Unmasking the nodal quasiparticle dynamics in cuprate superconductors using low-energy photoemission

A. Fujimori; A. Ino; H. Namatame; K. Yamazaki; M. Arita; M. Ishikado; M. Taniguchi; S. Uchida; T. Yamasaki; Z.-X. Shen

REVIEW

Unmasking the nodal quasiparticle dynamics in cuprate superconductors using low-energy photoemission

T. Yamasaki, K. Yamazaki, A. Ino, M. Arita, H. Namatame, M. Taniguchi, A. Fujimori, Z.-X. Shen

show 2 more authors

M. Ishikado, S. Uchida

Superconductivity · Submitted 1 Mar 2006 · 27 references

Pith's verdict: A genuinely new bilayer-resolved nodal scattering-rate measurement, but the band-resolved ordering rests on a fit of a barely resolved doublet and the paper does not show the error bars needed to trust that ordering.

T0 · AI review

How this review was made: An AI referee (deepseek-v4-flash) read the paper on August 28, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 3 major objections · 5 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDcond-mat/0603006 (version 2)

Pith IDEUDVZ7BT, Pith's permanent record of this paper and its review

CitationA. Fujimori, A. Ino, H. Namatame, K. Yamazaki, M. Arita, M. Ishikado, M. Taniguchi, S. Uchida, T. Yamasaki, Z.-X. Shen. "Unmasking the nodal quasiparticle dynamics in cuprate superconductors using low-energy photoemission." arXiv:cond-mat/0603006 (2006). https://pith.science/paper/EUDVZ7BT

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

The useful new thing here is real: 7.57 eV tunable photons let this group resolve the nodal bilayer splitting in Bi2212 directly and give separate linewidths for the bonding and antibonding bands. That settles a live experimental contradiction, because the 6 eV laser study saw only one band and the circular-dichroism work implied the opposite band ordering. The paper is worth taking seriously. It is also honest about what is direct measurement and what is interpretation.

What it does well: the photon-energy tuning is not routine, the momentum resolution is clearly improved, the 0.0075 Å⁻¹ splitting is reproduced across several samples with a quoted uncertainty, and the Kramers-Kronig consistency between the width-derived ImΣ and the dispersion-derived ReΣ is a proper internal check. The comparison with optical transport scattering rates is a nice sanity check. These are real experimental contributions.

Where I would push back: the central band-resolved result is the antibonding scattering rate growing faster with energy, and that result currently rests on decomposing a doublet whose 0.0075 Å⁻¹ separation is only slightly larger than the 0.0065 Å⁻¹ single-peak width. Two overlapping Lorentzians with a flat background can produce almost any width asymmetry if the fit is not constrained, and the paper gives no error bars, no residuals, and no sensitivity analysis for the Fig. 2(d) fits. The later wide-range fits fix the width ratio to 1 and the intensity ratio to 0.78; if even some of that fixing leaks into the fits behind Fig. 2(d), the apparent band ordering could be a fitting artifact rather than a quasiparticle property. The interpretation about scatterers outside the CuO₂ bilayer depends on that ordering, so this is load-bearing. The abrupt drop across Tc is also claimed from only two temperatures inside the superconducting state (9 and 50 K) and two above (95 and 200 K); that supports a sizable reduction but not an abrupt discontinuity at Tc.

The stress-test note is stronger than the paper deserves in one respect: the text says Fig. 2(d) widths come from two independent Lorentzians, so the different slopes are not simply forced by the fixed-ratio constraint. But the absence of error bars still leaves the ordering unproven.

Who should read this: anyone working on cuprate nodal quasiparticles, bilayer effects, or impurity-scattering models. It is a solid experimental paper that needs a revision with full fitting details, error propagation, and denser temperature sampling. It deserves a serious referee, not a desk rejection, and I would want it cited for the resolved splitting even if the band-resolved slopes prove fragile.

Referee report

Significance

If the bilayer-resolved scattering rates are correct, the paper provides a rare direct experimental probe of the spatial origin of quasiparticle scattering in a bilayer cuprate, with implications for the nature of intrinsic disorder and for theories of nodal transport. The low-photon-energy measurement achieves exceptionally sharp momentum resolution and resolves a nodal splitting that was not seen in a laser-ARPES study, a notable experimental advance. The reproducibility of the splitting width across several samples and the Kramers-Kronig consistency of the averaged self-energy are strengths that support the overall quality of the data. However, the central band-resolved claim currently rests on fits of a barely resolved doublet without statistical validation, so the significance of the conclusion about out-of-plane scatterers is not yet firmly established.

Major objections (3)

[Fig. 2(d) and accompanying text] The bilayer-resolved scattering rates in Fig. 2(d) are the paper's central new result, but their statistical reliability is not established. The doublet separation (k_b − k_a = 0.0075 Å⁻¹) is only slightly larger than the claimed single-peak FWHM (0.0065 Å⁻¹) at ω = 0, so the two Lorentzians are heavily overlapping. The manuscript reports no error bars on the widths, no fit residuals, and no test of the stability of the two-peak decomposition under variations of the assumed line shape, background, or initial parameters. The later wide-range fitting procedure (text near Fig. 4) fixes the width ratio Δk_a/Δk_b = 1 and intensity ratio I_a/I_b = 0.78; if analogous constraints were used for Fig. 2(d), they would directly force the two widths to be equal at ω = 0 and could bias the energy dependence, while if they were not used, the unconstrained fits need to be shown to be well-determined. Because the paper's inference about out-of-plane scatterers rests on the larger linear slope of the antibonding width (≈0.21 vs. ≈0.11 Å⁻¹ eV⁻¹), this is a load-bearing issue. I request a bootstrap or Monte Carlo error analysis, representative fits with residuals, and a demonstration that the qualitative ordering (antibonding broader at finite ω) is robust to reasonable changes in the fitting model.
[Figs. 4(c), 4(d) and the Kramers-Kronig discussion] The Kramers-Kronig consistency check between the width-derived ImΣ(ω) and the dispersion-derived ReΣ′(ω) is performed on the bilayer-averaged quantities. The text explicitly states that the wide-range fitting 'obtained the momentum width and dispersion, which are averaged between the bonding and antibonding quasiparticles.' Therefore the good agreement in Figs. 4(c) and 4(d) supports the reliability of the average self-energy but does not validate the band-resolved width difference shown in Fig. 2(d). The manuscript should state this distinction explicitly so that readers do not take the Kramers-Kronig check as evidence for the bilayer-resolved claim.
[Fig. 5 and discussion of the temperature dependence] The claim of an abrupt suppression of the zero-energy scattering rate at the superconducting transition is based on only four temperature points (9, 50, 95, 200 K), with no error bars on the widths. The change between T = 50 K and T = 95 K could in principle be gradual, and a single normal-state point near Tc does not establish 'abruptness.' The authors should report the statistical uncertainty of the widths and, if possible, measure additional temperatures around Tc to resolve the transition behavior. This is important because the interpretation that elastic scattering is suppressed by the d-wave gap relies on the sudden drop.

Minor objections (5)

[Title (text)] The title in the manuscript contains 'supe rconductors' with an unnecessary space; please check the typography.
[Text near Fig. 4] The origin of the fixed parameters I_a/I_b = 0.78 and Δk_a/Δk_b = 1 used in the wide-range fits is not stated; the authors should explain how these values were determined and whether they are consistent with free fits to the high-resolution data in Fig. 2.
[Fig. 4(b) and Eq. (1)] The scaling factor v0 = 2.8 eV Å is taken from Ref. 18; the paper should indicate the uncertainty in this value and its propagation into the reported ImΣ(ω).
[Inset of Fig. 4(b)] The comparison with the optical transport scattering rate would benefit from a definition of the plotted quantities and the normalization procedure used.
[Discussion of Ref. 15] The discrepancy with the laser-ARPES result of Ref. 15, where only a single nodal band was observed, is mentioned but not discussed in detail; a brief comment on why the present low-energy tunable-photon measurement resolves the doublet would help the reader assess the conflict.

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

The paper

The paper claims

In nearly optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, the nodal quasiparticle scattering rate drops abruptly at the superconducting transition, rises linearly with energy, and is larger for the antibonding band — evidence for…

The reading

This paper claims that in nearly optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, the nodal single-particle scattering rate drops abruptly when the material becomes superconducting, then grows linearly with energy at low energies. The authors use low-energy tunable photons to resolve a small bilayer splitting along the nodal direction, which lets them extract scattering rates for the bonding and antibonding bands separately. They find that the two rates are equal at $\omega=0$ but the antibonding rate rises faster with $|\omega|$, a difference they trace to the spatial location of the dominant scatterers. If the interpretation is right, elastic impurity scattering in a $d$-wave superconductor is not a fixed background: the superconducting gap shuts off large-angle elastic channels, leaving small-angle scattering from impurities outside the CuO$_2$ bilayer to control low-energy quasiparticles.

What carries the argument

The central machinery is low-energy tunable-photon angle-resolved photoemission at $h\nu=7.57$ eV, tuned to a final state so that in-plane momenta are magnified into large emission angles and the 0.0075 Å$^{-1}$ nodal bilayer splitting becomes visible. The analysis then rests on decomposing every momentum distribution curve into two independent Lorentzians whose peak widths give the bilayer-resolved scattering rates; the width is converted to the imaginary part of the self-energy through $\mathrm{Im}\,\Sigma(\omega)=-\tfrac12 v_0\,\Delta k$ with the unrenormalized velocity $v_0=2.8$ eV Å. Conceptually, the mechanism that carries the physical conclusion is the opening of the $d$-wave gap: it removes elastic scattering between different segments of the Fermi surface, leaving only forward scattering into the vicinity of the node, and the phase space for those events grows linearly with $|\omega|$ because the nodal density of states is proportional to $|\omega|$.

Extended reading notes

Core claim

By resolving the 0.0075 Å$^{-1}$ nodal bilayer doublet at a photon energy of 7.57 eV, the paper exposes the intrinsic nodal scattering rate of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. Fitting each momentum distribution curve with two independent Lorentzians gives momentum widths $\Delta k_a$ and $\Delta k_b$ that are identical at $\omega=0$ and then separate linearly, with the antibonding width growing at about 0.21 Å$^{-1}$eV$^{-1}$ versus 0.11 Å$^{-1}$eV$^{-1}$ for the bonding band. The zero-energy width drops by 60–70% on cooling through $T_c=86$ K, and the wide-range imaginary self-energy follows a linear energy dependence at low energies, with a step near 70 meV attributed to optical-phonon coupling. The paper argues that these three features — the abrupt drop at $T_c$, the $\omega$-linear rise, and the band ordering of the widths — cannot be explained by magnetic scattering or by ordinary inelastic processes, and instead indicate elastic, small-angle (forward) scattering by impurities located outside the CuO$_2$ bilayer.

Load-bearing premise

The argument stands on the assumption that each momentum distribution curve is a clean sum of two independent Lorentzians, that the 0.0075 Å$^{-1}$ doublet is the true bonding/antibonding pair, and that fixing the intensity ratio $I_a/I_b=0.78$ and the width ratio $\Delta k_a/\Delta k_b=1$ in the wide-range fits does not bias which band appears broader.

Editorial extensions

If this is right

Nodal quasiparticles in optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ travel at least about 150 Å without scattering at the Fermi level in the superconducting state.
A large fraction, 60–70%, of the zero-energy nodal scattering rate disappears at $T_c$, so elastic impurity scattering in these materials is not a temperature-independent constant.
In any $d$-wave superconductor with elastic forward scatterers, the low-energy single-particle scattering rate should grow linearly with $|\omega|$, tracking the nodal density of states.
The antibonding-versus-bonding scattering-rate difference provides a spectroscopic probe of where the dominant scatterers sit relative to the CuO$_2$ bilayer.
Small-angle elastic scattering can dominate single-particle spectra while leaving transport largely unaffected, reconciling ARPES widths with optical-conductivity scattering rates.

Reading between the lines

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

A clean test would be to measure the node of a single-layer cuprate: the same sharp drop at $T_c$ and the same linear low-energy width should appear without any bilayer doublet, which would separate the physics of forward scattering from the bilayer-fitting procedure.
The spatial sensitivity suggested by the band ordering could be developed into a quantitative probe: controlled changes to the oxygen content in the BiO/SrO layers should move the antibonding-versus-bonding width difference in a predictable direction.
If the elastic term is as clean as the paper suggests, higher-resolution measurements at lower temperatures should show the $\omega=0$ residual width approaching a disorder-limited floor, whose size would directly count the out-of-plane impurity concentration.

Original abstract

Nodal quasiparticles of Bi2Sr2CaCu2O8 have been studied by angle-resolved photoemission spectroscopy with high momentum and energy resolution. Low-energy tunable photons have enabled us to resolve a small nodal bilayer splitting, unmasking the intrinsic single-particle scattering rate. The nodal scattering rate is abruptly suppressed upon the superconducting transition, and shows a linear energy dependence at low energies, indicating the nontrivial effect of elastic scatterings on the quasiparticles. With increasing energy, the antibonding-band scattering rate becomes higher than the bonding one. The observations imply the character of the scatterers dominant at low energies.

The compiled record

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, 4,261 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.08 · human participants 0.02 · controlled comparison 0.15 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.16 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

Nodal quasiparticles of Bi2Sr2CaCu2O8 have been studied by angle-resolved photoemission spectroscopy with high momentum and energy resolution. Low-energy tunable photons have enabled us to resolve a small nodal bilayer splitting, unmasking the intrinsic single-particle scattering rate. The nodal scattering rate is abruptly suppressed upon the superconducting transition, and shows a linear energy dependence at low energies, indicating the nontrivial effect of elastic scatterings on the quasiparticles. With increasing energy, the antibonding-band scattering rate becomes higher than the bonding one. The observations imply the character of the scatterers dominant at low energies.

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	Nodal quasiparticles of Bi2Sr2CaCu2O8 have been studied by angle-resolved photoemission spectroscopy with high momentum and energy resolution.	method 0.54	0.88	0.03	asserted 1.00
s1	Low-energy tunable photons have enabled us to resolve a small nodal bilayer splitting, unmasking the intrinsic single-particle scattering rate.	result 0.43	0.94	0.20	asserted 1.00
s2	The nodal scattering rate is abruptly suppressed upon the superconducting transition, and shows a linear energy dependence at low energies, indicating the nontrivial effect of elastic scatterings on the quasiparticles.	result 0.96	0.91	0.46	asserted 0.77
s3	With increasing energy, the antibonding-band scattering rate becomes higher than the bonding one.	result 1.00	0.88	0.11	asserted 1.00
s4	The observations imply the character of the scatterers dominant at low energies.	interpretation 1.00	0.50	0.25	hedged possibility 0.64

What kind of paper the classifier reports this is: empirical study 1.00 · evidence from observation or experiment 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

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

Figures

**Figure 1.** FIG. 1: Overview of low-energy ARPES result at

**Figure 3.** FIG. 3: Single-particle spectral function in the supercond

**Figure 5.** FIG. 5: (a) Temperature dependence of the MDC at

Showing 3 of the paper's 5 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:cond-mat/0603006 by the authors.

References

Works cited (27)

[1]

D. A. Bonn et al. , Phys. Rev. B 47 , 11314 (1993)

View on Pith 1993
[2]

K. Krishana, J. M. Harris, and N. P. Ong, Phys. Rev. Lett. 75 , 3529 (1995)

View on Pith 1995
[3]

A. Hosseini et al. , Phys. Rev. B 60 , 1349 (1999)

View on Pith 1999
[4]

A. V. Puchkov, D. N. Basov, and T. Timusk, J. Phys.: Condens. Matter 8 , 10049 (1996)

View on Pith 1996
[5]

J. Takeya et al. , Phys. Rev. Lett. 88 , 077001 (2002)

View on Pith 2002
[6]

D. L. Feng et al. , Phys. Rev. Lett. 86 , 5550 (2001)

View on Pith 2001
[7]

Y. D. Chuang et al. , Phys. Rev. Lett. 87 , 117002 (2001)

View on Pith 2001
[8]

A. Damascelli, Z. Hussain, and Z.-X. Shen, Rev. Mod. Phys. 75 , 473 (2003)

View on Pith 2003
[9]

T. Valla et al. , Science 285 , 2110 (2001); T. Valla, et al. , Phys. Rev. Lett. 85 , 828 (2000); Z. M. Yusof et al. , ibid. 88 , 167006 (2002)

View on Pith 2001
[10]

P. V. Bogdanov et al. , Phys. Rev. Lett. 85 , 2581 (2000)

View on Pith 2000
[11]

A. Lanzara et al. , Nature (London) 412 , 510 (2001)

View on Pith 2001
[12]

T. Valla et al. , Phys. Rev. B 73 , 184518 (2006)

View on Pith 2006
[13]

A. A. Kordyuk et al. , Phys. Rev. B 70 , 214525 (2004)

View on Pith 2004
[14]

S. V. Borisenko et al. , Phys. Rev. Lett. 96 , 067001 (2006)

View on Pith 2006
[15]

J. D. Koralek et al. , Phys. Rev. Lett. 96 , 017005 (2006)

View on Pith 2006
[16]

M. P. Seah and W. A. Dench, Surf. Interface Anal. 1 , 2 (1979)

View on Pith 1979
[17]

O. K. Andersen, A. I. Liechtenstein, O. Jepsen, and F. Paulsen, J. Phys. Chem. Solids 56 , 1573 (1995)

View on Pith 1995
[18]

When the momentum dependence of ( ,k) is much smaller than the energy dependence, Im ( ) = - 1 2 v_ 0 k

View on Pith
[19]

On the presumption that the momentum dependence of ( ,k) is much smaller than the energy dependence, Im ( ) = - 1 2 v_ 0 k , where k is the momentum width and v_0 is the unrenormalized velocity

View on Pith
[20]

When the electron-electron scattering is quadratic as in Fermi liquid, Im _el-el^FL ^2 , the renormalization energy would be linear, Re _el-el^FL( ) , and thus be excluded from the deviation from the straight dispersion, Re '( )

View on Pith
[21]

E. Abrahams and C. M. Varma, Proc. Natl. Acad. Sci. 97 , 5714 (2000)

View on Pith 2000
[22]

L. Zhu, P. J. Hirschfeld, and D. J. Scalapino, Phys. Rev. B 70 , 214503 (2004); T. Dahm, P. J. Hirschfeld, D. J. Scalapino, and L. Zhu, ibid. 72 , 214512 (2005)

View on Pith 2004
[23]

M. Franz and Z. Te s anovi\' c , Phys. Rev. Lett. 87 , 257003 (2001)

View on Pith 2001
[24]

G. Kastrinakis, Phys. Rev. B 71 , 014520 (2005)

View on Pith 2005
[25]

D. J. Scalapino, T. S. Nunner, and P. J. Hirschfeld, arXiv:cond-mat/0409204 (unpublished)

View on Pith Pith review arXiv
[26]

H. Eisaki et al. , Phys. Rev. B 69 , 064512 (2004)

View on Pith 2004
[27]

A. C. Durst and P. A. Lee, Phys. Rev. B 62 , 1270 (2000)

View on Pith 2000

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] [1]

D. A. Bonn et al. , Phys. Rev. B 47 , 11314 (1993)

View on Pith 1993

[2] [2]

K. Krishana, J. M. Harris, and N. P. Ong, Phys. Rev. Lett. 75 , 3529 (1995)

View on Pith 1995

[3] [3]

A. Hosseini et al. , Phys. Rev. B 60 , 1349 (1999)

View on Pith 1999

[4] [4]

A. V. Puchkov, D. N. Basov, and T. Timusk, J. Phys.: Condens. Matter 8 , 10049 (1996)

View on Pith 1996

[5] [5]

J. Takeya et al. , Phys. Rev. Lett. 88 , 077001 (2002)

View on Pith 2002

[6] [6]

D. L. Feng et al. , Phys. Rev. Lett. 86 , 5550 (2001)

View on Pith 2001

[7] [7]

Y. D. Chuang et al. , Phys. Rev. Lett. 87 , 117002 (2001)

View on Pith 2001

[8] [8]

A. Damascelli, Z. Hussain, and Z.-X. Shen, Rev. Mod. Phys. 75 , 473 (2003)

View on Pith 2003

[9] [9]

T. Valla et al. , Science 285 , 2110 (2001); T. Valla, et al. , Phys. Rev. Lett. 85 , 828 (2000); Z. M. Yusof et al. , ibid. 88 , 167006 (2002)

View on Pith 2001

[10] [10]

P. V. Bogdanov et al. , Phys. Rev. Lett. 85 , 2581 (2000)

View on Pith 2000

[11] [11]

A. Lanzara et al. , Nature (London) 412 , 510 (2001)

View on Pith 2001

[12] [12]

T. Valla et al. , Phys. Rev. B 73 , 184518 (2006)

View on Pith 2006

[13] [13]

A. A. Kordyuk et al. , Phys. Rev. B 70 , 214525 (2004)

View on Pith 2004

[14] [14]

S. V. Borisenko et al. , Phys. Rev. Lett. 96 , 067001 (2006)

View on Pith 2006

[15] [15]

J. D. Koralek et al. , Phys. Rev. Lett. 96 , 017005 (2006)

View on Pith 2006

[16] [16]

M. P. Seah and W. A. Dench, Surf. Interface Anal. 1 , 2 (1979)

View on Pith 1979

[17] [17]

O. K. Andersen, A. I. Liechtenstein, O. Jepsen, and F. Paulsen, J. Phys. Chem. Solids 56 , 1573 (1995)

View on Pith 1995

[18] [18]

When the momentum dependence of ( ,k) is much smaller than the energy dependence, Im ( ) = - 1 2 v_ 0 k

View on Pith

[19] [19]

On the presumption that the momentum dependence of ( ,k) is much smaller than the energy dependence, Im ( ) = - 1 2 v_ 0 k , where k is the momentum width and v_0 is the unrenormalized velocity

View on Pith

[20] [20]

When the electron-electron scattering is quadratic as in Fermi liquid, Im _el-el^FL ^2 , the renormalization energy would be linear, Re _el-el^FL( ) , and thus be excluded from the deviation from the straight dispersion, Re '( )

View on Pith

[21] [21]

E. Abrahams and C. M. Varma, Proc. Natl. Acad. Sci. 97 , 5714 (2000)

View on Pith 2000

[22] [22]

L. Zhu, P. J. Hirschfeld, and D. J. Scalapino, Phys. Rev. B 70 , 214503 (2004); T. Dahm, P. J. Hirschfeld, D. J. Scalapino, and L. Zhu, ibid. 72 , 214512 (2005)

View on Pith 2004

[23] [23]

M. Franz and Z. Te s anovi\' c , Phys. Rev. Lett. 87 , 257003 (2001)

View on Pith 2001

[24] [24]

G. Kastrinakis, Phys. Rev. B 71 , 014520 (2005)

View on Pith 2005

[25] [25]

D. J. Scalapino, T. S. Nunner, and P. J. Hirschfeld, arXiv:cond-mat/0409204 (unpublished)

View on Pith Pith review arXiv

[26] [26]

H. Eisaki et al. , Phys. Rev. B 69 , 064512 (2004)

View on Pith 2004

[27] [27]

A. C. Durst and P. A. Lee, Phys. Rev. B 62 , 1270 (2000)

View on Pith 2000