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REVIEW 3 major objections 5 minor 65 references

Nematicity in iron pnictides: phase competition and emergent symmetry

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Pith's one-line read At the first-order transition between nematic and charge-C4 phases in iron pnictides, a hidden Lie algebra generates an emergent U(1) symmetry, yielding a gapless Goldstone mode and near-divergent fluctuations that explain the observed…

desk verdict New hidden-symmetry mechanism with a solid exact core, but the quantitative pseudo-Goldstone gap claim is not justified in the experimentally relevant magnetic phase. read the letter →

arxiv 2505.24847 v1 pith:YVTL2NG5 submitted 2025-05-30 cond-mat.str-el cond-mat.supr-con

Yiming Wang , Changle Liu , Shan Wu , Jianda Wu , Qimiao Si , Rong Yu This is my paper · ORCID
classification cond-mat.str-elcond-mat.supr-con
keywords emergentsymmetryhiddenLiealgebranematicorderchargeC4ironpnictidesGoldstonemodeGinzburg-Landautheorycomposite
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that at the first-order transition between the nematic (single-Q antiferromagnetic) and charge-C4 (collinear double-Q antiferromagnetic) phases of iron-based superconductors, the Ginzburg-Landau free energy acquires an emergent continuous U(1) symmetry, even though the transition itself is first-order. The symmetry is not put in by hand; it follows from a hidden Lie algebra that connects the composite order parameters of the two phases, so the nematic and charge-C4 orders can rotate into each other exactly at the transition. If the claim is right, the transition supports a gapless Goldstone mode and strongly enhanced (near-divergent) fluctuations in both order-parameter channels, which would explain why nematic fluctuations remain strong inside the double-Q phase. The paper backs this with a fit to inelastic X-ray scattering data showing phonon softening in Sr0.64Na0.36Fe2As2, and it predicts a divergent Grüneisen ratio. A sympathetic reader would care because this turns a seemingly first-order boundary into a hidden quantum critical point with measurable consequences.

What carries the argument

The hidden Lie algebra is the load-bearing mechanism. With $m = (m_A, m_B)^T$, the nematic, charge-C4, and (for N=2) chiral-C4 composite order parameters are bilinears $m^T N_i m$, where $N_1 = \tau_x\otimes I_N/2$, $N_2 = \tau_z\otimes I_N/2$, and $N_3 = \tau_y\otimes \sigma_y/2$. Together with generators $L_i$ built from the Pauli matrices, the $N_i$ close an SO(3) algebra for $N>2$ and an SO(4) algebra for $N=2$, so the order parameters transform as vectors under a continuous rotation. When the bare couplings $v_1$ and $v_2$ are equal, the free energy is invariant under this rotation, which is what upgrades the discrete $\mathbb{Z}_2\times\mathbb{Z}_2$ symmetry to $U(1)$ exactly at the transition. The anisotropic XZ spin model is used as the intuitive analogue, with the nematic and charge-C4 order parameters playing the roles of $S_x$ and $S_z$.

What would settle it

Measure the dispersion of the soft mode in the charge-C4 (double-Q) phase by inelastic neutron or X-ray scattering. The theory predicts that the ratio of the pseudo-Goldstone gap to the Higgs-mode gap scales as $(w/c)^4 \approx 10^{-2}$ for typical iron pnictides; observing a much larger gap, or no gap collapse as the nematic transition is approached, would falsify the emergent-symmetry picture. Equivalently, the in-plane transverse acoustic phonon velocity should vanish as the correlation length diverges ($v \propto \xi^{-1}$) on approach to the transition; a finite velocity with no softening would rule it out.

Watch

Extended reading notes

Core claim

The central claim is that the composite-order Landau theory for iron pnictides has an emergent U(1) symmetry at the nematic/charge-C4 transition. Writing the staggered moments as a 2N-component vector, the nematic and charge-C4 order parameters are bilinears $m^T N_1 m$ and $m^T N_2 m$ with $N_1 = \tau_x\otimes I_N/2$ and $N_2 = \tau_z\otimes I_N/2$; together with $L_3 = -\tau_y\otimes I_N/2$ they generate an SO(3) Lie algebra (SO(4) for N=2). Because of this algebra, when the quadratic coefficients $r_1$ and $r_2$ are equal the quartic free energy depends only on the total amplitude $\rho = \sqrt{\rho_1^2+\rho_2^2}$, not on the relative phase, so a continuous $O(2)\sim U(1)$ symmetry emerges at the transition. Spontaneous breaking of this symmetry yields a gapless Goldstone mode, and the susceptibility in whichever channel is not ordered diverges on approach to the transition from either side. The paper argues the symmetry is robust to spin anisotropy up to corrections of order $(w/c)^4$, and that it survives inside the magnetically ordered phases because spin and lattice sectors decouple in the absence of spin-orbit coupling.

Load-bearing premise

The derivation of the effective free energy (Eq. 3) assumes a large-N saddle point with the composite order parameter small compared to the magnetic mass ($\rho \ll m$); if higher-order or finite-N terms make the quartic couplings in the nematic and charge-C4 channels unequal, the U(1) becomes approximate and the Goldstone mode acquires a gap.

Editorial extensions

If this is right

  • The first-order single-Q to double-Q transition is accompanied by a soft, gapless (or nearly gapless) Goldstone mode, resolving the puzzle of enhanced nematic fluctuations inside the C4-symmetric double-Q phase.
  • The nematic and charge-C4 susceptibilities diverge as the transition is approached from either ordered phase, giving a quantum-critical-like response despite the first-order jump.
  • The in-plane transverse acoustic phonon velocity softens to zero at the transition, quantitatively matching the inelastic X-ray scattering data for Sr0.64Na0.36Fe2As2.
  • The Grüneisen ratio should diverge as $T^{-1/(\nu z)}$ near the transition, a thermodynamic signature that can be tested by thermal-expansion and specific-heat measurements.
  • The emergent symmetry persists under a realistic spin anisotropy $w$, with the Goldstone-mode gap suppressed by a factor of $(w/c)^4 \approx 10^{-2}$, so the soft mode remains detectable.

Reading between the lines

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

  • If the hidden Lie algebra is generic, similar emergent U(1) symmetries could occur at transitions between any two composite orders that share a common parent vector, not just in iron pnictides; candidate settings include the triple-Q states proposed in Kitaev magnets.
  • The near-divergent fluctuations at this first-order transition provide a natural route to enhanced superconductivity: the optimal Tc observed near the single-Q to double-Q boundary may be driven by the same soft fluctuations, which the present static theory does not yet feed back into the pairing channel.
  • A clean testable extension is to look for the predicted soft charge-C4 mode in Raman or RIXS spectra in Ba1-xNaxFe2As2; the theory assigns it a specific energy scale set by the nematic correlation length, so its absence or a large gap would immediately discriminate the mechanism.
  • Tuning the anisotropy $w$ to zero, e.g. by lattice strain, should convert the pseudo-Goldstone mode into a truly gapless excitation and sharpen the first-order boundary into an emergent continuous transition—an experimental knob the paper leaves implicit.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper studies a Ginzburg-Landau model of coupled magnetic (single-Q, double-Q, chiral double-Q) and composite (nematic, charge-C4, chiral-C4) orders in iron pnictides. It derives an effective free energy for the composite order parameters, shows that at the first-order transition between the nematic and charge-C4 orders the free energy has an emergent U(1) symmetry generated by a hidden SO(3)/SO(4) Lie algebra, and predicts a gapless Goldstone mode and divergent composite-order susceptibilities. The authors compare the predicted phonon softening with inelastic X-ray data on Sr1-xNaxFe2As2 and propose thermodynamic signatures such as a divergent Grüneisen ratio. The central derivation is analytic in a large-N limit and assumes the composite order is small compared with the magnetic mass (ρ ≪ m).

Significance. If the central claims hold, the paper identifies an appealing mechanism by which a continuous symmetry emerges at a first-order transition between two electronically ordered phases, with concrete experimental signatures. The hidden Lie algebra argument is exact at the model level for v1=v2 and w=0, so the emergent symmetry is not an artifact of the large-N or quartic truncation. The paper also provides falsifiable predictions: divergent nematic/charge susceptibilities, a pseudo-Goldstone mode with a specific gap hierarchy, a divergent Grüneisen ratio, and phonon softening. These strengths make the paper of interest to the iron-pnictide and quantum-criticality communities. However, the quantitative reach of the central claim in the magnetically ordered phase is not fully established, as detailed below.

major comments (3)
  1. [Main text, 'Stability of the emergent symmetry'; SM G, Eqs. (58)-(62); SM F, Eqs. (42)-(45)] The estimate that the pseudo-Goldstone gap is of order (w/c)^4 relative to the Higgs mode is derived only in the paramagnetic phase under the assumption ρ ≪ m (SM G, Eqs. (58)-(62)). In the magnetically ordered phases relevant to the experiment, the saddle-point solution satisfies m = ρ (SM F, Eqs. (42)-(45)), so the ρ/m expansion underlying Eq. (58) is not valid. No calculation of the w-induced gap is provided in the single-Q or double-Q AFM phase. Because the phonon-softening comparison in Fig. 3 is made in these phases, the quantitative prediction that the pseudo-Goldstone mode is nearly gapless (gap ratio ≈ 10^-2) is unverified in the regime where the comparison is performed. If the gap scales as (w/c)^2 instead, the pseudo-Goldstone mode is substantially gapped and the proposed softening signature would be weakened. I ask the authors to compute the w-perturbation in the magnetic phase without the ρ≪m expansion, or to provide a numerical estimate of the gap at the m=ρ saddle point.
  2. [Abstract and 'Emergent Goldstone mode at the transition point'; SM F, free energy Eq. (46) and final paragraph] The paper presents the emergent U(1) and the Goldstone mode as properties of the first-order transition between the single-Q and double-Q AFM phases. In the large-N magnetic-phase analysis, however, the enhanced symmetry and the divergent susceptibility appear only in the limit v1 → v2 (SM F, final paragraph), while the free energy Eq. (46) has unequal quadratic coefficients for ρ1 and ρ2 when v1 ≠ v2. For generic v1 ≠ v2 the first-order transition between the two ordered phases still exists, but no U(1) symmetry or Goldstone mode is shown. The paramagnetic analysis shows that the first-order transition between the two composite orders occurs at r1 = r2, which corresponds to v1 = v2; this condition should be stated as an assumption of near-degeneracy of the two channels. The manuscript should either prove that the magnetic-phase transition forces v1 = v2, or explicitly qualify the central claim as applying to the multicritical point and argue that the relevant materials are close to it.
  3. [SM I, Eq. (70) and Fig. 3] The phonon-softening formula Eq. (6) is derived from the paramagnetic Gaussian action of SM Eq. (25), yet the comparison with Sr0.64Na0.36Fe2As2 (Fig. 3) is made in the single-Q and double-Q AFM phases, where SM F gives a different susceptibility structure. The text does not demonstrate that Eq. (6) remains valid in the magnetically ordered phases; the fit parameters a, b, ε, r1c, and ξ may compensate for missing magnetic-phase renormalizations. This weakens the stated experimental support for the proposed effects, since the key comparison is a fit rather than an independent parameter-free prediction. I ask the authors to clarify how Eq. (6) is extended to the magnetic phases, or to present the fit as a phenomenological consistency check rather than as a direct test of the emergent U(1).
minor comments (5)
  1. [Main text, Eq. (6) region] The symbols δ, ε, and k̃ are used in Eq. (6) before they are defined; please define them immediately before the equation.
  2. [SM A, final paragraph] The sentence 'However, it usually requires fine-tuning to approach to Therefore' is incomplete and should be rephrased.
  3. [Main text, 'Emergent U(1) symmetry' section and Fig. 1 caption] There is a duplicated definite article in 'the the A, B sublattices', and the Fig. 1 caption contains the word 'Sketch' where 'Schematic' is likely intended.
  4. [SM G, first paragraph] The statement that 'the gapless Goldstone mode is robust up to the (w/c)^3 order' is ambiguous; the subsequent ratio suggests the pseudo-Goldstone gap is of order (w/c)^4, so the wording should be made precise.
  5. [SM I, fit parameters] The reported fit parameters (a, b, ε, r1c, ξ) are given without uncertainties or a goodness-of-fit measure; reporting these would help the reader assess the claimed agreement.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: emergent U(1) is derived from the stated GL model; self-citation and phonon fit are not load-bearing.

full rationale

The paper's derivation chain is self-contained. The central result—an emergent U(1) symmetry and Goldstone mode at the v1=v2 first-order boundary—is obtained from the stated O(N) Ginzburg-Landau action (Eqs. 1-2) by Hubbard-Stratonovich decoupling and a large-N saddle-point calculation (SM E). At v1=v2, r1=r2 and the quartic terms of Eq. (3) are manifestly O(2)-invariant; the hidden Lie algebra (N1=τx/2, N2=τz/2, L3=-τy/2) shows this is not a fine-tuned accident but a symmetry of the microscopic action at the phase boundary. This is a derivation, not a fit: no parameter is adjusted to produce the U(1). SM A explicitly states the general Landau criterion (r1=r2, g1=g2=g12 gives U(1)) and cites a textbook, so the paper is not presenting a known result as new without attribution. The phonon-softening comparison (SM I, Fig. 3b/S1) is an explicit fit using parameters a, b, epsilon, r1c, xi, and is labeled 'fit' in the caption; it is not the load-bearing evidence for the emergent symmetry. Self-citations (Ref. 47 for the GL model, Ref. 52 for the conventional quartic form) establish the starting model but do not carry the new claim; the emergent U(1) is computed within the present paper. The main limitation is quantitative: SM G's pseudo-Goldstone gap estimate (w/c)^4 assumes the paramagnetic phase and rho<<m, while at the magnetic single-Q/double-Q transition SM F finds m=rho (Eqs. 42-45); this affects the size of the pseudo-Goldstone gap in the experimentally relevant phase but is a correctness/robustness concern, not circularity. No step reduces by construction to its input, so the circularity score is low.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the GL model and the large-N/rho<<m approximations; the phonon comparison adds five fitted parameters. No new entities (particles, forces) are invented.

free parameters (5)
  • a = 0.027/K (main text); 0.07/K (SM)
    Temperature slope of the inverse nematic susceptibility r1/r1c in the phonon-softening fit (SM Sec. I).
  • b = 0.033/K (main text); 0.075/K (SM)
    Temperature slope of the inverse charge-C4 susceptibility r2/r1c in the phonon-softening fit.
  • epsilon = 0.77 (main text); 0.59 (SM)
    Ratio c_T^2/K controlling the coupling between phonon and nematic fluctuations.
  • r1c = 2.36 meV (main text); 2.58 meV (SM)
    Critical nematic mass renormalized by spin-phonon coupling, set by the phonon dispersion fit.
  • xi = 25.7/r.l.u. (main text); 26/r.l.u. (SM)
    Nematic correlation length in reciprocal lattice units, adjusted to match the momentum dependence of the phonon softening.
assumptions (6)
  • domain assumption The Ginzburg-Landau action (Eqs. 1-2) with O(N) moments and three quartic channels describes the composite orders in iron pnictides.
    The model is adopted from Ref. [47] and is assumed to capture the magnetic and composite-order physics relevant to the single-Q, double-Q, and chiral phases.
  • domain assumption Leading-order large-N saddle-point treatment is valid for the physical case N=3.
    The effective free energy Eq. (3) and the susceptibilities are computed to leading order in 1/N; corrections are not estimated, so the N=3 result rests on the assumption that leading order is representative.
  • ad hoc to paper The composite order parameter is small compared with the magnetic mass (rho << m) near the transition.
    Stated in SM Sec. E before Eq. (24); used to derive the simple quartic free energy. The paper does not quantify this inequality for N=3 or for the actual transition of interest.
  • domain assumption The eighth-order term (mA^2-mB^2)^2(mA*mB)^2 is negligible.
    Argued in SM Sec. C from |mA|,|mB|<<1 near the magnetic transition; the crossover scale is not estimated.
  • domain assumption Magnetic fluctuations are overdamped with dynamical exponent z=2.
    Standard for itinerant magnets and used to set the effective dimension d+z=4 in the large-N analysis; cited from Ref. [52].
  • standard math The bilinears N1, N2, L3 form an SO(3) Lie algebra (SO(4) for N=2).
    Commutation relations verified in SM Sec. D; this underlies the claim that the two composite orders transform as a vector under a continuous rotation.

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Pith. "Pith review of Nematicity in iron pnictides: phase competition and emergent symmetry." pith.science (2026). https://pith.science/paper/YVTL2NG5

@misc{pith2026250524847,
  author       = {Pith},
  title        = {Pith review of: Nematicity in iron pnictides: phase competition and emergent symmetry},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YVTL2NG5}},
  note         = {Machine review of arXiv:2505.24847}
}
abstract

The phase diagram of iron-based superconductors contains a host of electronic orders, which are intimately connected with their superconductivity. Here we analyze the fluctuations of one type of nematic order in another. Our analysis leads to an emergent U(1) symmetry at a first-order transition between a nematic phase and a $C_4$-symmetric charge-ordered phase. We characterize the continuous symmetry in terms of a certain hidden Lie algebra that links the different orders. This emergent symmetry leads to a Goldstone mode at the transition and causes softening of excitations in the nematic and charge sectors near the transition. The underlying physics bears a resemblance to the anisotropic XZ spin model, with the nematic order and charge $C_4$ order parameters playing the roles of the $x$ and $z$ components of the magnetization vector, respectively. We provide the experimental evidence in support of the proposed effects, and discuss the general implications of our results for the physics of iron-based superconductors and other correlated systems.

Figures

Figures reproduced from arXiv: 2505.24847 by the authors.

Figure 1
Figure 1. FIG. 1: Ground-state phase diagram of the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: (a) Sketech of the free energy [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: (a) Calculated phonon energy [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

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Works this paper leans on

65 extracted references · 57 canonical work pages

  1. [1]

    Keimer and J

    B. Keimer and J. Moore, Nature Physics13, 1045 (2017)

    2017

  2. [2]

    S.PaschenandQ.Si,NatureReviewsPhysics 3,9(2021)

    work page 2021

  3. [3]

    Fradkin, S

    E. Fradkin, S. A. Kivelson, and J. M. Tranquada, Re- views of Modern Physics87, 457 (2015)

    2015

  4. [4]

    Balents, nature464, 199 (2010)

    L. Balents, nature464, 199 (2010)

    2010

  5. [5]

    Takagi, T

    H. Takagi, T. Takayama, G. Jackeli, G. Khaliullin, and S. E. Nagler, Nature Reviews Physics1, 264 (2019)

    2019

  6. [6]

    Kirchner, S

    S. Kirchner, S. Paschen, Q. Chen, S. Wirth, D. Feng, J. D. Thompson, and Q. Si, Reviews of Modern Physics 92, 011002 (2020)

    work page 2020

  7. [7]

    P. A. Lee, N. Nagaosa, and X.-G. Wen, Reviews of mod- ern physics78, 17 (2006)

    work page 2006

  8. [8]

    Zhang, Science275, 1089 (1997)

    S.-C. Zhang, Science275, 1089 (1997)

    1997

Show all 65 references
  1. [9]

    Grover, D

    T. Grover, D. Sheng, and A. Vishwanath, Science344, 280 (2014)

    2014

  2. [10]

    Li, Y.-F

    Z.-X. Li, Y.-F. Jiang, and H. Yao, Physical Review Let- ters 119, 107202 (2017)

    2017

  3. [11]

    Z.-X. Li, A. Vaezi, C. B. Mendl, and H. Yao, Science advances4, eaau1463 (2018)

    2018

  4. [12]

    Moessner and S

    R. Moessner and S. L. Sondhi, Physical Review B63, 224401 (2001)

    2001

  5. [13]

    Balents, M

    L. Balents, M. P. Fisher, and S. M. Girvin, Physical Re- 6 view B65, 224412 (2002)

    2002

  6. [14]

    Hermele, M

    M. Hermele, M. P. Fisher, and L. Balents, Physical Re- view B69, 064404 (2004)

    2004

  7. [15]

    IsakovandR.Moessner,PhysicalReviewB 68,104409 (2003)

    S. IsakovandR.Moessner,PhysicalReviewB 68,104409 (2003)

    2003

  8. [16]

    Blankschtein, M

    D. Blankschtein, M. Ma, A. N. Berker, G. S. Grest, and C. Soukoulis, Physical Review B29, 5250 (1984)

    1984

  9. [17]

    Coldea, D

    R. Coldea, D. Tennant, E. Wheeler, E. Wawrzynska, D. Prabhakaran, M. Telling, K. Habicht, P. Smeibidl, and K. Kiefer, Science327, 177 (2010)

    2010

  10. [18]

    H. Zou, Y. Cui, X. Wang, Z. Zhang, J. Yang, G. Xu, A. Okutani, M. Hagiwara, M. Matsuda, G. Wang, G. Mussardo, K. Hódsági, M. Kormos, Z. He, S. Kimura, R. Yu, W. Yu, J. Ma, and J. Wu, Phys. Rev. Lett.127, 077201 (2021)

    2021

  11. [19]

    Tanaka and X

    A. Tanaka and X. Hu, Phys. Rev. Lett. 95, 036402 (2005)

    2005

  12. [20]

    Somoza, Phys

    A.Nahum, P.Serna, J.T.Chalker, M.Ortuño,andA.M. Somoza, Phys. Rev. Lett.115, 267203 (2015)

    2015

  13. [21]

    Kamihara, T

    Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono, Journal of the American Chemical Society 130, 3296 (2008)

    2008

  14. [22]

    D. C. Johnston, Advances in Physics59, 803 (2010)

    2010

  15. [23]

    Dai, Reviews of Modern Physics87, 855 (2015)

    P. Dai, Reviews of Modern Physics87, 855 (2015)

    2015

  16. [24]

    Q. Si, R. Yu, and E. Abrahams, Nature Reviews Materi- als 1, 1 (2016)

    2016

  17. [25]

    P. J. Hirschfeld, Comptes Rendus Physique 17, 197 (2016)

    2016

  18. [26]

    Wang and D.-H

    F. Wang and D.-H. Lee, Science332, 200 (2011)

    2011

  19. [27]

    M. Yi, D. Lu, J.-H. Chu, J. G. Analytis, A. P. Sorini, A. F. Kemper, B. Moritz, S.-K. Mo, R. G. Moore, M. Hashimoto, et al., Proceedings of the National Academy of Sciences108, 6878 (2011)

    2011

  20. [28]

    Chu, H.-H

    J.-H. Chu, H.-H. Kuo, J. G. Analytis, and I. R. Fisher, Science 337, 710 (2012)

    2012

  21. [29]

    Si and N

    Q. Si and N. E. Hussey, Physics Today76, 34 (2023)

    2023

  22. [30]

    C. Fang, H. Yao, W.-F. Tsai, J. Hu, and S. A. Kivelson, Phys. Rev. B77, 224509 (2008)

    2008

  23. [31]

    C. Xu, M. Müller, and S. Sachdev, Phys. Rev. B 78, 020501 (2008)

    2008

  24. [32]

    J. Dai, Q. Si, J.-X. Zhu, and E. Abrahams, Proceedings of the National Academy of Sciences106, 4118 (2009)

    2009

  25. [33]

    Fernandes, A

    R. Fernandes, A. Chubukov, and J. Schmalian, Nature physics 10, 97 (2014)

    2014

  26. [34]

    Yu and Q

    R. Yu and Q. Si, Phys. Rev. Lett.115, 116401 (2015)

    2015

  27. [35]

    A. E. Böhmer, J.-H. Chu, S. Lederer, and M. Yi, Nature Physics 18, 1412 (2022)

    2022

  28. [36]

    S. Avci, O. Chmaissem, J. Allred, S. Rosenkranz, I. Eremin, A. V. Chubukov, D. Bugaris, D. Chung, M. Kanatzidis, J.-P. Castellan, et al., Nature commu- nications 5, 3845 (2014)

    2014

  29. [37]

    Böhmer, F

    A. Böhmer, F. Hardy, L. Wang, T. Wolf, P. Schweiss, and C. Meingast, Nature communications6, 7911 (2015)

    2015

  30. [38]

    Allred, K

    J. Allred, K. Taddei, D. Bugaris, M. Krogstad, S. Lapidus, D. Chung, H. Claus, M. Kanatzidis, D. Brown, J. Kang,et al., Nature Physics12, 493 (2016)

    2016

  31. [39]

    Hassinger, G

    E. Hassinger, G. Gredat, F. Valade, S. R. De Cotret, O. Cyr-Choinière, A. Juneau-Fecteau, J.-P. Reid, H. Kim, M. Tanatar, R. Prozorov,et al., Physical Re- view B93, 144401 (2016)

    2016

  32. [40]

    W. R. Meier, Q.-P. Ding, A. Kreyssig, S. L. Bud’ko, A. Sapkota, K. Kothapalli, V. Borisov, R. Valentí, C. D. Batista, P. P. Orth,et al., npj Quantum Materials3, 5 (2018)

    2018

  33. [41]

    A. E. Böhmer, K. Kothapalli, W. T. Jayasekara, J. M. Wilde, B. Li, A. Sapkota, B. G. Ueland, P. Das, Y. Xiao, W. Bi,et al., Physical Review B100, 064515 (2019)

    2019

  34. [42]

    J. M. Ok, S.-H. Baek, C. Hoch, R. Kremer, S. Park, S. Ji, B. Büchner, J.-H. Park, S. Hyun, J. Shim,et al., Nature Communications 8, 2167 (2017)

    2017

  35. [43]

    Lorenzana, G

    J. Lorenzana, G. Seibold, C. Ortix, and M. Grilli, Phys- ical review letters101, 186402 (2008)

    2008

  36. [44]

    P. M. R. Brydon, J. Schmiedt, and C. Timm, Phys. Rev. B 84, 214510 (2011)

    2011

  37. [45]

    Giovannetti, C

    G. Giovannetti, C. Ortix, M. Marsman, M. Capone, J. Van Den Brink, and J. Lorenzana, Nature commu- nications 2, 398 (2011)

    2011

  38. [46]

    Fernandes, S

    R. Fernandes, S. Kivelson, and E. Berg, Physical Review B 93, 014511 (2016)

    2016

  39. [47]

    R. Yu, M. Yi, B. A. Frandsen, R. J. Birgeneau, and Q. Si, arXiv preprint arXiv:1706.07087 (2017)

    2017 arXiv

  40. [48]

    Because it breaks lattice translational symmetry, it should be linearly coupled to a (π, π) charge order, which is denoted here

    In this phase the order parameter is the(π, π) compo- nent of the squared spin density. Because it breaks lattice translational symmetry, it should be linearly coupled to a (π, π) charge order, which is denoted here

  41. [49]

    B. A. Frandsen, K. M. Taddei, M. Yi, A. Frano, Z. Guguchia, R. Yu, Q. Si, D. E. Bugaris, R. Stadel, R. Osborn, S. Rosenkranz, O. Chmaissem, and R. J. Bir- geneau, Phys. Rev. Lett.119, 187001 (2017)

    2017

  42. [50]

    L. Wang, M. He, F. Hardy, P. Adelmann, T. Wolf, M. Merz, P. Schweiss, and C. Meingast, Phys. Rev. B 97, 224518 (2018)

    2018

  43. [51]

    The fit in (b) is in terms of our analytical results (solid line)

    (a) atk = 0 and two nonzerok values and (b) at k = 0.05 r.l.u (solid symbols). The fit in (b) is in terms of our analytical results (solid line). The regions Tc < T < Tr, Tr < T < Ts and T > Ts correspond to double-Q AFM, single-Q AFM and tetragonal PM phases, respectively. Th...

  44. [52]

    S. Wu, Y. Song, Y. He, A. Frano, M. Yi, X. Chen, H. Uchiyama, A. Alatas, A. H. Said, L. Wang, T. Wolf, C. Meingast, and R. J. Birgeneau, Phys. Rev. Lett.126, 107001 (2021)

    2021

  45. [53]

    J. Wu, Q. Si, and E. Abrahams, Phys. Rev. B93, 104515 (2016)

    2016

  46. [54]

    See Supplemental Material at URLwillbeinsertedbypublisher for details on the large-N calculation of the Ginzburg-Landau model for the composite orders with and without the presence of magnetic orders and the effects of anisotropic spin fluctuations

  47. [55]

    Y. Wang, W. Hu, R. Yu, and Q. Si, Phys. Rev. B100, 100502 (2019)

    2019

  48. [56]

    Beneke and M

    C. Beneke and M. Vojta, Phys. Rev. B 103, 174420 (2021)

    2021

  49. [57]

    L. Zhu, M. Garst, A. Rosch, and Q. Si, Phys. Rev. Lett. 91, 066404 (2003)

    2003

  50. [58]

    Y. Li, Z. Yamani, Y. Song, W. Wang, C. Zhang, D. W. Tam, T. Chen, D. Hu, Z. Xu, S. Chi, K. Xia, L. Zhang, S. Cui, W. Guo, Z. Fang, Y. Liu, and P. Dai, Phys. Rev. X 8, 021056 (2018)

    2018

  51. [59]

    Stadel, D

    R. Stadel, D. D. Khalyavin, P. Manuel, K. Yokoyama, S. Lapidus, M. H. Christensen, R. M. Fernandes, D. Phe- lan, D. Y. Chung, R. Osborn, et al., Communications Physics 5, 146 (2022)

    2022

  52. [60]

    X. Liu, R. Tao, M. Ren, W. Chen, Q. Yao, T. Wolf, Y. Yan, T. Zhang, and D. Feng, Nature communications 10, 1039 (2019)

    2019

  53. [61]

    W. Chen, X. Li, Z. Hu, Z. Hu, L. Yue, R. Sutarto, F. He, K. Iida, K. Kamazawa, W. Yu, X. Lin, and Y. Li, Phys. Rev. B103, L180404 (2021)

    2021

  54. [62]

    P. M. Chaikin, T. C. Lubensky, and T. A. Witten, Principles of condensed matter physics, Vol. 10 (Cam- bridge university press Cambridge, 1995). 7 SUPPLEMENTAL MATERIAL – EMERGENT SYMMETRY AT TRANSITION BETWEEN INTERTWINED COMPOSITE ORDERS IN IRON-BASED SUPERCONDUCTORS A. Clas...

    1995

  55. [63]

    In this case, the transition between nematic and charge order occurs at r2 1 g(1 − ϵ2 1 − ϵ4

    − ϵ4 2(ρ4 1 + ρ4 2), (58) where ϵ2 1 = 1 g w c 2 1 βV X q,ωl c2q4 (m + cq2 + γ|ωl|)6 = 1 g w c 2 1 120(2π)2cγm2 (59) ϵ4 2 = 3 8g w c 4 1 βV X q,ωl c4q8 (m + cq2 + γ|ωl|)8 = 1 g w c 4 1 560(2π)2cγm2 , (60) and r1, r2, gare correspondingly shifted from their isotropic values. In...

  56. [64]

    = r2 2 g(1 + ϵ2 1 − ϵ4

  57. [65]

    (61) This means that the original transition point (r1/r2 = 1) is shifted by the order ofO w c 2 . The mass (gap) of the nematic fluctuations approaching to the new transition point from the chargeC4 phase is then δnem =r1 − r2 1 + ϵ2 1 − ϵ4 2 = δcha 2 1 2 ϵ4 1 + ϵ4 2 , (62) w...

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.