Effects of Electron Correlation near Spin-Density-Wave on Angle Dependence of Magnetoconductivity

Hirono Kaneyasu; Keita Kishigi; Yasumasa Hasegawa

REVIEW

Effects of Electron Correlation near Spin-Density-Wave on Angle Dependence of Magnetoconductivity

Hirono Kaneyasu, Keita Kishigi, Yasumasa Hasegawa

Strongly Correlated Electrons · Submitted 3 Mar 2006 · 21 references

Pith's verdict: A useful but provisional calculation: the separation of lifetime and velocity renormalization in AMRO is clear, but the missing analytic continuation makes the central attribution unverifiable as written.

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CitationHirono Kaneyasu, Keita Kishigi, Yasumasa Hasegawa. "Effects of Electron Correlation near Spin-Density-Wave on Angle Dependence of Magnetoconductivity." arXiv:cond-mat/0603072 (2006). https://pith.science/paper/UXWZJEOI

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Editor's note

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Two things to know. First, the calculation is a real step past earlier AMRO work: it takes an RPA self-energy from the full unlinearized dispersion and uses both the momentum-dependent lifetime and velocity renormalization in the Boltzmann conductivity, then separates their effects by toggling each momentum dependence on and off. The attributions—tau(k) suppresses sigma_xx at 45°, average upsilon_sx enhances sigma_zz at 0°—come directly from those toggles, with a U=0 baseline computed independently; nothing is fitted to experiment. Second, the paper is honest about what it does not explain: the calculated peak heights are smaller than the measured ones, so the mechanism is offered as a partial origin, not a full solution.

Where the paper is solid: the numerical decomposition is internally consistent and the figures are convincing. The self-citation to ref. 9 is legitimate—it motivates the setup, not an input that predetermines the outcome. The Q1D FS is treated with the unlinearized dispersion, which matters for sigma_xx, and the RPA treatment of spin fluctuations is appropriate near an SDW.

The load-bearing soft spot is exactly the one the stress-test note flags: the Matsubara self-energy in Eq. (1) is continued to the retarded Sigma^R(k,E*) used in Eqs. (2)-(4), but the continuation procedure is never described. Near an SDW instability, Im Sigma^R varies strongly in frequency and momentum, so the location of the small-tau region on the FS depends on how the continuation is done. Different shortcuts—Padé, lowest-Matsubara evaluation, spectral approximation—can plausibly change whether the 45° dip in sigma_xx survives or how large the velocity enhancement at 0° is. Because tau appears in the exponent of the conductivity integrand, this is not a detail: the central attribution is only as secure as that step. The single parameter set (U=1.98, T=0.008, tb=tc=0.1) is a smaller issue; a scan would help but a Letter can legitimately show one representative case.

This paper is for specialists in organic conductors and correlated magnetotransport. It deserves a serious referee: the question is real, the approach is promising, and the internal logic is clear. I would send it out with a request to specify the analytic continuation, define E*(k), and ideally add a brief U or temperature scan. If that can be provided, the result becomes reproducible rather than provisional.

Referee report

Significance

The numerical decomposition is well controlled: the U=0 baseline is computed independently, the comparisons with averaged quantities isolate each physical effect, and the final attribution is based on visual and quantitative inspection of the figures. No target quantity is fitted: the magic angles arise from the Fermi-surface geometry, and the magnetic-field strength appears only through the dimensionless product B<tau(k)>. The paper is honest about the limitations of the comparison with experiment. If the underlying retarded self-energy calculation is reliable, the distinction between lifetime-driven suppression of sigma_xx and average-velocity-driven enhancement of sigma_zz is a useful step for interpreting AMRO in organic conductors. The central claim, however, is only as secure as the unspecified analytic continuation used to obtain the retarded self-energy from the Matsubara self-energy.

Major objections (1)

[Eqs. (1)-(4), paragraph defining quasiparticle quantities] The central numerical claim rests on the retarded self-energy Sigma^R(k,E*) used in Eqs. (2)-(4) for the velocity, lifetime, and Z-factor, but the paper never specifies how Sigma^R is obtained from the Matsubara self-energy Sigma(k,i omega_n) defined in Eq. (1). In particular, the on-shell condition defining E*(k) is not stated. Because Im Sigma^R enters tau(k) through the exponential in Eqs. (5) and (6), and the velocity correction enters sigma_zz through both <upsilon_sx> and the pseudogap argument, an unstable or poorly chosen analytic continuation could change the sign and location of the small-tau region on the Fermi surface and either create or remove the 45-degree dip in sigma_xx and the 0-degree enhancement in sigma_zz. The authors should state the continuation method (e.g., Pade approximants, evaluation at the lowest Matsubara frequency, or a spectral-function inversion), define E*(k) explicitly, and provide a convergence test (e.g., dependence on the number of Matsubara frequencies or on the continuation order). This is a necessary methodological check for the decomposition claim.

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The paper

The paper claims

In organic conductors near spin-density-wave order, electron correlation suppresses the 45° peak in chain-axis magnetoconductivity through lifetime momentum dependence and enhances the 0° peak in interchain conductivity through average…

The reading

This paper addresses a mismatch between theory and experiment in angle-dependent magnetoresistance oscillations of quasi-one-dimensional organic conductors: noninteracting models give peaks at magic angles but with wrong relative heights. The authors argue that the missing ingredient is electron correlation near the spin-density-wave instability, and they trace its effect to two separate momentum-dependent quantities on the Fermi surface. A momentum-dependent quasiparticle lifetime, shortened near the nesting regions that feed the spin-density wave, suppresses the one-dimensional-axis conductivity $\sigma_{xx}$ at the magic angle $45^\circ$. An increase in the average quasiparticle velocity along the chain direction, connected to the spin-fluctuation pseudo-gap, enhances the interchain-axis conductivity $\sigma_{zz}$ at $0^\circ$. If correct, this decomposition explains why correlation changes the relative heights of magic-angle peaks even when it does not change their positions.

What carries the argument

The load-bearing object is the retarded self-energy $\Sigma^R(k,E^*)$ evaluated on the Fermi surface, from which the paper constructs three momentum-dependent quasiparticle quantities: the lifetime $\tau(k) = -1/\mathrm{Im}\,\Sigma^R(k,E^*)$, the renormalized velocity $\upsilon_i(k) = \partial E_0(k)/\partial k_i + \partial \mathrm{Re}\,\Sigma^R(k,E^*)/\partial k_i$, and the renormalization factor $Z(k)$. These enter the semiclassical transport formulas for $\sigma_{xx}$ and $\sigma_{zz}$ through the dressed velocity $\tilde{\upsilon}_i = Z\,\upsilon_i$ and dressed lifetime $\tilde{\tau} = \tau/Z$, with $k(t)$ following the magnetic-field equation of motion in a field tilted in the $y$--$z$ plane. The magic angles $\theta = \tan^{-1}(p/q)$ are where electrons move on commensurate Fermi-surface orbits, and the paper's argument is that correlation-induced momentum dependence of $\tau(k)$ and $\upsilon_s(k)$ modulates precisely these orbits: $\tau(k)$ variations spoil the velocity pattern at $45^\circ$, while the average velocity increase changes the relative weight of the $0^\circ$ orbit through the $1/\upsilon_x$ density-of-states factor.

Extended reading notes

Core claim

On the paper's own terms, the central discovery is a separation of effects: correlation acts on the angle-dependent magnetoconductivity through the momentum dependence of the quasiparticle lifetime and through the correlation-induced correction to the quasiparticle velocity, and the two act on different conductivity components at different magic angles. Using a random-phase-approximation self-energy for an on-site repulsion model at quarter filling and semiclassical transport equations with the full unlinearized dispersion, the authors find that $\sigma_{xx}$ at $\theta = 45^\circ$ ($\tan^{-1}(1)$) is strongly suppressed only when the momentum dependence of $\tau(k)$ is kept; replacing $\tau(k)$ by its Fermi-surface average restores the peak. In contrast, the enhancement of $\sigma_{zz}$ at $\theta = 0^\circ$ appears when the average chain-direction velocity correction $\langle \upsilon_{sx}(k)\rangle \approx 0.3$ is included, while $\langle \upsilon_{sz}(k)\rangle \approx 0$ contributes nothing; the momentum dependence of the $Z$-factor nearly cancels in both conductivities. The authors state the implication directly: the momentum dependence of the lifetime and the change in velocity originating from electron correlation near the spin-density wave govern the angle dependence of $\sigma_{xx}$ and $\sigma_{zz}$, respectively.

Load-bearing premise

Everything hinges on the retarded self-energy $\Sigma^R(k,E^*)$ evaluated on the Fermi surface, but the paper never states how that retarded self-energy is obtained from the Matsubara self-energy; if the analytic continuation is unstable or wrong, the momentum-dependent lifetime, velocity, and all peak-height changes are not established.

Editorial extensions

If this is right

If the central claim is right, the $45^\circ$ peak in the one-dimensional-axis magnetoconductivity should be read as a probe of the momentum-dependent scattering rate near the spin-density-wave nesting, not of the band structure alone.
The $0^\circ$ peak in the interchain-axis conductivity carries information about the average velocity renormalization, i.e. the pseudo-gap scale, and is almost insensitive to the lifetime's momentum dependence.
The near-cancellation of the $Z$-factor means correlation effects must be sought through the velocity and lifetime channels separately rather than through an overall energy-scale rescaling.
Since the effects produce different signatures in $\sigma_{xx}$ and $\sigma_{zz}$, comparing both measured magnetoconductivity directions can separate the two correlation channels in experiment.
The authors' finding that correlation changes relative peak heights but not enough to match experiment implies that additional mechanisms, such as vertex corrections in a strong-field linear-response formula or spin splitting of the bands, are needed for a complete quantitative description.

Reading between the lines

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

I infer that the same decomposition should hold continuously as the system approaches the spin-density-wave transition: the $45^\circ$ $\sigma_{xx}$ peak should shrink and the $0^\circ$ $\sigma_{zz}$ peak should grow as the interaction strength increases toward the SDW boundary, a trend one could test by pressure or doping sweeps.
I infer a temperature signature: because the velocity correction and pseudo-gap shrink as temperature rises away from the SDW regime, the $0^\circ$ enhancement in $\sigma_{zz}$ should weaken with increasing $T$, while the $45^\circ$ suppression in $\sigma_{xx}$ should weaken as the lifetime's momentum dependence flattens.
I infer that joint fits of both angle sweeps could extract the real and imaginary parts of the retarded self-energy on the Fermi surface without full momentum-resolved data, since $\sigma_{xx}$ at $45^\circ$ isolates the lifetime channel and $\sigma_{zz}$ at $0^\circ$ isolates the velocity channel.
I infer that the quantitative peak ratios may shift if the interchain-anisotropy ratio is changed from the symmetric $t_b = t_c = 0.1$ used here to realistic values such as $t_c = 0.03$, while the qualitative split between lifetime-driven and velocity-driven effects should survive; this is a testable prediction for parameter variations.

Original abstract

The effect of electron correlation on the angle dependence of magnetoconductivity is studied in quasi-one-dimensional organic conductors. We investigated the effect on the basis of the momentum dependence of both quasi-particle's lifetime and velocity near the spin-density-wave (SDW). We found that the momentum dependence of quasi-particle's lifetime mainly governs the angle dependence of one-dimensional axis magnetoconductivity. On the other hand, the change in velocity originating from the electron correlation gives the dominant effects on the angle dependence of the interchain axis magnetoconductivity. The effect of electron correlation is clarified from the association of the momentum dependences of lifetime and velocity with the momentum dependences of commensurate orbitals on a Fermi surface in magnetic fields.

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, 4,296 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.07 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

The effect of electron correlation on the angle dependence of magnetoconductivity is studied in quasi-one-dimensional organic conductors. We investigated the effect on the basis of the momentum dependence of both quasi-particle's lifetime and velocity near the spin-density-wave (SDW). We found that the momentum dependence of quasi-particle's lifetime mainly governs the angle dependence of one-dimensional axis magnetoconductivity. On the other hand, the change in velocity originating from the electron correlation gives the dominant effects on the angle dependence of the interchain axis magnetoconductivity. The effect of electron correlation is clarified from the association of the momentum dependences of lifetime and velocity with the momentum dependences of commensurate orbitals on a Fermi surface in magnetic fields.

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	The effect of electron correlation on the angle dependence of magnetoconductivity is studied in quasi-one-dimensional organic conductors.	contribution 0.83	0.83	0.04	asserted 0.83
s1	We investigated the effect on the basis of the momentum dependence of both quasi-particle's lifetime and velocity near the spin-density-wave (SDW).	method 0.89	0.91	0.05	asserted 0.90
s2	We found that the momentum dependence of quasi-particle's lifetime mainly governs the angle dependence of one-dimensional axis magnetoconductivity.	result 1.00	0.96	0.34	asserted 1.00
s3	On the other hand, the change in velocity originating from the electron correlation gives the dominant effects on the angle dependence of the interchain axis magnetoconductivity.	result 0.99	0.90	0.26	asserted 1.00
s4	The effect of electron correlation is clarified from the association of the momentum dependences of lifetime and velocity with the momentum dependences of commensurate orbitals on a Fermi surface in magnetic fields.	interpretation 0.96	0.82	0.27	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.92 · evidence from proof or derivation 0.51.

What was examined, and what was not

sources read

arXiv listing abstract v1

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.** (a) Angle dependence of σxx. (b) Angle dependence of σzz. The solid lines mean the magnetoconductivities with using the momentum dependent τ(k), Z(k) and υsx(k) (and υsz(k)in(b)). The dash lines indicate the magnetoconductivies in the case that we neglect the momentum dependence of τ(k), Z(k) and υsx(k) (and υsz(k) in (b)) by using hτ(k)i, hZ(k)i, and υsx(k) = 0 (and υsz(k) = 0 in (b)). model. Σ(k, ωn) is given by Σ(k, ωn) = T N X k′ ,m U 2 [ 3 2 χs(k ′ , ωm) + 1 2 χc(k ′ , ωm) −χ0(k ′ , ωm)]G0(k − k ′ , ωn−m). (1) Here, spin and charge susceptibilities are respectively χs(k ′ ,…

**Figure 3.** (a) Angle dependence of σxx. (b) Angle dependence of σzz. The solid lines mean the magnetoconductivities with using the momentum dependent τ(k), Z(k) and υsx(k) (and υsz(k) in (b)). The dash lines indicate the magnetoconductivies in the case that the momentum dependence of υsx(k) (and υsz(k) in (b)) is neglected by using υsx(k) = 0 (and υsz(k) = 0 in (b)). The dash line with dot means the magnetoconductivies in the case that the constant component of υsx(k) is treated by using hυsx(k)i (and υsz(k) = 0 in (b)). in Figs. 1(a) and 1(b). The effect is small at other angles θ = 26.4 ◦…

**Figure 4.** (a) τ(k), (b) υsx(k) and (c) υsz(k) on FS and commensurate orbitals at a magic angles 45◦ and 0◦. ity due to υsx(k). EC increases the velocity υx(k). The averaged value hυsx(k)i is 0.3, as shown in

Showing 3 of the paper's 4 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:cond-mat/0603072 by the authors.

References

Works cited (21)

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[2]

T. Ishiguro, K. Yamaji and G. Sato: Organic Superconducto rs, Springer-Verlag, Berlin (1998)

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T. Osada, A. Kawasumi, S. Kagoshima, N. Miura, and G. Saito : Phys. Rev. Lett. 66 (1991) 1525

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W. Kang, S. T. Hannas and P. M. Chaikin: Phys. Rev. Lett. 69 (1992) 2827

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T. Osada, S. Kagoshima and N. Miura: Phys. Rev. B. 46 (1992) 1812

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T. Osada, S. Kagoshima and N. Miura: Phys. Rev. Lett. 77 (1996) 5261

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K. Maki: Phys. Rev. B 45 (1992) 5111

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Y. Hasegawa, H. Kaneyasu and K. Kishigi:J. Phys. Soc. Jpn. 75 (2006) No.4, In press

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L. B. Ioﬀe and A. J. Millis: Phys Rev. B 58 (1998) 11631

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A. G. Lebed and P. Bak: Phys. Rev. Lett. 63 (1989) 1315

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P. M. Chaikin: Phys. Rev. Lett. 69 (1992) 2831

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A. T. Zheleznyak and V. M. Yakovenko: Synthetic Metals 70 (1995) 1005

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[14]

P. Moses and R. H. McKenzie: Phys. Rev. B 63 (2000) 024414

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[15]

S. Takada: J. Phys. Soc. Jpn. 53 (1984) 2193

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K. Maki and A. Virosztek: Phys. Rev. B 36 (1987) 511

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[17]

Y.Yanase and K.Yamada: J. Phys. Soc. Jpn. 68 (1999) 548

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[18]

N. W. Ashcroft and N. D. Mermin: Solid State Physics (Saun - ders, Philadelphia) (1975)

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[19]

H.Shimahara: J. Phys. Soc. Jpn. 58 (1989) 1735

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H. Kino and H.Kontani: J. Phys. Soc. Jpn. 68 (1999) 1481

View on Pith 1999
[21]

H. Kontani: J. Phys. Soc. Jpn. 68 (1999j614

View on Pith

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. Jerome and H. J. Schulz: Adv. Phys. 31 (1982) 299

View on Pith 1982

[2] [2]

T. Ishiguro, K. Yamaji and G. Sato: Organic Superconducto rs, Springer-Verlag, Berlin (1998)

View on Pith 1998

[3] [3]

M. J. Naughton, O. H. Chung and M. Chaparala: Phys. Rev. Lett. 67 (1991) 3712

View on Pith 1991

[4] [4]

T. Osada, A. Kawasumi, S. Kagoshima, N. Miura, and G. Saito : Phys. Rev. Lett. 66 (1991) 1525

View on Pith 1991

[5] [5]

W. Kang, S. T. Hannas and P. M. Chaikin: Phys. Rev. Lett. 69 (1992) 2827

View on Pith 1992

[6] [6]

T. Osada, S. Kagoshima and N. Miura: Phys. Rev. B. 46 (1992) 1812

View on Pith 1992

[7] [7]

T. Osada, S. Kagoshima and N. Miura: Phys. Rev. Lett. 77 (1996) 5261

View on Pith 1996

[8] [8]

K. Maki: Phys. Rev. B 45 (1992) 5111

View on Pith 1992

[9] [9]

Y. Hasegawa, H. Kaneyasu and K. Kishigi:J. Phys. Soc. Jpn. 75 (2006) No.4, In press

View on Pith 2006

[10] [10]

L. B. Ioﬀe and A. J. Millis: Phys Rev. B 58 (1998) 11631

View on Pith 1998

[11] [11]

A. G. Lebed and P. Bak: Phys. Rev. Lett. 63 (1989) 1315

View on Pith 1989

[12] [12]

P. M. Chaikin: Phys. Rev. Lett. 69 (1992) 2831

View on Pith 1992

[13] [13]

A. T. Zheleznyak and V. M. Yakovenko: Synthetic Metals 70 (1995) 1005

View on Pith 1995

[14] [14]

P. Moses and R. H. McKenzie: Phys. Rev. B 63 (2000) 024414

View on Pith 2000

[15] [15]

S. Takada: J. Phys. Soc. Jpn. 53 (1984) 2193

View on Pith 1984

[16] [16]

K. Maki and A. Virosztek: Phys. Rev. B 36 (1987) 511

View on Pith 1987

[17] [17]

Y.Yanase and K.Yamada: J. Phys. Soc. Jpn. 68 (1999) 548

View on Pith 1999

[18] [18]

N. W. Ashcroft and N. D. Mermin: Solid State Physics (Saun - ders, Philadelphia) (1975)

View on Pith 1975

[19] [19]

H.Shimahara: J. Phys. Soc. Jpn. 58 (1989) 1735

View on Pith 1989

[20] [20]

H. Kino and H.Kontani: J. Phys. Soc. Jpn. 68 (1999) 1481

View on Pith 1999

[21] [21]

H. Kontani: J. Phys. Soc. Jpn. 68 (1999j614

View on Pith