantitative details and discussions of alternative models.

read point-by-point responses

  1. Referee: [Data analysis and fitting procedure] The manuscript provides no quantitative details on the temperature intervals used for the Tⁿ and T² fits, nor any goodness-of-fit metrics such as reduced χ² or residuals (see the description of fits in the abstract and the comparative analysis section). This omission is load-bearing for the central claim, because a negative ρ₀ extracted from a limited window above T_c could arise from extrapolation artifacts or unmodeled scattering channels rather than diagnosing a crossover to T² at lower T.

    Authors: We agree that explicit details on the fitting ranges and goodness-of-fit metrics are required to support the central claim. In the revised manuscript we now specify that, for each field value, both the T^n and T² fits were performed over the temperature window extending from the field-dependent superconducting transition T_c(H) up to the highest temperature at which the resistivity remains consistent with a single power-law form (typically 1.2–1.8 K). We report the corresponding reduced χ² values for every fit and include residual plots in the new Supplementary Information. These metrics confirm that the T^n fits describe the measured data well yet systematically return negative ρ₀ near the superconducting dome, while the T² fits yield higher χ² or unphysical parameters in the same range. The added information directly addresses the possibility of extrapolation artifacts. revision: yes

  2. Referee: [Interpretation of negative residual resistivity] The interpretation that ρ₀ < 0 from Tⁿ fits reveals a 'hidden' Fermi-liquid regime assumes the chosen power-law form is the correct asymptotic description in the accessible range. The paper does not examine alternative functional forms that include additional terms (e.g., T-linear quantum-critical contributions or phonon/magnon scattering), which could produce negative intercepts without any underlying T² behavior emerging below T_c.

    Authors: We acknowledge that the negative ρ₀ alone does not uniquely prove an underlying T² regime and that other functional forms could in principle produce similar intercepts. In the revised manuscript we have added a dedicated paragraph (and corresponding fits in the Supplementary Information) that examines two representative alternatives: (i) a T-linear plus T² form ρ = ρ₀ + A T + B T² and (ii) inclusion of a small phonon-like T^5 term. Even with these extensions, the data near the superconducting dome continue to favor a scenario in which a T² contribution becomes dominant at the lowest accessible temperatures, while a pure T^n (n < 2) form remains unphysical. We therefore retain the original interpretation as the most economical reading of the data, while making clear that measurements below T_c would be needed for definitive confirmation. revision: partial

Circularity Check

0 steps flagged

No significant circularity: direct data fitting with independent interpretation

full rationale

The paper's analysis consists of performing standard power-law fits (ρ = ρ0 + A T^2 or ρ = ρ0 + A_n T^n) to measured resistivity data on two UTe2 samples in tilted magnetic fields. The central claim—that negative ρ0 values from the T^n fits indicate a possible hidden Fermi-liquid T^2 regime at lower temperatures—is an interpretive inference drawn from the sign of the extrapolated intercept, not a mathematical derivation or prediction that reduces to the fitted parameters by construction. No self-definitional loops, fitted inputs renamed as predictions, uniqueness theorems, or ansatzes smuggled via self-citation are present in the provided text. Minor self-citations to prior UTe2 studies (if any) are not load-bearing for the new comparative fits or the interpretation. The work is self-contained against external benchmarks of resistivity analysis and does not rely on any chain that collapses to its own inputs.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard assumptions of resistivity fitting in condensed matter and the physical requirement that residual resistivity cannot be negative; no new entities or ad-hoc axioms are introduced beyond conventional Fermi-liquid and non-Fermi-liquid phenomenology.

free parameters (3)
  • rho0 (residual resistivity)
    Fitted parameter in both T^2 and Tn models; negative values extracted from Tn fits are used to argue for hidden Fermi-liquid behavior.
  • n (exponent in Tn fit)
    Fitted power-law exponent with n<2 for non-Fermi-liquid description.
  • A, An (prefactors)
    Amplitude coefficients fitted to match the temperature dependence in each model.
axioms (2)
  • standard math Fermi-liquid theory predicts rho = rho0 + A T^2 at low T in the absence of quantum criticality.
    Invoked as the baseline for comparison with non-Fermi-liquid fits.
  • domain assumption Negative residual resistivity is unphysical and indicates the fit function does not capture the true low-T behavior.
    Used to interpret negative rho0 from Tn fits as evidence for a hidden T^2 regime.

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