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REVIEW 3 major objections 4 minor 76 references

Magnetic catalysis and Hall conductivity of excitonic insulators in a planar four-Fermi model

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A perpendicular magnetic field strengthens the excitonic condensate, raises its critical temperature, and leaves a Hall-conductivity slope change as a transport signature.

desk verdict Good idea, broken numerics: the analytic framework and Hall-slope proposal are worth a look, but Section IV violates the model's own equations, so the quantitative claims are unsupported. read the letter →

arxiv 2608.04986 v1 pith:VJSHRUBH submitted 2026-08-05 cond-mat.mes-hall hep-ph

William R. Tavares , Rudnei O. Ramos , Nei Lopes This is my paper · ORCID
classification cond-mat.mes-hallhep-ph
keywords excitonicinsulatormagneticcatalysisGross-NeveumodelLandaulevelsHallconductivitylarge-Napproximationfour-Fermiphasediagram
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 studies the excitonic-insulator (EI) phase of an extended planar four-Fermi (Gross-Neveu) model in a perpendicular magnetic field, working in the semiconductor regime at leading order in the large-N approximation. Its central claim is that Landau quantization produces an excitonic realization of magnetic catalysis: the EI condensate grows with the field, the zero-density critical temperature rises monotonically, and a sufficiently strong field can induce the EI phase at temperatures where it is absent at zero field. At finite density the picture changes: the zero-temperature chemical-potential transition remains first order, but its critical value varies nonmonotonically with the field because successive Landau levels are occupied, and the field shifts the tricritical point and enlarges the first-order region of the temperature-chemical-potential phase diagram. The paper also derives the Hall conductivity and shows that the onset or strengthening of the EI condensate is accompanied by a characteristic slope change, with mean-field scaling $\bar{\eta}_c \propto (eB-eB_c)^{1/2}$ and a linear variation of the Hall conductivity near the continuous transition. These results give transport signatures that can complement the usual gap-opening evidence in identifying excitonic order in planar systems.

What carries the argument

The argument is carried by the large-N effective potential for the two coupled condensates, obtained by Hubbard-Stratonovich transformation and Landau quantization of the (2+1)-dimensional Dirac fermions. The key identity is the pinning relation $\bar{\sigma}_c = \sigma_0 = g_R^e M (g_R^c |M|+\pi)/(\pi(g_R^e - g_R^c))$ valid whenever $\bar{\eta}_c \neq 0$, which follows because the fermionic contribution $F(\rho;T,\mu,b)$ depends on the two condensates only through $\rho^2 = \sigma_c^2 + \eta_c^2$; eliminating the common function $K(\rho)$ from the two gap equations leaves $\sigma_c$ fixed. The Hall conductivity is then computed from the derivative of the thermodynamic potential with respect to $\mu$, giving the Landau-level filling formula $\sigma_{xy} = \mathrm{sgn}(eB)\, e^2 n/b$, whose thresholds depend self-consistently on the condensates. Near the continuous transition, expanding the Fermi-Dirac sum in $\bar{\eta}_c^2$ yields the square-root law for the EI order parameter and the linear Hall scaling.

What would settle it

Measure the DC Hall conductivity of an InAs/GaSb bilayer as a function of magnetic field at fixed temperature and gate-tuned chemical potential near the reported excitonic transition: the claim predicts a kink in $\sigma_{xy}$ at a field of order $eB_c \simeq 13.6\,\sigma_0^2$ (about 9.6 T for the paper's calibration), so a smooth, featureless Hall response through that field would disprove the predicted transport signature.

Watch

Extended reading notes

Core claim

The paper claims that inside the EI phase the scalar (chiral) condensate is pinned at a constant value $\sigma_0$, independent of temperature, chemical potential, and magnetic field, so all field dependence of the quasiparticle gap is carried by the excitonic condensate $\bar{\eta}_c$. At zero chemical potential this makes the EI gap and critical temperature monotonically increasing functions of $|eB|$: the excitonic analogue of magnetic catalysis. At zero temperature the EI transition driven by chemical potential is first order, with a critical $\mu_c(B)$ that oscillates weakly at small fields and then passes through a broad minimum before rising again; the $T$-$\mu$ phase boundary develops a tricritical point that moves to higher temperature as the field grows. For the parameter values studied, the Hall conductivity vanishes inside the EI phase and jumps to its first plateau at the same first-order transition where the EI condensate collapses, while near the continuous field-induced transition the Hall response obeys $|\bar{\sigma}_{xy}-\bar{\sigma}_{xy,c}| \propto eB-eB_c$, a linear consequence of the mean-field square-root behaviour of the condensate. Restoring physical units, the paper estimates that these effects are accessible in InAs/GaSb bilayers at fields of a few tesla.

Load-bearing premise

The whole phase diagram and Hall signature rest on treating the homogeneous large-N mean-field solution as exact, even though in a strictly two-dimensional system collective phase fluctuations can destroy true long-range order at finite temperature.

Editorial extensions

If this is right

  • At zero density, increasing the perpendicular field raises both the zero-temperature excitonic gap and the critical temperature, so a sufficiently strong field can turn a normal semiconductor into an excitonic insulator at fixed temperature.
  • Inside the EI phase the scalar condensate is fixed at $\sigma_0$, so any measured magnetic-field or temperature dependence of the single-particle gap in that phase is a direct measure of the excitonic condensate.
  • At zero temperature the density-driven transition is first order, and the nonmonotonic $\mu_c(B)$ with Landau-level oscillations gives a sharp prediction for the chemical-potential boundary of the EI phase.
  • The field enlarges the first-order region of the $T$-$\mu$ phase diagram by moving the tricritical point to higher temperature.
  • Hall conductivity plateaus broaden with increasing field, and the EI transition leaves either a jump (first order) or a slope change with linear scaling (continuous), providing a transport signature of excitonic order.

Reading between the lines

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

  • If the pinning relation holds beyond the single parameter set explored, then Hall and gap data taken together in a planar material could isolate the excitonic component of the order parameter from the scalar gap contribution.
  • The coincidence between the first Hall plateau and the first-order EI collapse is parameter-dependent; mapping where that coincidence breaks as the couplings or mass are varied would tell experiment when Hall onset marks excitonic order and when it merely marks Landau-level occupation.
  • Because strictly two-dimensional systems can have collective phase fluctuations that suppress true long-range order at finite temperature, the predicted critical temperature and Hall slope change may describe a pair-formation scale rather than the actual coherence temperature; measuring that coherence scale would quantify the correction.
  • Adding Zeeman splitting would lift the lowest-Landau-level degeneracy and could either enhance or suppress the excitonic gap, offering a direct way to test whether the orbital Landau-quantization effect is the source of the predicted catalysis.
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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 / 4 minor

Summary. The manuscript studies the excitonic-insulator (EI) phase of an extended planar four-Fermi Gross-Neveu model in a perpendicular magnetic field. In the large-N approximation the authors derive a renormalized thermodynamic potential with Landau-level quantization, solve the coupled scalar and excitonic gap equations, and compute the Hall conductivity. They report magnetic catalysis in the excitonic channel (η_c and T_c increase with eB), a scalar condensate pinned to σ0 throughout the EI phase, a nonmonotonic field dependence of the critical chemical potential, a field-shifted tricritical point, and a slope change in the Hall conductivity at a continuous field-driven EI transition. The appendices contain the renormalization procedure, the derivation of the pinning relation, and the near-critical Hall scaling.

Significance. If correct, the paper would provide a clean effective-field-theory demonstration that magnetic catalysis extends to the excitonic channel and that Hall transport can serve as a signature of excitonic order. The analytic framework—Hubbard-Stratonovich decoupling, the renormalized potential, and the near-critical expansion in Appendix C—is presented carefully and is internally coherent. The authors also acknowledge the homogeneous mean-field and BKT limitations honestly. However, the numerical section rests on a parameter set that contradicts the model's own gap equations; the quantitative results, including all figures and the material estimates in Table I, are therefore not supported as submitted.

major comments (3)
  1. [§IV, Eqs. (4.1)-(4.2)] The parameter set (4.1) is inconsistent with the derived relation (4.2). Substituting g_R^e = -11 σ0^{-1}, g_R^c = 9 σ0^{-1}, and M = 0.24 σ0 into Eq. (4.2) gives σ0 = 0.2228 σ0, a contradiction unless σ0 = 0. Equivalently, with these couplings Eq. (4.2) is an identity only for M/σ0 ≈ 0.641, not 0.24. Since σ0 is used throughout as the EI-phase scalar condensate, the stated inputs do not define a consistent model.
  2. [Appendix B, Eq. (B12)] The zero-field EI existence condition is violated by the chosen coupling. Equation (B12) gives η_0^2 = π^2/(g_R^e)^2 - σ_0^2; for g_R^e = -11 σ_0^{-1} this is (π^2/121 - 1) σ_0^2 ≈ -0.918 σ_0^2 < 0. Hence no real zero-field EI condensate exists, yet Fig. 1 reports η_c ≈ 0.8 σ_0 at B=0 and T=0. The curves in Figs. 1–13 therefore cannot be stationary points of the potential (3.10).
  3. [§IV and Table I] Because the numerical solutions are not stationary points, the quantitative conclusions built on them—the critical temperatures in Eqs. (4.3)–(4.4), the μ_c(B) curve in Fig. 8, the tricritical points in Fig. 9, the Hall slope change and scaling in Eqs. (4.6)–(4.7), and the experimental field estimates in Table I—are unsupported. The Appendix C derivation is formally correct, but it is applied to a transition that does not exist for the stated parameters. A demonstration with a parameter set satisfying both Eq. (4.2) and |g_R^e| < π/σ_0 is needed before the qualitative claims can be assessed.
minor comments (4)
  1. [§III] In the paragraph after Eq. (3.3), 'eletromagnetic' should be 'electromagnetic'.
  2. [Fig. 13 caption] The phrase 'slope chance' should be 'slope change'.
  3. [§IV, Eq. (4.2)] The dual use of σ0 as both a normalization unit and the predicted EI-phase scalar condensate is confusing; a sentence stating that Eq. (4.2) is a self-consistency condition for σ0 would help prevent the kind of inconsistency identified above.
  4. [§IV, footnote 1] The relation between the renormalized couplings in Eq. (4.1) and the quoted bare-coupling hierarchy g_e > g_Λ > g_c should be spelled out, since the renormalized values have opposite signs.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the magnetic-catalysis and Hall-scaling results are genuine outputs of the model equations, not inputs; the severe parameter inconsistency is a correctness issue, not a circular reduction.

full rationale

Walking the derivation chain shows no circular reduction. The model is defined by the Lagrangian (2.1), the thermodynamic potential is derived by Hubbard-Stratonovich linearization and large-N integration (Eqs. 2.12-2.14), the magnetic-field version follows from the Landau-level replacement (3.9) and is displayed in Eq. (3.10), and the gap equations (3.15)-(3.16) are solved as stationary points of that potential. The claimed enhancement of the EI condensate and critical temperature by the field is an output of solving these coupled equations, not an input. The Hall conductivity is computed from the thermodynamic density via Eqs. (3.24)-(3.30), and the near-critical scalings (4.6)-(4.7) are derived in Appendix C from the analytic dependence of the Hall response on eta_c^2, with the exponent 1/2 being the standard mean-field order-parameter exponent; no fitted parameter is renamed as a prediction, and the experimental calibrations in Sec. IV E are explicitly labeled representative estimates. The only self-citation is Ref. [30] for the model and the zero-field parameter region; that is a published independent starting point and is not used to deduce the new magnetic-field or Hall results, so it is not load-bearing in a circular way. A non-circularity caveat must be flagged: the chosen parameters g_R^e = -11 sigma_0^{-1}, g_R^c = 9 sigma_0^{-1}, M = 0.24 sigma_0 are internally inconsistent with the paper's own Eq. (4.2), which evaluates to sigma_0 about 0.223 sigma_0, and with the zero-field existence condition Eq. (B12), which gives eta_0^2 < 0. This invalidates the numerical solutions in Sec. IV, but it is a consistency and correctness failure rather than a reduction of the predictions to the inputs.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The model uses three dimensionful parameters (g_R^c, g_R^e, M) chosen by hand; no new particles or forces are introduced. The main theoretical input beyond the model itself is the large-N mean-field approximation and the Streda formula for the Hall conductivity.

free parameters (3)
  • g_R^e (renormalized excitonic coupling) = -11 sigma_0^{-1} as stated
    Controls the strength of the interband pairing channel; chosen to put the system in the EI regime. The stated value is not consistent with Eq. (4.2) and Fig. 1.
  • g_R^c (renormalized scalar coupling) = 9 sigma_0^{-1} as stated
    Controls the chiral or scalar channel; chosen representative value.
  • M (explicit mass or source scale) = 0.24 sigma_0 (0.15 sigma_0 in Fig. 2)
    Sets the bare semiconductor gap; chosen by hand to define the semiconductor regime.
assumptions (5)
  • domain assumption Large-N expansion valid to leading order, with fluctuations and BKT physics neglected
    All gap equations and the thermodynamic potential are derived at leading order in 1/N (Sec II). In strictly 2D systems this omits phase fluctuations that can remove long-range order.
  • standard math Four-component reducible Dirac representation is appropriate for planar fermions
    Allows gamma_5 and the two independent condensates; follows Ref [70].
  • domain assumption Local four-fermion interaction faithfully captures the interband coherence channel
    The model is presented as a low-energy effective theory, not a microscopic Coulomb model (Sec I).
  • domain assumption Zero-field renormalization suffices at finite magnetic field
    Stated in Sec III and Appendix A; the UV divergence is independent of B.
  • domain assumption Hall conductivity is given by the clean Streda relation sigma_xy = e^2 n/b at the mean-field saddle point
    Used without derivation in Sec III, citing Refs [54,72]; neglects disorder, Zeeman splitting, and vertex corrections.

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Cite this review

Pith. "Pith review of Magnetic catalysis and Hall conductivity of excitonic insulators in a planar four-Fermi model." pith.science (2026). https://pith.science/paper/VJSHRUBH

@misc{pith2026260804986,
  author       = {Pith},
  title        = {Pith review of: Magnetic catalysis and Hall conductivity of excitonic insulators in a planar four-Fermi model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VJSHRUBH}},
  note         = {Machine review of arXiv:2608.04986}
}
abstract

We study the effects of a perpendicular magnetic field on the excitonic insulator (EI) phase in the semiconductor regime using an extended planar four-Fermi model. Within the large-$N$ approximation, we determine the coupled scalar and excitonic condensates at finite temperature, chemical potential, and magnetic field. The field enhances the EI condensate and raises its critical temperature, providing an excitonic realization of magnetic catalysis, while the scalar condensate remains constant throughout the EI phase. By contrast, the critical chemical potential depends nonmonotonically on the field because of the successive occupation of Landau levels. The magnetic field also shifts the mean-field tricritical point and enlarges the first-order region of the temperature--chemical-potential phase diagram. We further analyze the Hall conductivity and find that increasing the field reduces the number of plateaus and modifies the threshold for a finite Hall response. For the parameters considered, the emergence of the EI condensate is accompanied by a characteristic change in the Hall conductivity, including a field-dependent change of slope near a continuous transition. These results show that the combined phase structure and Hall response can provide complementary signatures of excitonic ordering in planar fermionic systems.

Figures

Figures reproduced from arXiv: 2608.04986 by the authors.

Figure 1
Figure 1. FIG. 1. Normalized EI condensate (solid curves) and scalar con [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Normalized EI condensate as a function of the perpendicular [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Normalized EI condensate (solid curves) and scalar conden [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figures from the paper (7 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Normalized EI condensate as a function of chemical potential [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Critical chemical potential of the EI phase at [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Normalized Hall conductivity at [PITH_FULL_IMAGE:figures/full_fig_p010_10.png]
Figure 9
Figure 9. Figure 9: FIG. 9. EI phase boundaries in the [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Normalized Hall conductivity and EI condensate as func [PITH_FULL_IMAGE:figures/full_fig_p010_11.png]
Figure 13
Figure 13. Figure 13: FIG. 13. Normalized Hall conductivity (black solid curve), EI con [PITH_FULL_IMAGE:figures/full_fig_p011_13.png]
Figure 12
Figure 12. Figure 12: FIG. 12. Results for (a) the normalized EI condensate, (b) the scalar [PITH_FULL_IMAGE:figures/full_fig_p011_12.png]

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Reference graph

Works this paper leans on

76 extracted references · 70 canonical work pages

  1. [30]

    L. H. C. M. Nunes, R. L. S. Farias, and E. C. Marino, Supercon- ducting and excitonic quantum phase transitions in doped Dirac electronic systems, Phys. Lett. A376, 779 (2012)

    work page 2012

  2. [1]

    0.05 0.1 1.279 1.281 1.283 FIG. 8. Critical chemical potential of the EI phase at𝑇=0 as a function of magnetic field. The inset resolves the weak-field oscilla- tions caused by changes in Landau-level occupation. At intermediate field,𝜇 𝑐 reaches a broad minimum and then rises on the strong-field magnetic-catalysis branch. The zero-density critical line p...

    work page

  3. [2]

    In this limit, the fermionic part of the renormalized potential is F(𝜌; 0,0,0)= 𝜌3 3𝜋,(B9) so that K(𝜌; 0,0,0)= 𝜌 𝜋.(B10) For a nonvanishing EI condensate, Eqs. (B6) and (B10) yield 𝜌0=− 𝜋 𝑔𝑅𝑒 .(B11) The EI vacuum solution therefore requires𝑔𝑅 𝑒 <0 and has 𝜂2 0= 𝜋2 (𝑔𝑅𝑒)2−𝜎 2 0, 𝜂 0=± √︄ 𝜋2 (𝑔𝑅𝑒)2−𝜎 2 0.(B12) A real nonzero EI stationary solution conseque...

    work page

  4. [3]

    N. F. Mott, The transition to the metallic state, Philos. Mag.6, 287 (1961)

    1961

  5. [4]

    R. S. Knox, Theory of Excitons, Solid State Physics, Suppl. 5 (Academic Press, New York, 1963)

    work page 1963

  6. [5]

    des Cloizeaux, Excitonic instability and crystallographic anomalies in semiconductors, J

    J. des Cloizeaux, Excitonic instability and crystallographic anomalies in semiconductors, J. Phys. Chem. Solids26, 259 (1965)

    work page 1965

  7. [6]

    L. V. Keldysh and Yu. V. Kopaev, Possible instability of the semimetallic state toward Coulomb interaction, Fiz. Tverd. Tela 6, 2791 (1964) [Sov. Phys. Solid State6, 2219 (1965)]

    work page 1964

  8. [7]

    J ´erome, T

    D. J ´erome, T. M. Rice, and W. Kohn, Excitonic insulator, Phys. Rev.158, 462 (1967)

    1967

Show all 76 references
  1. [8]

    B. I. Halperin and T. M. Rice, Possible anomalies at a semimetal- semiconductor transition, Rev. Mod. Phys.40, 755 (1968)

    1968

  2. [9]

    Zittartz, Theory of the excitonic insulator in the presence of normal impurities, Phys

    J. Zittartz, Theory of the excitonic insulator in the presence of normal impurities, Phys. Rev.162, 752 (1967). 18

    1967

  3. [10]

    Bardeen, L

    J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Microscopic theory of superconductivity, Phys. Rev.106, 162 (1957)

    1957

  4. [11]

    F. X. Bronold and H. Fehske, Possibility of an excitonic insulator at the semiconductor-semimetal transition, Phys. Rev. B74, 165107 (2006)

    2006

  5. [12]

    Comte and P

    C. Comte and P. Nozi `eres, Exciton Bose condensation: The ground state of an electron-hole gas. I. Mean-field description of a simplified model, J. Phys. France43, 1069 (1982)

    1982

  6. [13]

    Du,et al, Evidence for a topological excitonic insulator in InAs/GaSb bilayers, Nat

    L. Du,et al, Evidence for a topological excitonic insulator in InAs/GaSb bilayers, Nat. Commun.8, 1971 (2017)

    2017

  7. [14]

    J. P. Eisenstein and A. H. MacDonald, Bose–Einstein conden- sation of excitons in bilayer electron systems, Nature (London) 432, 691 (2004)

    2004

  8. [15]

    Gupta, A

    S. Gupta, A. Kutana, and B. I. Yakobson, Heterobilayers of two- dimensional materials as a platform for excitonic superfluidity, Nat. Commun.11, 2989 (2020)

    2020

  9. [16]

    Ma,et al, Strongly correlated excitonic insulator in atomic double layers, Nature (London)598, 585 (2021)

    L. Ma,et al, Strongly correlated excitonic insulator in atomic double layers, Nature (London)598, 585 (2021)

    2021

  10. [17]

    Y. Jia, P. Wang, C.-L. Chiu,et al., Evidence for a monolayer excitonic insulator, Nat. Phys.18, 87 (2022)

    2022

  11. [18]

    Y. F. Lu,et al, Zero-gap semiconductor to excitonic insulator transition in Ta2NiSe5, Nat. Commun.8, 14408 (2017)

    2017

  12. [19]

    P. A. Volkov,et al, Critical charge fluctuations and emergent co- herence in a strongly correlated excitonic insulator, npj Quantum Mater.6, 52 (2021)

    2021

  13. [20]

    Sugimoto, S

    K. Sugimoto, S. Nishimoto, T. Kaneko, and Y. Ohta, Strong- coupling nature of the excitonic insulator state in Ta 2NiSe5, Phys. Rev. Lett.120, 247602 (2018)

    2018

  14. [21]

    K. Kim, H. Kim, J. Kim, C. Kwon, J. S. Kim, and B. J. Kim, Direct observation of excitonic instability in Ta 2NiSe5, Nat. Commun.12, 1969 (2021)

    2021

  15. [22]

    F. J. Di Salvo,et al, Physical and structural properties of the new layered compounds Ta 2NiS5 and Ta2NiSe5, J. Less-Common Met.116, 51 (1986)

    1986

  16. [23]

    Wakisaka,et al, Excitonic insulator state in Ta2NiSe5 probed by photoemission spectroscopy, Phys

    Y. Wakisaka,et al, Excitonic insulator state in Ta2NiSe5 probed by photoemission spectroscopy, Phys. Rev. Lett.103, 026402 (2009)

    2009

  17. [24]

    Wakisaka,et al., Photoemission spectroscopy of Ta 2NiSe5, J

    Y. Wakisaka,et al., Photoemission spectroscopy of Ta 2NiSe5, J. Supercond. Nov. Magn.25, 1231 (2012)

    2012

  18. [25]

    Windg ¨atter,et al, Common microscopic origin of the phase transitions in Ta 2NiS5 and the excitonic insulator candidate Ta2NiSe5, npj Comput

    L. Windg ¨atter,et al, Common microscopic origin of the phase transitions in Ta 2NiS5 and the excitonic insulator candidate Ta2NiSe5, npj Comput. Mater.7, 210 (2021)

    2021

  19. [26]

    Varsano, M

    D. Varsano, M. Palummo, E. Molinari, and M. Rontani, A mono- layer transition-metal dichalcogenide as a topological excitonic insulator, Nat. Nanotechnol.15, 367 (2020)

    2020

  20. [27]

    Sun,et al., Evidence for equilibrium exciton condensation in monolayer WTe2, Nat

    B. Sun,et al., Evidence for equilibrium exciton condensation in monolayer WTe2, Nat. Phys.18, 94 (2022)

    2022

  21. [28]

    J. Liu, H. Qu, and Y. Li, One-dimensional magnetic excitonic insulators, New J. Phys.26, 103034 (2024)

    2024

  22. [29]

    P. B. Littlewood and X. Zhu, Possibilities for exciton condensa- tion in semiconductor quantum-well structures, Phys. Scr.T68, 56 (1996)

    1996

  23. [31]

    Mazza, Magnetic field control of the excitonic transition in Ta2NiSe5, arXiv:2601.23136

    G. Mazza, Magnetic field control of the excitonic transition in Ta2NiSe5, arXiv:2601.23136

  24. [32]

    Lopes, M

    N. Lopes, M. A. Continentino, and D. G. Barci, Excitonic in- sulators and Gross–Neveu models, Phys. Rev. B105, 165125 (2022)

    2022

  25. [33]

    R. J. Elliott and R. Loudon, Theory of the absorption edge in semiconductors in a high magnetic field, J. Phys. Chem. Solids 15, 196 (1960)

    1960

  26. [34]

    E. W. Fenton, Excitonic insulator in a magnetic field, Phys. Rev. 170, 816 (1968)

    1968

  27. [35]

    Yafet, R

    Y. Yafet, R. W. Keyes, and E. N. Adams, Hydrogen atom in a strong magnetic field, J. Phys. Chem. Solids1, 137 (1956)

    1956

  28. [36]

    Zhu,et al, Magnetic field tuning of an excitonic insulator between the weak- and strong-coupling regimes in quantum- limit graphite, Sci

    Z. Zhu,et al, Magnetic field tuning of an excitonic insulator between the weak- and strong-coupling regimes in quantum- limit graphite, Sci. Rep.7, 1733 (2017)

    2017

  29. [37]

    D. V. Khveshchenko, Magnetic-field-induced insulating behav- ior in highly oriented pyrolitic graphite, Phys. Rev. Lett.87, 206401 (2001)

    2001

  30. [38]

    E. V. Gorbar, V. P. Gusynin, V. A. Miransky, and I. A. Shovkovy, Magnetic-field-driven metal-insulator phase transition in planar systems, Phys. Rev. B66, 045108 (2002)

    2002

  31. [39]

    Leal and D

    H. Leal and D. V. Khveshchenko, Excitonic instability in two- dimensional degenerate semimetals, Nucl. Phys. B687, 323 (2004)

    2004

  32. [40]

    V. P. Gusynin and S. G. Sharapov, Unconventional integer quan- tum Hall effect in graphene, Phys. Rev. Lett.95, 146801 (2005)

    2005

  33. [41]

    V. P. Gusynin, V. A. Miransky, S. G. Sharapov, and I. A. Shovkovy, Excitonic gap, phase transition, and quantum Hall effect in graphene, Phys. Rev. B74, 195429 (2006)

    2006

  34. [42]

    G. W. Semenoff, I. A. Shovkovy, and L. C. R. Wijewardhana, Phase transition induced by a magnetic field, Mod. Phys. Lett. A13, 1143 (1998)

    1998

  35. [43]

    Krishana, N

    K. Krishana, N. P. Ong, Y. Zhang,et al., Quasiparticle thermal Hall angle and magnetoconductance in YBa2Cu3O𝑥, Phys. Rev. Lett.82, 5108 (1999)

    1999

  36. [44]

    D. V. Khveshchenko and W. F. Shively, Excitonic pairing be- tween nodal fermions, Phys. Rev. B73, 115104 (2006)

    2006

  37. [45]

    K. S. Novoselov,et al, Two-dimensional gas of massless Dirac fermions in graphene, Nature (London)438, 197 (2005)

    2005

  38. [46]

    D. J. Gross and A. Neveu, Dynamical symmetry breaking in asymptotically free field theories, Phys. Rev. D10, 3235 (1974)

    1974

  39. [47]

    K. G. Klimenko, Three-dimensional Gross–Neveu model at nonzero temperature and in an external magnetic field, Theor. Math. Phys.90, 1 (1992) [Teor. Mat. Fiz.90, 3 (1992)]

    1992

  40. [48]

    K. G. Klimenko, Three-dimensional Gross–Neveu model at nonzero temperature and in an external magnetic field, Z. Phys. C54, 323 (1992)

    1992

  41. [49]

    K. G. Klimenko, Three-dimensional Gross–Neveu model in an external magnetic field, Theor. Math. Phys.89, 1161 (1992) [Teor. Mat. Fiz.89, 211 (1991)]

    1992

  42. [50]

    V. P. Gusynin, V. A. Miransky, and I. A. Shovkovy, Catalysis of dynamical flavor symmetry breaking by a magnetic field in (2+1) dimensions, Phys. Rev. Lett.73, 3499 (1994) [Erratum: Phys. Rev. Lett.76, 1005 (1996)]

    1994

  43. [51]

    V. P. Gusynin, V. A. Miransky, and I. A. Shovkovy, Dynamical flavor symmetry breaking by a magnetic field in (2+1) dimen- sions, Phys. Rev. D52, 4718 (1995)

    1995

  44. [52]

    A. S. Vshivtsev, B. V. Magnitsky, and K. G. Klimenko, Spon- taneous breaking of chiral invariance by an external magnetic field in (2+1) dimensions, JETP Lett.62, 283 (1995)

    1995

  45. [53]

    V. C. Zhukovsky, K. G. Klimenko, and V. V. Khudyakov, Mag- netic catalysis in a𝑃-even, chiral-invariant three-dimensional model with four-fermion interaction, Theor. Math. Phys.124, 1132 (2000)

    2000

  46. [54]

    Y. M. P. Gomes, E. Martins, M. B. Pinto and R. O. Ramos, First-order phase transitions within Weyl type of materials at low temperatures, Phys. Rev. B108, no.8, 085107 (2023)

    2023

  47. [55]

    Caldas and R

    H. Caldas and R. O. Ramos, Magnetization of planar four- fermion systems, Phys. Rev. B80, 115428 (2009)

    2009

  48. [56]

    R. O. Ramos and P. H. A. Manso, Chiral phase transition in a planar four-Fermi model in a tilted magnetic field, Phys. Rev. D 87, 125014 (2013)

    2013

  49. [57]

    K. G. Klimenko and R. N. Zhokhov, Magnetic catalysis effect 19 in the (2+1)-dimensional Gross–Neveu model with Zeeman in- teraction, Phys. Rev. D88, 105015 (2013)

    2013

  50. [58]

    K. G. Klimenko, R. N. Zhokhov, and V. C. Zhukovsky, Super- conductivity phenomenon induced by an external in-plane mag- netic field in a (2+1)-dimensional Gross–Neveu-type model, Mod. Phys. Lett. A28, 1350096 (2013)

    2013

  51. [59]

    K. G. Klimenko, R. N. Zhokhov, and V. C. Zhukovsky, Super- conducting phase transitions induced by chemical potential in a (2+1)-dimensional four-fermion quantum field theory, Phys. Rev. D86, 105010 (2012)

    2012

  52. [60]

    Y. M. P. Gomes and R. O. Ramos, Superconducting phase tran- sition in planar fermionic models with Dirac cone tilting, Phys. Rev. B107, no.12, 125120 (2023)

    2023

  53. [61]

    J. L. Kneur, M. B. Pinto, and R. O. Ramos, Phase diagram of the magnetized planar Gross–Neveu model beyond the large-𝑁 approximation, Phys. Rev. D88, 045005 (2013)

    2013

  54. [62]

    J. L. P. Mauldin and D. H. Rischke, The(2+1)-dimensional Gross-Neveu-Yukawa model at finite temperature, density, and magnetic field within the Functional Renormalization Group, [arXiv:2608.02280 [hep-ph]]

    arXiv

  55. [63]

    J. J. Lenz, M. Mandl, and A. Wipf, Magnetic catalysis in the (2+1)-dimensional Gross–Neveu model, Phys. Rev. D107, 094505 (2023)

    2023

  56. [64]

    J. J. Lenz, M. Mandl and A. Wipf, Magnetized (2+1)- dimensional Gross-Neveu model at finite density, Phys. Rev. D108, no.7, 074508 (2023)

    2023

  57. [65]

    I. A. Shovkovy, Magnetic catalysis: A review, Lect. Notes Phys. 871, 13 (2013)

    2013

  58. [66]

    V. A. Miransky and I. A. Shovkovy, Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals, Phys. Rep.576, 1 (2015)

    2015

  59. [67]

    J. L. Kneur, M. B. Pinto, and R. O. Ramos, Critical and tricritical points for the massless two-dimensional Gross–Neveu model beyond large𝑁, Phys. Rev. D74, 125020 (2006)

    2006

  60. [68]

    Barducci, R

    A. Barducci, R. Casalbuoni, M. Modugno, G. Pettini, and R. Gatto, Thermodynamics of the massive Gross–Neveu model, Phys. Rev. D51, 3042 (1995)

    1995

  61. [69]

    K. G. Klimenko, Massive Gross–Neveu model in the leading order of the 1/𝑁expansion: Allowance for temperature and chemical potential, Theor. Math. Phys.75, 487 (1988)

    1988

  62. [70]

    Nambu and G

    Y. Nambu and G. Jona-Lasinio, Dynamical model of elementary particles based on an analogy with superconductivity. I, Phys. Rev.122, 345 (1961)

    1961

  63. [71]

    Nambu and G

    Y. Nambu and G. Jona-Lasinio, Dynamical model of elementary particles based on an analogy with superconductivity. II, Phys. Rev.124, 246 (1961)

    1961

  64. [72]

    T. W. Appelquist, M. J. Bowick, D. Karabali, and L. C. R. Wijewardhana, Spontaneous chiral-symmetry breaking in three- dimensional QED, Phys. Rev. D33, 3704 (1986)

    1986

  65. [73]

    Flachi, Strongly interacting fermions and phases of the Casimir effect, Phys

    A. Flachi, Strongly interacting fermions and phases of the Casimir effect, Phys. Rev. Lett.110, 060401 (2013)

    2013

  66. [74]

    Kittel,Introduction to Solid State Physics, 6th ed

    C. Kittel,Introduction to Solid State Physics, 6th ed. (Wiley, New York, 1986)

    1986

  67. [75]

    Vi ˜nas Bostr ¨om, A

    F. Vi ˜nas Bostr ¨om, A. Tsintzis, M. Hell, and M. Leijnse, Band structure and end states in InAs/GaSb core-shell-shell nanowires, Phys. Rev. B102, 195434 (2020)

    2020

  68. [76]

    Y. H. Kwan, T. Devakul, S. L. Sondhi, and S. A. Parameswaran, Theory of competing excitonic orders in insulating WTe2 mono- layers, Phys. Rev. B104, 125133 (2021)

    2021

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Reviewed August 6, 2026 · model on record in the stance chip above.