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arxiv: 2109.14032 · v2 · pith:WLNQ5ELInew · submitted 2021-09-28 · ❄️ cond-mat.str-el · cond-mat.supr-con

Quantum-Critical, Spin-Fluctuation-driven Residual Resistivity and Emergent Universal Correlations in the Fermi-Liquid Regime of Heavy-Fermion Superconductors

M. ElMassalami , P. B. Castro , M. B. Silva Neto This is my paper

Pith reviewed 2026-05-24 13:23 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.supr-con
keywords heavy-fermion superconductorsquantum critical pointspin fluctuationsresidual resistivityFermi liquid regimeunconventional superconductivityMigdal-Eliashberg theory
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The pith

Quantum-critical spin fluctuations in heavy-fermion superconductors generate an effective elastic scattering channel that produces a residual resistivity correlated with the scattering coefficient and superconducting transition temperature.

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

The paper tracks the pressure dependence of spin-fluctuation-driven residual resistivity, the Fermi-liquid scattering coefficient A, and the superconducting transition temperature Tc in heavy-fermion systems. It identifies three empirical correlations linking these quantities that do not appear in conventional Fermi-liquid superconductors. The authors conclude that quantum-critical fluctuations create an elastic channel in addition to mediating inelastic scattering and pairing. They model this by calculating the residual resistivity on the high-pressure side of the quantum critical point and introducing a length scale to derive relations for Tc and A.

Core claim

Quantum-critical spin fluctuations not only mediate inelastic scattering and Cooper pairing but also generate an effective elastic channel responsible for the temperature-independent residual resistivity ρ^sf_0. Using data from archetypal systems, three correlations are identified: ln(Tc/θ) ∝ A^{-1/2}, A ∝ (ρ^sf_0)^2, and ln(Tc/θ) ∝ (ρ^sf_0)^{-1}. Explicit calculation of ρ^sf_0 and introduction of ℓ ∼ (ρ^sf_0)^{-1} within the Migdal-Eliashberg framework and Boltzmann transport theory yield analytic expressions for Tc(ℓ) and A(ℓ) consistent with the trends.

What carries the argument

The characteristic length scale ℓ ∼ (ρ^sf_0)^{-1} capturing the spatial extent of fluctuation-induced scattering, which enables derivation of Tc(ℓ) and A(ℓ) relations.

If this is right

  • The three empirical correlations follow directly from the spin-fluctuation mechanism generating both pairing and the elastic channel.
  • Analytic expressions for Tc(ℓ) and A(ℓ) are obtained from the length scale.
  • The quantum-critical Fermi-liquid regime is an intrinsically correlated phase with unconventional transport and pairing.
  • These relations are absent in conventional superconductors because they lack the quantum-critical elastic channel.

Where Pith is reading between the lines

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

  • The length scale ℓ may be accessible through independent scattering or spectroscopic probes in the same materials.
  • Similar correlations could appear in other quantum-critical systems if an analogous elastic channel exists.
  • Pressure-dependent measurements in additional compounds would provide a systematic test of the derived interrelations.

Load-bearing premise

The Migdal-Eliashberg framework combined with Boltzmann transport theory remains valid on the high-pressure side of the quantum critical point.

What would settle it

A direct test in new heavy-fermion compounds showing that the three reported correlations fail while the high-pressure regime still satisfies the conditions for the Migdal-Eliashberg plus Boltzmann analysis.

Figures

Figures reproduced from arXiv: 2109.14032 by M. B. Silva Neto, M. ElMassalami, P. B. Castro.

Figure 1
Figure 1. Figure 1: FIG. 1. A sketch of a fluctuation-mediated e-e interaction [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) The [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) The generalized plot of [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
read the original abstract

We investigate correlations within the unconventional Fermi-liquid (FL) regime of quantum-critical (QC) heavy-fermion superconductors (HFSs) by tracking the pressure dependence of three quantities: the temperature-independent, SF-driven residual resistivity, $\rho^{ sf}_{0}(P)$; the FL scattering coefficient, $A(P)$; and the superconducting transition temperature, $T_c(P)$. The first two define the spin-fluctuation contribution to the resistivity, $\rho(T)=\rho^{sf}_0+AT^2$. Using experimental data from archetypal heavy-fermion systems, we identify three robust empirical correlations: $\ln(\frac{T_c}{\theta}) \propto A^{-1/2}$, $A \propto (\rho^{sf}_0)^2$, and $\ln(\frac{T_c}{\theta}) \propto \big(\rho^{sf}_0\big)^{-1}$ ($\theta$ is a characteristic temperature scale). Absent in conventional FL superconductors, these relationships indicate that QC fluctuations not only mediate inelastic scattering and Cooper pairing, but also generate an effective elastic channel responsible for $\rho^{sf}_0$. We explicitly calculate $\rho^{sf}_0$ on the high-pressure side of the quantum critical point (QCP) and introduce a characteristic length scale, $\ell \sim \big(\rho^{sf}_0\big)^{-1}$, that captures the spatial extent of fluctuation-induced scattering. Within this regime, and within the Migdal--Eliashberg framework combined with Boltzmann transport theory, we derive analytic expressions for $T_c(\ell)$ and $A(\ell)$, together with their interrelations, which are consistent with the observed empirical trends. These findings highlight the quantum-critical FL regime in HFSs as an intrinsically correlated phase, governed by fluctuations and marked by unconventional transport and pairing mechanisms.

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

3 major / 2 minor

Summary. The manuscript claims that in the unconventional Fermi-liquid regime of quantum-critical heavy-fermion superconductors, spin fluctuations generate not only inelastic scattering and Cooper pairing but also an effective elastic scattering channel responsible for the temperature-independent residual resistivity ρ^sf_0. From experimental data on archetypal systems, three empirical correlations are identified: ln(Tc/θ) ∝ A^{-1/2}, A ∝ (ρ^sf_0)^2, and ln(Tc/θ) ∝ (ρ^sf_0)^{-1}. The authors explicitly calculate ρ^sf_0 on the high-pressure side of the QCP, introduce a length scale ℓ ~ (ρ^sf_0)^{-1}, and within the Migdal-Eliashberg framework combined with Boltzmann transport derive analytic expressions for Tc(ℓ) and A(ℓ) whose interrelations match the observed trends.

Significance. If the central derivations are independent of the empirical trends and the Migdal-Eliashberg plus Boltzmann framework remains controlled on the high-pressure side of the QCP, the work would establish that the quantum-critical FL regime is intrinsically correlated, with QC fluctuations simultaneously controlling residual resistivity, T^2 scattering, and Tc. This would offer a unified microscopic picture for transport and pairing absent in conventional FL superconductors and provide falsifiable relations between measurable quantities.

major comments (3)
  1. [derivation of ρ^sf_0 and subsequent analytic expressions] The explicit calculation of ρ^sf_0 from QC spin fluctuations (described in the main text following the empirical correlations) must demonstrate that the Migdal-Eliashberg + Boltzmann treatment remains quantitatively valid sufficiently close to the QCP; the neglect of vertex corrections and assumption of well-defined quasiparticles with T^2 scattering may be uncontrolled even where resistivity remains FL-like, directly affecting the emergence of the elastic channel.
  2. [analytic expressions for Tc(ℓ) and A(ℓ)] The analytic expressions for Tc(ℓ) and A(ℓ) and their interrelations are stated to be consistent with the three empirical correlations identified from the same data sets; it is necessary to clarify whether the characteristic temperature θ enters as an independent input or is adjusted to the trends, and whether the length scale ℓ is introduced in a manner that makes the relations hold by construction rather than as independent predictions.
  3. [identification of empirical correlations] The data-selection criteria, error bars, and pressure ranges used to extract the three correlations (ln(Tc/θ) ∝ A^{-1/2}, A ∝ (ρ^sf_0)^2, ln(Tc/θ) ∝ (ρ^sf_0)^{-1}) are not specified; without these, it cannot be verified that the correlations are robust rather than the result of post-hoc selection among archetypal systems.
minor comments (2)
  1. [abstract and introduction] Notation for the characteristic temperature θ should be defined at first use and its relation to microscopic parameters clarified.
  2. [introduction of length scale ℓ] The physical interpretation of the invented length scale ℓ ~ (ρ^sf_0)^{-1} as the spatial extent of fluctuation-induced scattering requires additional justification beyond dimensional analysis.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed report. Below we respond point by point to the major comments, indicating where the manuscript will be revised.

read point-by-point responses

  1. Referee: The explicit calculation of ρ^sf_0 from QC spin fluctuations must demonstrate that the Migdal-Eliashberg + Boltzmann treatment remains quantitatively valid sufficiently close to the QCP; the neglect of vertex corrections and assumption of well-defined quasiparticles with T^2 scattering may be uncontrolled even where resistivity remains FL-like.

    Authors: The derivation is restricted to the high-pressure side of the QCP where clear T^2 resistivity confirms well-defined quasiparticles. The Migdal-Eliashberg framework is applied in the standard limit where spin-fluctuation energies are much smaller than the Fermi energy, for which vertex corrections are suppressed. We will add an expanded discussion of the applicability regime, including estimates based on the observed FL window, to address the concern about quantitative control. revision: partial

  2. Referee: The analytic expressions for Tc(ℓ) and A(ℓ) and their interrelations are stated to be consistent with the three empirical correlations; it is necessary to clarify whether the characteristic temperature θ enters as an independent input or is adjusted to the trends, and whether the length scale ℓ is introduced in a manner that makes the relations hold by construction rather than as independent predictions.

    Authors: θ is an independent input taken from the spin-fluctuation energy scale reported in the literature for each compound (e.g., from resistivity or susceptibility). The length ℓ is defined directly from the microscopically calculated ρ^sf_0. The expressions for Tc(ℓ) and A(ℓ) are obtained from the Migdal-Eliashberg equations plus Boltzmann transport without reference to the empirical correlations; the interrelations then emerge and match the trends. We will revise the text to make this independence explicit and avoid any suggestion of construction. revision: yes

  3. Referee: The data-selection criteria, error bars, and pressure ranges used to extract the three correlations are not specified; without these, it cannot be verified that the correlations are robust rather than the result of post-hoc selection among archetypal systems.

    Authors: We agree that full transparency on data handling is required. The revised manuscript will include (in the main text or a new supplementary section) the list of compounds, pressure ranges examined, determination of θ for each system, fitting procedures for A and ρ^sf_0, and reported uncertainties. This will permit independent verification of the correlations. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivations are independent of identified empirical trends.

full rationale

The paper first extracts three empirical correlations directly from experimental resistivity and Tc data on heavy-fermion systems. It then states that it explicitly calculates ρ^sf_0 and, within the Migdal-Eliashberg plus Boltzmann transport framework, derives analytic expressions for Tc(ℓ) and A(ℓ) together with their interrelations. These expressions are reported as consistent with the trends rather than fitted to them or defined in terms of them. No self-citations, ansatzes smuggled via prior work, or reductions of the derived quantities to the input correlations by construction appear in the provided text. The derivation chain is therefore self-contained against external benchmarks and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The central claim rests on standard condensed-matter frameworks plus empirical data from archetypal heavy-fermion systems; the novel elements are the interpretation of ρ^sf_0 as fluctuation-induced elastic scattering and the auxiliary length ℓ.

free parameters (1)
  • characteristic temperature θ
    Appears in the reported correlations ln(Tc/θ); its value per material is not derived from first principles in the abstract.
axioms (2)
  • domain assumption Migdal-Eliashberg framework applies on the high-pressure side of the QCP
    Invoked to derive Tc(ℓ) and A(ℓ)
  • standard math Boltzmann transport theory governs the resistivity expressions
    Combined with Migdal-Eliashberg to obtain analytic forms
invented entities (1)
  • length scale ℓ ~ (ρ^sf_0)^{-1} no independent evidence
    purpose: Captures the spatial extent of fluctuation-induced scattering
    Introduced to relate ρ^sf_0 to Tc and A; no independent falsifiable prediction supplied in abstract

pith-pipeline@v0.9.0 · 5895 in / 1634 out tokens · 32845 ms · 2026-05-24T13:23:40.419628+00:00 · methodology

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Reference graph

Works this paper leans on

62 extracted references · 62 canonical work pages

  1. [1]

    Gegenwart , author Q

    author author P. Gegenwart , author Q. Si , \ and\ author F. Steglich ,\ @noop journal journal Nat. Phys. \ volume 4 ,\ pages 186 ( year 2008 ) NoStop

    work page 2008

  2. [2]

    Coleman ,\ @noop journal journal Handbook of Magnetism and Advanced Magnetic Materials \ ( year 2007 ) NoStop

    author author P. Coleman ,\ @noop journal journal Handbook of Magnetism and Advanced Magnetic Materials \ ( year 2007 ) NoStop

    work page 2007

  3. [3]

    Jaccard , author H

    author author D. Jaccard , author H. Wilhelm , author K. Alami-Yadri , \ and\ author E. Vargoz ,\ @noop journal journal Physica B \ volume 259-261 ,\ pages 1 ( year 1999 ) NoStop

    work page 1999

  4. [4]

    author author H. Q. \ Yuan , author F. M. \ Grosche , author M. Deppe , author C. Geibel , author G. Sparn , \ and\ author F. Steglich ,\ @noop journal journal Science \ volume 302 ,\ pages 2104 ( year 2003 ) NoStop

    work page 2003

  5. [5]

    o hneysen , author A. Rosch , author M. Vojta , \ and\ author P. W\

    author author H. v. \ L\" o hneysen , author A. Rosch , author M. Vojta , \ and\ author P. W\" o lfle ,\ @noop journal journal Rev. Mod. Phys. \ volume 79 ,\ pages 1015 ( year 2007 ) NoStop

    work page 2007

  6. [6]

    author author N. D. \ Mathur , author F. M. \ Grosche , author S. R. \ Julian , author I. R. \ Walker , author D. M. \ Freye , author R. K. W. \ Haselwimmer , \ and\ author G. G. \ Lonzarich ,\ @noop journal journal Nature \ volume 394 ,\ pages 39 ( year 1998 ) NoStop

    work page 1998

  7. [7]

    Miyake \ and\ author S

    author author K. Miyake \ and\ author S. Watanabe ,\ @noop journal journal Philos. Mag. \ volume 97 ,\ pages 3495 ( year 2017 ) NoStop

    work page 2017

  8. [8]

    author author A. T. \ Holmes , author D. Jaccard , \ and\ author K. Miyake ,\ @noop journal journal Phys. Rev. B \ volume 69 ,\ pages 024508 ( year 2004 ) NoStop

    work page 2004

  9. [9]

    Pines ,\ @noop journal journal J

    author author D. Pines ,\ @noop journal journal J. Phys. Chem. B \ volume 117 ,\ pages 13145 ( year 2013 ) NoStop

    work page 2013

  10. [10]

    author author D. J. \ Scalapino ,\ @noop journal journal Reviews of Modern Physics \ volume 84 ,\ pages 1383 ( year 2012 ) NoStop

    work page 2012

  11. [11]

    author author T. A. \ Maier , author S. Karakuzu , \ and\ author D. J. \ Scalapino ,\ @noop journal journal Phys. Rev. Research \ volume 2 ,\ pages 033132 ( year 2020 ) NoStop

    work page 2020

  12. [12]

    Li , author S

    author author Z. Li , author S. Kivelson , \ and\ author D. Lee ,\ @noop journal journal npj Quantum Mater \ volume 6 ,\ pages 36 ( year 2021 ) NoStop

    work page 2021

  13. [13]

    Dean , author G

    author author M. Dean , author G. Dellea , author R. S. \ Springell , author F. Yakhou-Harris , author K. Kummer , author N. Brookes , author X. Liu , author Y. Sun , author J. Strle , author T. Schmitt , et al. ,\ @noop journal journal Nature materials \ volume 12 ,\ pages 1019 ( year 2013 ) NoStop

    work page 2013

  14. [14]

    Lee-Hone , author H

    author author N. Lee-Hone , author H. \"O zdemir , author V. Mishra , author D. Broun , \ and\ author P. Hirschfeld ,\ @noop journal journal Phys. Rev. Res. \ volume 2 ,\ pages 013228 ( year 2020 ) NoStop

    work page 2020

  15. [15]

    Lee-Hone , author J

    author author N. Lee-Hone , author J. Dodge , \ and\ author D. Broun ,\ @noop journal journal Phys. Rev, B \ volume 96 ,\ pages 024501 ( year 2017 ) NoStop

    work page 2017

  16. [16]

    Sidorov , author M

    author author V. Sidorov , author M. Nicklas , author P. Pagliuso , author J. Sarrao , author Y. Bang , author A. V. \ Balatsky , \ and\ author J. D. \ Thompson ,\ @noop journal journal Phys. Rev. Lett. \ volume 89 ,\ pages 157004 ( year 2002 ) NoStop

    work page 2002

  17. [17]

    This assumption is is invoked for taking care of the excess residual resistivity and its usefulness in reconciling the influence from each of disorder, pressure or magnetic field

    @noop note The assumption of a formation of a patch within which quantum critical fluctuations emerge does not contradict the requirement that quantum critical fluctuations are scale invariant and extend over a large-sized region.This is because the length scale of each patch is taken to be longer than the mean free path and coherence length. This assumpt...

    work page

  18. [18]

    Bergmann ,\ @noop journal journal Phys

    author author G. Bergmann ,\ @noop journal journal Phys. Rev. B \ volume 3 ,\ pages 3797 ( year 1971 ) NoStop

    work page 1971

  19. [19]

    Bergmann ,\ @noop journal journal Phys

    author author G. Bergmann ,\ @noop journal journal Phys. Rep. \ volume 27 ,\ pages 159 ( year 1976 ) NoStop

    work page 1976

  20. [20]

    Gurvitch ,\ @noop journal journal Phys

    author author M. Gurvitch ,\ @noop journal journal Phys. Rev. Lett. \ volume 56 ,\ pages 647 ( year 1986 ) NoStop

    work page 1986

  21. [21]

    @noop note In cases where X_ ^ 0 , one considers X X_ tot . Stop

    work page

  22. [22]

    @noop note An incorporation of nonmagnetic impurities Smith84-UBe13-Impurity-Incorporation, Adrian88-CeCu2Si2-CeCu6-Lattice-Disorder,Adrian88-CeCu2Si2-CeCu6-UPt3-Lattice-Disorder,Adrian89-HF-SUCs-LatticeDisorder leads to a reduction in ( ) and V^ sf _ ee and, as a consequence, to a drop in both A and T _c . Stop

    work page

  23. [23]

    Rosch ,\ @noop journal journal Phys

    author author A. Rosch ,\ @noop journal journal Phys. Rev. Lett. \ volume 82 ,\ pages 4280 ( year 1999 ) NoStop

    work page 1999

  24. [24]

    Kambe \ and\ author J

    author author S. Kambe \ and\ author J. Flouquet ,\ @noop journal journal Solid State Commun. \ volume 103 ,\ pages 551 ( year 1997 ) NoStop

    work page 1997

  25. [25]

    Sheikin , author D

    author author I. Sheikin , author D. Braithwaite , author J.-P. \ Brison , author W. Assmus , \ and\ author J. Flouquet ,\ @noop journal journal J. Low Temp. Phys. \ volume 118 ,\ pages 113 ( year 2000 ) NoStop

    work page 2000

  26. [26]

    Gegenwart , author C

    author author P. Gegenwart , author C. Langhammer , author C. Geibel , author R. Helfrich , author M. Lang , author G. Sparn , author F. Steglich , author R. Horn , author L. Donnevert , author A. Link , \ and\ author W. Assmus ,\ @noop journal journal Phys. Rev. Lett. \ volume 81 ,\ pages 1501 ( year 1998 ) NoStop

    work page 1998

  27. [27]

    Honda , author T

    author author F. Honda , author T. Maeta , author Y. Hirose , author Y. \=O nuki , author A. Miyake , \ and\ author R. Settai ,\ @noop journal journal J. Korean Phys. Soc. \ volume 63 ,\ pages 345 ( year 2013 ) NoStop

    work page 2013

  28. [28]

    Bellarbi , author A

    author author B. Bellarbi , author A. Benoit , author D. Jaccard , author J. M. \ Mignot , \ and\ author H. F. \ Braun ,\ @noop journal journal Phys. Rev. B \ volume 30 ,\ pages 1182 ( year 1984 ) NoStop

    work page 1984

  29. [29]

    \ Rueff , author S

    author author J.-P. \ Rueff , author S. Raymond , author M. Taguchi , author M. Sikora , author J.-P. \ Iti\'e , author F. Baudelet , author D. Braithwaite , author G. Knebel , \ and\ author D. Jaccard ,\ @noop journal journal Phys. Rev. Lett. \ volume 106 ,\ pages 186405 ( year 2011 ) NoStop

    work page 2011

  30. [30]

    Miranda \ and\ author V

    author author E. Miranda \ and\ author V. Dobrosavljevi \'c ,\ @noop journal journal Rep. on Prog. in Phys. \ volume 68 ,\ pages 2337 ( year 2005 ) NoStop

    work page 2005

  31. [31]

    Paglione , author M

    author author J. Paglione , author M. A. \ Tanatar , author D. G. \ Hawthorn , author E. Boaknin , author R. W. \ Hill , author F. Ronning , author M. Sutherland , author L. Taillefer , author C. Petrovic , \ and\ author P. C. \ Canfield ,\ @noop journal journal Phys. Rev. Lett. \ volume 91 ,\ pages 246405 ( year 2003 ) NoStop

    work page 2003

  32. [32]

    Bianchi , author R

    author author A. Bianchi , author R. Movshovich , author I. Vekhter , author P. G. \ Pagliuso , \ and\ author J. L. \ Sarrao ,\ @noop journal journal Phys. Rev. Lett. \ volume 91 ,\ pages 257001 ( year 2003 ) NoStop

    work page 2003

  33. [33]

    author author E. D. \ Bauer , author C. Capan , author F. Ronning , author R. Movshovich , author J. D. \ Thompson , \ and\ author J. L. \ Sarrao ,\ @noop journal journal Phys. Rev. Lett. \ volume 94 ,\ pages 047001 ( year 2005 ) NoStop

    work page 2005

  34. [34]

    Ronning , author C

    author author F. Ronning , author C. Capan , author E. D. \ Bauer , author J. D. \ Thompson , author J. L. \ Sarrao , \ and\ author R. Movshovich ,\ @noop journal journal Phys. Rev. B \ volume 73 ,\ pages 064519 ( year 2006 ) NoStop

    work page 2006

  35. [35]

    Kotegawa , author K

    author author H. Kotegawa , author K. Takeda , author T. Miyoshi , author S. Fukushima , author H. Hidaka , author T. C. Kobayashi , author T. Akazawa , author Y. Ohishi , author M. Nakashima , author A. Thamizhavel , et al. ,\ @noop journal journal J. Phys. Soc. Jpn. \ volume 75 ,\ pages 044713 ( year 2006 ) NoStop

    work page 2006

  36. [36]

    Araki , author M

    author author S. Araki , author M. Nakashima , author R. Settai , author T. C. \ Kobayashi , \ and\ author Y. Onuki ,\ @noop journal journal J. Phys.: Condens. Matter \ volume 14 ,\ pages L377 ( year 2002 ) NoStop

    work page 2002

  37. [37]

    Nakashima , author K

    author author M. Nakashima , author K. Tabata , author A. Thamizhavel , author T. C. \ Kobayashi , author M. Hedo , author Y. Uwatoko , author K. Shimizu , author R. Settai , \ and\ author Y. Onuki ,\ @noop journal journal J. Phys.: Condens. Matter \ volume 16 ,\ pages L255 ( year 2004 ) NoStop

    work page 2004

  38. [38]

    Nakashima , author H

    author author M. Nakashima , author H. Kohara , author A. Thamizhavel , author T. D. \ Matsuda , author Y. Haga , author M. Hedo , author Y. Uwatoko , author R. Settai , \ and\ author Y. \=O nuki ,\ @noop journal journal Physica B: Cond Matter \ volume 378 ,\ pages 402 ( year 2006 ) NoStop

    work page 2006

  39. [39]

    Onuki , author Y

    author author Y. Onuki , author Y. Miyauchi , author M. Tsujino , author Y. Ida , author R. Settai , author T. Takeuchi , author N. Tateiwa , author T. D. Matsuda , author Y. Haga , \ and\ author H. Harima ,\ @noop journal journal J. Phys. Soc. Jpn. \ volume 77 ,\ pages 37 ( year 2008 ) NoStop

    work page 2008

  40. [40]

    Hassinger , author G

    author author E. Hassinger , author G. Knebel , author K. Izawa , author P. Lejay , author B. Salce , \ and\ author J. Flouquet ,\ @noop journal journal Phys. Rev. B \ volume 77 ,\ pages 115117 ( year 2008 ) NoStop

    work page 2008

  41. [41]

    de Visser , author J

    author author A. de Visser , author J. Franse , \ and\ author A. Menovsky ,\ @noop journal journal J. Magn. Magn. Mater. \ volume 43 ,\ pages 43 ( year 1984 ) NoStop

    work page 1984

  42. [42]

    author author H. R. \ Ott , author H. Rudigier , author Z. Fisk , \ and\ author J. L. \ Smith ,\ @noop journal journal Phys. Rev. Lett. \ volume 50 ,\ pages 1595 ( year 1983 ) NoStop

    work page 1983

  43. [43]

    Nunez-Regueiro , author G

    author author M. Nunez-Regueiro , author G. Garbarino , \ and\ author M. D. \ Nunez-Regueiro ,\ @noop journal journal J Phys: Conf. Series \ volume 400 ,\ pages 022085 ( year 2012 ) NoStop

    work page 2012

  44. [44]

    author author P. B. \ Castro , author J. L. \ Ferreira , author M. B. S. \ Neto , \ and\ author M. ElMassalami ,\ @noop journal journal J. Phys.: Conf. Ser. \ volume 969 ,\ pages 012050 ( year 2018 ) NoStop

    work page 2018

  45. [45]

    Soares , author M

    author author C. Soares , author M. ElMassalami , author Y. Yanagisawa , author M. Tanaka , author H. Takeya , \ and\ author Y. Takano ,\ @noop journal journal Sci. Rep. \ volume 8 ,\ pages 7041 ( year 2018 ) NoStop

    work page 2018

  46. [46]

    author author J. P. \ Carbotte ,\ @noop journal journal Rev. Mod. Phys. \ volume 62 ,\ pages 1027 ( year 1990 ) NoStop

    work page 1990

  47. [47]

    ElMassalami \ and\ author M

    author author M. ElMassalami \ and\ author M. B. S. \ Neto ,\ @noop journal journal Phys. Rev. B \ volume 104 ,\ pages 014520 ( year 2021 ) NoStop

    work page 2021

  48. [48]

    author author W. E. \ Lawrence \ and\ author J. W. \ Wilkins ,\ @noop journal journal Phys. Rev. B \ volume 7 ,\ pages 2317 ( year 1973 ) NoStop

    work page 1973

  49. [49]

    author author W. E. \ Lawrence ,\ @noop journal journal Phys. Rev. B \ volume 13 ,\ pages 5316 ( year 1976 ) NoStop

    work page 1976

  50. [50]

    author author A. H. \ MacDonald ,\ @noop journal journal Phys. Rev. Lett. \ volume 44 ,\ pages 489 ( year 1980 ) NoStop

    work page 1980

  51. [51]

    author author A. H. \ MacDonald , author R. Taylor , \ and\ author D. J. W. \ Geldart ,\ @noop journal journal Phys. Rev. B \ volume 23 ,\ pages 2718 ( year 1981 ) NoStop

    work page 1981

  52. [52]

    Patton \ and\ author A

    author author B. Patton \ and\ author A. Zaringhalam ,\ @noop journal journal Phys. Lett. A \ volume 55 ,\ pages 95 ( year 1975 ) NoStop

    work page 1975

  53. [53]

    author author C. J. \ Pethick , author D. Pines , author K. F. \ Quader , author K. S. \ Bedell , \ and\ author G. E. \ Brown ,\ @noop journal journal Phys. Rev. Lett. \ volume 57 ,\ pages 1955 ( year 1986 ) NoStop

    work page 1955

  54. [54]

    21-FL-SC-Defectal-Reconciled for a discussion on the two reported exceptions

    @noop ( a ),\ note see Ref. 21-FL-SC-Defectal-Reconciled for a discussion on the two reported exceptions. Stop

    work page

  55. [55]

    (5) of Ref

    @noop ( b ),\ note based on Eq. (5) of Ref. Bergmann69-In-Sn-ee , for low defects, one obtains _ 1 _ . Stop

    work page

  56. [56]

    @noop ( c ),\ note such an argument, supported by the aforementioned agreement between theory and experiments, is not in contradiction with the fact that there are difference in the details of the corresponding phase diagrams (e.g. the number and type of T_c -domes, the number and type of the critical/crossover points p_m , p_v , etc.): In fact, irrespect...

    work page

  57. [57]

    author author J. L. \ Smith , author Z. Fisk , author J. O. \ Willis , author B. Batlogg , \ and\ author H. R. \ Ott ,\ @noop journal journal J Appl Phys \ volume 55 ,\ pages 1996 ( year 1984 ) NoStop

    work page 1996

  58. [58]

    Adrian \ and\ author G

    author author G. Adrian \ and\ author G. Saemann-Ischenko ,\ @noop journal journal Zeitschrift f \"u r Physik B Condensed Matter \ volume 72 ,\ pages 235 ( year 1988 ) NoStop

    work page 1988

  59. [59]

    Adrian \ and\ author H

    author author G. Adrian \ and\ author H. Adrian ,\ @noop journal journal Physica C: Superconductivity \ volume 153-155 ,\ pages 435 ( year 1988 ) NoStop

    work page 1988

  60. [60]

    Adrian \ and\ author H

    author author G. Adrian \ and\ author H. Adrian ,\ @noop journal journal J Less Common Met \ volume 149 ,\ pages 313 ( year 1989 ) NoStop

    work page 1989

  61. [61]

    author author A. C. \ Jacko , author J. O. \ Fjærestad , \ and\ author B. J. \ Powell ,\ @noop journal journal Nat Phys \ volume 5 ,\ pages 422 ( year 2009 ) NoStop

    work page 2009

  62. [62]

    Bergmann ,\ @noop journal journal Z

    author author G. Bergmann ,\ @noop journal journal Z. Physik \ volume 228 ,\ pages 25 ( year 1969 ) NoStop

    work page 1969