Phase Diagram of Heavy Fermion Metal CeCoIn5

A.Z. Msezane; E.V. Kirichenko; V.A. Stephanovich; V.R. Shaginyan

REVIEW

Phase Diagram of Heavy Fermion Metal CeCoIn5

V.R. Shaginyan, A.Z. Msezane, V.A. Stephanovich, E.V. Kirichenko

Strongly Correlated Electrons · Submitted 25 Feb 2006 · 34 references

Pith's verdict: A coherent but parameter-heavy fermion-condensation application to CeCoIn5; the central mechanism hangs on an assumed finite zero-temperature entropy, and the T*(H) formula contains a sign slip, but the two concrete predictions make it worth refereeing.

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arXiv IDcond-mat/0602602 (version 1)

Pith IDQC43B5BG, Pith's permanent record of this paper and its review

CitationA.Z. Msezane, E.V. Kirichenko, V.A. Stephanovich, V.R. Shaginyan. "Phase Diagram of Heavy Fermion Metal CeCoIn5." arXiv:cond-mat/0602602 (2006). https://pith.science/paper/QC43B5BG

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Editor's note

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Colleague,

Quick take on Shaginyan et al. (cond-mat/0602602): it is a self-contained letter that applies the fermion-condensation (FC) framework to CeCoIn5 and makes two concrete predictions. It deserves a careful referee, but don't let the plausible phase-diagram fit hide the fact that the keystone — a finite zero-temperature entropy S0 in the normal state — is imported from earlier FC papers, and the paper gives no microscopic argument for why CeCoIn5 sits in the FC regime. If S0 is zero, the first-order SC transition argument and the fluctuation suppression collapse.

What's genuinely new: the application to CeCoIn5, plus the two falsifiable predictions — a resistivity exponent change from c=-4/3 to c=-1 below Hcr≈1.02 Hc0, and asymmetric tunneling conductance from particle-hole asymmetry. The paper also argues Hc0≈Hc2 is accidental, which is a testable statement. Using one framework to tie together the NFL/LFL crossover, the A(H) divergence, the specific-heat jump, and the second-to-first-order transition is a real explanatory ambition, and the qualitative agreement with the phase diagram is non-trivially good.

The soft spots are real. Hc0 is treated as a fitting parameter (the paper says so), δpFC≈0.044 is extracted from the same specific-heat jump that the theory then "explains," and c1≈5 is estimated from the same A(H) data it is used to fit. That's circularity at the parameter level. The T*(H) formula also looks wrong as written: matching M*(T)∝1/T with M*(H)∝(H-Hc0)^(−2/3) gives T*∝(H-Hc0)^(2/3), not the displayed (H-Hc0)^(−2/3). The high-field crossover T*∝(H-Hc0) is stated without derivation. These need fixing before acceptance, but they are fixable.

The deeper issue is the FC ground state itself. Eq. (8) at T→0 only says ε=μ on an interval; it does not select the continuous n0(p) or prove it minimizes the free energy against the Fermi step. Stability of the flat-band solution is not shown here or, from what I can tell, in the cited FC literature in a way most condensed matter referees will treat as settled. So the stress-test is right: the explanatory power is conditional on a non-standard premise.

Bottom line: the paper is serious, the predictions are crisp, and the authors are open about many fitting parameters. It should go to peer review; a good referee can separate fixable issues (sign slip, parameter estimation) from the foundational question (is S0 finite in a real metal?). I wouldn't desk-reject it. If I worked on CeCoIn5, I'd cite it as the FC/QCP counterpoint.

Referee report

Significance

If correct, the paper would provide a single quasiparticle-based framework unifying the NFL and LFL regimes of a heavy-fermion compound, explaining the first-order superconducting transition, the enhanced specific-heat jump, the field dependence of the T^2 resistivity coefficient, and the crossover line T*(H). The paper also makes falsifiable predictions that could be tested by resistivity and tunneling experiments. However, the current version does not fully deliver this potential because the key inputs—the existence and entropy of the FC state, the condensate width δpFC, and the constant c1—are either imported from prior work or fitted to the very data the theory is meant to explain. The qualitative mechanism is coherent, and the predictions are specific, but the quantitative explanatory claim is not yet independently anchored.

Major objections (3)

[§2, Eq. (8) and following paragraph] The argument that the normal state has a finite zero-temperature entropy S0 rests entirely on the existence of the special FC solution n0(p) with 0<n0(p)<1 and flat dispersion ε(p)=μ, which is taken from Refs [13,14,20] rather than derived here. Equation (8) at T=0 only states ε(p)−μ=0; it does not select the equilibrium n0(p) or show that this flat-band solution is stable against the ordinary step-function Fermi-liquid solution. Since Eq. (10) forces the transition to become first order only because SSC→0 cannot match SNFL→S0, the entire first-order-transition and fluctuation-suppression scenario collapses if S0=0. The manuscript should either derive S0 from a microscopic model of CeCoIn5 or provide independent experimental evidence, and it should clarify the stability of the FC solution.
[§3, after Eq. (10)] The condensate width δpFC≃0.044 is estimated from the experimental specific-heat jump ΔC/Cn≃4.5 and the spin susceptibility, citing Ref. [23]. The same ΔC/Cn data are then used as evidence that the large specific-heat jump is a signature of the FC state, and δpFC is used to compute Hcr and to conclude that CeCoIn5 lies on the disordered side of the FCQPT. This makes the comparison with the specific-heat data and the resulting exponent A(H)∝(H−Hc0)^(−4/3) partly circular, because the parameter of the theory is calibrated on the data it claims to explain. Please state explicitly which parameters are fixed a priori and which are fitted, and separate calibrated curves from predictions.
[§4, A(H) and T*(H)] The central quantitative results A(H)∝(H−Hc0)^(−4/3) and T*(H)∝(H−Hc0)^(−2/3) are not derived from the equations of this paper; their derivation is delegated to Refs [28,29,31]. In addition, the constant c1≈5 is 'estimated on the basis of the experimental function A(H)', so the reduced field (Hcr−Hc0)/Hc0≈0.02 is fitted to the same data that are used to validate the exponent. A self-contained derivation of these scaling laws from the FC mechanism, with all constants determined independently of the CeCoIn5 data being explained, is needed to support the claim that the diagram is explained rather than parametrized.

Minor objections (5)

[§2, paragraph after Eq. (8)] The sentence 'the FC solutions are characterized by infinitesimal value of superconducting gap, Δ→0, while the order parameter κ0(p) remains finite and the entropy S=0' is confusing, because the normal FC state is later assigned finite entropy SNFL; please clarify that S=0 refers to the superconducting state, not to the FC normal state.
[Notation, Eqs. (3)-(4)] The symbol κ(p) is used both for the order parameter in Eq. (3) and for the function defined by the frequency integral in Eq. (4); please use distinct notation to avoid confusion.
[Abstract and References] There are several typos: 'BSC' should be 'BCS', 'Theretical' in Ref. [19] should be 'Theoretical', and 'upported' in the acknowledgments should be 'supported'.
[Fig. 1 caption] The caption has awkward grammar ('The solid squares (solid and dashed lines represent the calculated dependence ...) obtained from resistivity measurements denote the crossover boundaries'); please rephrase for clarity.
[§3, Hc0] The statement that Hc0 'can be treated as fitting parameter' makes explicit that one of the input parameters is not predicted by the theory; for a paper claiming to explain the phase diagram, it would be helpful to state the total number of free parameters and their values.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

The paper argues that the low-temperature H-T phase diagram of CeCoIn5 follows from Fermi-liquid theory once quasiparticles form a fermion-condensate state with flat dispersion and a finite zero-temperature entropy.

The reading

The paper is trying to show that the unusual low-temperature features of the heavy-fermion metal CeCoIn5 do not require exotic quantum-critical fluctuations. According to the authors, the main universal features of the experimental H-T phase diagram follow from ordinary Fermi-liquid theory, provided the quasiparticles form a fermion-condensate state: a flat dispersion on a finite momentum interval with a temperature-independent entropy at $T\to0$. This single mechanism is claimed to explain the change of the superconducting transition from second to first order at low temperatures, the divergence $A(H)\propto (H-H_{c0})^{-4/3}$, and the crossover line $T^*(H)$ between non-Fermi-liquid and Landau-Fermi-liquid behavior. A sympathetic reader would care because it promises one quasiparticle-based explanation for both the NFL and LFL regimes of a material that has often been read as evidence for a quantum critical point.

What carries the argument

The central object is the fermion-condensate state, defined by a flat quasiparticle dispersion $\varepsilon(p)=\mu$ on a finite momentum interval and by occupation numbers $0<n_0(p)<1$ that solve the Landau and BCS equations in the limit of vanishing coupling. The load-bearing property is the temperature-independent entropy $S_0=S_{\mathrm{NFL}}(T\to0)$, which follows from the non-Fermi-Dirac occupation. This entropy does the work: Eq. (10) forces the superconducting-normal transition, which is second order at higher temperature, to become first order below $T_0(H)$; the same $S_0$ makes the thermal expansion coefficient tend to a constant and the Gr\"uneisen ratio diverge. In finite fields, the small condensate width $\delta p_{FC}\simeq0.044$ fixes how quickly the Zeeman splitting of the two Fermi surfaces crosses the condensate, producing the exponent $-4/3$ and the position of the crossover line $T^*(H)$.

Extended reading notes

Core claim

The central claim is that the normal state of CeCoIn5 at low temperatures is a Fermi liquid in which quasiparticles condense into a fermion-condensate state behind the fermion-condensation quantum phase transition. In that state, the single-particle spectrum is flat, $\varepsilon(p)=\mu$, on an interval $p_i\le p\le p_f$, and the occupation numbers $n_0(p)$ are smooth, $0<n_0(p)<1$. Because the occupation function is not the Fermi-Dirac distribution, the entropy contains a temperature-independent term $S_0$ even as $T\to0$, and it is this term that forces the superconducting transition to become first order at low temperature when the entropy of the ordered state must go to zero. The same state, the paper argues, explains why quasiparticles survive despite the purported quantum critical point: the fluctuations that would destroy them are suppressed because the transition is first order. Finally, applying a magnetic field Zeeman-splits the two Fermi surfaces; once the splitting $\delta p_F$ exceeds the small condensate width $\delta p_{FC}\simeq0.044$, the system moves to the disordered side of the transition and exhibits the observed $A(H)\propto (H-H_{c0})^{-4/3}$ with crossover $T^*(H)$ matching the measured curve.

Load-bearing premise

The load-bearing premise is that CeCoIn5 actually forms the special fermion-condensate state, with a flat quasiparticle dispersion over a narrow momentum range and a nonzero entropy at absolute zero, a state the paper takes from earlier theory and calibrates with the material's specific heat and susceptibility, so if that state is absent or its zero-temperature entropy vanishes, the entire explanation collapses.

Editorial extensions

If this is right

If the picture is right, the non-Fermi-liquid and Landau-Fermi-liquid regimes of CeCoIn5 are two sides of the same quasiparticle state, and no independent quantum-critical fluctuation mechanism is needed.
The superconducting transition in CeCoIn5 should become first order below a temperature $T_0(H)$, with an entropy jump $S_0$; the same reasoning says any ordered phase reached from the NFL state at $H=0$ would also change its transition order at low temperature.
In the field-tuned LFL regime, $A(H)\propto (H-H_{c0})^{-4/3}$ and $B(H)$ should share the same critical field and stay in a field-independent ratio.
At fields below roughly $(H_{cr}-H_{c0})/H_{c0}\sim0.02$, the exponent of $A(H)$ should cross from $-4/3$ to $-1$, and the crossover temperature $T^*(H)$ should change from $(H-H_{c0})^{-2/3}$ to linear at high fields.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Going beyond the paper, the same entropy-intercept test could be applied to other heavy-fermion compounds whose normal state is suspected to sit near fermion condensation: a finite $C/T$ intercept as $H\to H_{c0}$ would be a signature, and its absence would single out CeCoIn5.
The predicted exponent crossover at a reduced field of about 0.02 is a sharp, testable distinction; high-resolution resistivity measurements just above $H_{c0}$ could confirm or rule out the Zeeman-splitting mechanism.
If the fermion-condensate state is real, the tunneling-conductivity asymmetry predicted here gives a non-thermal probe: asymmetry should grow as the system enters the NFL regime above $T^*(H)$ and vanish in the LFL regime, independent of the superconducting gap.
The paper's mechanism implies that the apparent quantum critical point in CeCoIn5 is not a standard second-order quantum critical point; a corollary for neighboring materials is that similar H-T diagrams with first-order superconducting boundaries could be reinterpreted as fermion-condensation features rather than fluctuation-driven ones.

Original abstract

We present a comprehensive analysis of the low temperature experimental H-T phase diagram of CeCoIn5. The main universal features of the diagram can be explained within the Fermi-liquid theory provided that quasiparticles form so called fermion-condensate state. We show that in this case the fluctuations accompanying an ordinary quantum critical point are strongly suppressed and cannot destroy the quasiparticles. Analyzing the phase diagram and giving predictions, we demonstrate that the electronic system of CeCoIn5 provides a unique opportunity to study the relationship between quasiparticles properties and non-Fermi liquid behavior.

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The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,587 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.11 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.09 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We present a comprehensive analysis of the low temperature experimental H-T phase diagram of CeCoIn5. The main universal features of the diagram can be explained within the Fermi-liquid theory provided that quasiparticles form so called fermion-condensate state. We show that in this case the fluctuations accompanying an ordinary quantum critical point are strongly suppressed and cannot destroy the quasiparticles. Analyzing the phase diagram and giving predictions, we demonstrate that the electronic system of CeCoIn5 provides a unique opportunity to study the relationship between quasiparticles properties and non-Fermi liquid behavior.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We present a comprehensive analysis of the low temperature experimental H-T phase diagram of CeCoIn5.	contribution 1.00	0.94	0.05	asserted 0.96
s1	The main universal features of the diagram can be explained within the Fermi-liquid theory provided that quasiparticles form so called fermion-condensate state.	interpretation 0.87	0.36	0.53	asserted 0.68
s2	We show that in this case the fluctuations accompanying an ordinary quantum critical point are strongly suppressed and cannot destroy the quasiparticles.	result 0.58	0.74	0.21	asserted 1.00
s3	Analyzing the phase diagram and giving predictions, we demonstrate that the electronic system of CeCoIn5 provides a unique opportunity to study the relationship between quasiparticles properties and non-Fermi liquid behavior.	interpretation 0.78	0.90	0.40	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.66 · evidence from analysis of existing data 0.85.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
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references and citing sentences
relations to other papers

levels run

P abstract

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S sections
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (34)

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D. Takahashi et al., Phys. Rev. B 67, 180407 (2003)

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M.Ya. Amusia, A.Z. Msezane, and V.R. Shaginyan, Phys. Lett. A 320, 459 (2004)

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while in CeCoIn 5 it diverges as A(H) ∝ (H − Hc0)c with the exponent c ≃ − 4/ 3 [4, 5]. In magnetic ﬁelds, the exponent c = −1 characterizes the function A(H) of HF liquid with FC [28], while the exponent c = −4/ 3 de- scribes the function A(H) of HF liquid on the disordered side of FC[28, 29]. To understand this striking change in the behavior of CeCoIn5...

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V.R. Shaginyan, JETP Lett. 79, 286 (2004)

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J. W. Clark, V. A. Khodel, and M. V. Zverev, Phys. Rev. B 71, 012401 (2005)

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How the literature uses it

Papers whose main result relates to this one's

How each label was checked · JSON

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

We demonstrate, that the main universal features of the low temperature experimental $H-T$ phase diagram of CeCoIn5 and other heavy-fermion metals can be well explained using Landau paradigm of quasiparticles.

Quasiparticles and quantum phase transition in universal low-temperature properties of heavy-fermion metals · 0.90

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [23]

V.A. Khodel, M.V. Zverev, and V.M. Yakovenko, Phys. Rev. Lett. 95, 236402 (2005)

View on Pith 2005

[2] [1]

G.R. Stewart, Rev. Mod. Phys. 73, 797 (2001)

View on Pith 2001

[3] [2]

S. Sachdev, Quantum Phase Transitions (Cambridge, Cambridge University Press, 1999)

View on Pith 1999

[4] [3]

P. Coleman and A.J. Schoﬁeld, Nature 433, 226 (2005)

View on Pith 2005

[5] [4]

J. Paglione et al., Phys. Rev. Lett. 91, 246405 (2003); J. Paglione et al., unpublished (cond-mat/0405157)

View on Pith Pith review arXiv 2003

[6] [5]

A. Bianchi et al., Phys. Rev. Lett. 91, 257001 (2003)

View on Pith 2003

[7] [6]

F. Ronning et al., unpublished (cond-mat/0602089)

View on Pith Pith review arXiv

[8] [7]

A. Malinowski et al., Phys. Rev. B 72, 184506 (2005)

View on Pith 2005

[9] [8]

E. D. Bauer et al., Phys. Rev. Lett. 94, 047001 (2005)

View on Pith 2005

[10] [9]

K. Izawa et al., Phys. Rev. Lett. 87, 057002 (2001)

View on Pith 2001

[11] [10]

A. Bianchi et al., Phys. Rev. Lett. 89, 137002 (2002)

View on Pith 2002

[12] [11]

N. Oeschler et al., Phys. Rev. Lett. 91, 076402 (2003)

View on Pith 2003

[13] [12]

S. Fujimori et al., unpublished (cond-mat/0602296)

View on Pith Pith review arXiv

[14] [13]

V.A. Khodel and V.R. Shaginyan, JETP Lett. 51, 553 (1990)

View on Pith 1990

[15] [14]

G. E. Volovik, JETP Lett. 53, 222 (1991)

View on Pith 1991

[16] [15]

M.Ya. Amusia and V.R. Shaginyan, Phys. Rev. B 63, 224507 (2001)

View on Pith 2001

[17] [16]

E.M.Lifshitz and L.P.Pitaevskii, Statistical Physics (Part 2, Butterworth-Heinemann, Oxford, 1999). 5

View on Pith 1999

[18] [17]

M. Pﬁtzner and P. W¨ olﬂe, Phys. Rev. B 33, 2003 (1986)

View on Pith 1986

[19] [18]

J.Bardeen, L.Cooper, J.R.Schrieﬀer, Phys. Rev. 108, 1175 (1957)

View on Pith 1957

[20] [19]

K. Maki and T. Tsuneto, Progress of Theretical Physics 31, 945 (1964); K. Maki, Phys. Rev. 148, 362 (1966)

View on Pith 1964

[21] [20]

M. E. Zverev, JETP Lett. 65, 863 (1997)

View on Pith 1997

[22] [21]

D. Takahashi et al., Phys. Rev. B 67, 180407 (2003)

View on Pith 2003

[23] [22]

M.Ya. Amusia, A.Z. Msezane, and V.R. Shaginyan, Phys. Lett. A 320, 459 (2004)

View on Pith 2004

[24] [24]

M.Ya. Amusia, S.A. Artamonov, and V.R. Shaginyan, JETP Lett. 74, 435 (2001)

View on Pith 2001

[25] [25]

C. Petrovic et al., J. Phys. Condens. Matter 13, L337 (2001)

View on Pith 2001

[26] [26]

while in CeCoIn 5 it diverges as A(H) ∝ (H − Hc0)c with the exponent c ≃ − 4/ 3 [4, 5]. In magnetic ﬁelds, the exponent c = −1 characterizes the function A(H) of HF liquid with FC [28], while the exponent c = −4/ 3 de- scribes the function A(H) of HF liquid on the disordered side of FC[28, 29]. To understand this striking change in the behavior of CeCoIn5...

View on Pith

[27] [27]

J. Custers et al., Nature 424, 524 (2003)

View on Pith 2003

[28] [28]

P. Gegenwart et al., Phys. Rev. Lett. 94, 076402 (2005)

View on Pith 2005

[29] [29]

V.R. Shaginyan, JETP Lett. 79, 286 (2004)

View on Pith 2004

[30] [30]

J. W. Clark, V. A. Khodel, and M. V. Zverev, Phys. Rev. B 71, 012401 (2005)

View on Pith 2005

[31] [31]

P. Nozi` eres, J. Phys. I (France) 2, 443 (1992)

View on Pith 1992

[32] [32]

V.R. Shaginyan, JETP Lett. 80, 263 (2004)

View on Pith 2004

[33] [33]

V.R. Shaginyan, JETP Lett. 81, 222 (2005)

View on Pith 2005

[34] [34]

W. K. Park et al., Phys. Rev. B 72, 052509 (2005)

View on Pith 2005