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Dislocations and crystallization dynamics of chiral soliton lattices

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper proposes a field-theory model whose modified topological term makes chiral soliton lattices form dynamically, and shows in simulations that edge and screw dislocations are the agents of that crystallization.

desk verdict A useful, internally consistent numerical study of CSL formation in a proposed model, but the model's physical status is the real soft spot: the modified topological term is ad hoc and the strongest stability claim comes from relaxation, not real-time dynamics. read the letter →

arxiv 2506.16354 v1 pith:GVDRHEW5 submitted 2025-06-19 hep-th cond-mat.softhep-ph

Minoru Eto , Kentaro Nishimura , Muneto Nitta This is my paper
classification hep-thcond-mat.softhep-ph
keywords chiralsolitonlatticedislocationstopologicaldefectssine-GordonmodelaxionedgedislocationscrewQCDinmagneticfield
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

The paper is trying to show that dislocations, the defects that govern plasticity in atomic crystals, also arise dynamically in emergent soliton lattices described by continuum field theory. The obstacle is that the standard chiral sine-Gordon model gives the right ground state but its equations of motion ignore the external field, so the lattice can never form in real time. The authors fix this with a third model whose topological term, unlike in earlier versions, actually enters the equations of motion. In two dimensions their simulations show edge dislocations appearing spontaneously, guiding soliton growth and then annihilating to leave a clean chiral soliton lattice. In three dimensions both edge and screw dislocations appear, and a stable double-helical screw dislocation emerges that resembles a DNA double helix.

What carries the argument

The load-bearing object is model III, the axion model with a modified topological term: $L_{III} = |\partial_\mu\phi|^2 - V + \frac{\kappa}{v^2} j^\mu S_\mu$, where the phase current $j^\mu = \rho^2\partial^\mu\eta$ is written in terms of the amplitude $\rho$ and phase $\eta$ of the complex scalar $\phi = \rho e^{i\eta}$. Unlike the previous models, this term is not a total derivative, so the external background field $S^\mu$ enters the equations of motion directly and makes the energy of a chiral soliton depend on the field. This term is what lets a finite soliton suspended between vortices grow or shrink depending on the field strength, and it is what drives the dynamical formation of the chiral soliton lattice and its dislocations in the simulations.

What would settle it

A decisive test would be to derive the low-energy effective action from a specific ultraviolet theory, such as the chiral Lagrangian for QCD or the Dzyaloshinskii-Moriya spin model for chiral magnets, and check whether the resulting topological term takes the model III form $\frac{\kappa}{v^2} \rho^2 S^\mu \partial_\mu \eta$; a derivation yielding a total derivative, or a different coefficient, would show that the equations of motion do not actually depend on the external field in the ways the simulations assume.

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Extended reading notes

Core claim

The central claim is that the field-theoretical model III, defined by the modified topological term $\frac{\kappa}{v^2} j^\mu S_\mu$ with $j^\mu = -\frac{i}{2}(\phi^*\partial^\mu\phi - \phi\partial^\mu\phi^*)$, makes the equations of motion depend on the external field $S^\mu$ and thereby allows the real-time formation of chiral soliton lattices from random initial states. The paper argues that the chiral sine-Gordon model and the axion model with an unmodified topological term both fail at this: the former has singular dislocations and field-independent dynamics, while the latter still leaves the dynamics blind to the external field. Numerical simulations in model III then show that edge dislocations emerge spontaneously in two dimensions and both edge and screw dislocations in three dimensions, with a stable double helical screw dislocation resembling a double helix staircase or DNA. The paper also extracts a relation between the external field strength and the density and formation speed of the resulting soliton lattice.

Load-bearing premise

The load-bearing premise is that model III, with its modified topological term $\frac{\kappa}{v^2} j^\mu S_\mu$ introduced ad hoc in Sec. 2.3.1, correctly describes the low-energy dynamics of real physical systems such as chiral magnets or QCD in strong magnetic fields; if the actual topologically invariant coupling has a different form, the simulated dynamics and dislocation structures would not carry over.

Editorial extensions

If this is right

  • The real-time formation of chiral soliton lattices from random fluctuations becomes accessible in a continuum field theory, not just through static ground-state analysis or quantum nucleation.
  • Edge dislocations in two dimensions act as the carriers of soliton growth, with pair creation, motion, and annihilation providing a dynamical route to a defect-free lattice.
  • In three dimensions, screw dislocations with a field-locked helicity appear, and the external field selects which combination of vortex charge and handedness is stable.
  • A double helical screw dislocation is found to be stable while two separated screw dislocations relax to the pure lattice, suggesting that intertwining protects the defect against separation.
  • Larger external fields produce denser chiral soliton lattices and shorten the formation time, giving a quantitative handle on crystallization dynamics.

Reading between the lines

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

  • If model III is the correct low-energy description, the same dislocation mechanisms could be sought in actual chiral magnets, where edge dislocations should behave as merons and could mediate transitions between skyrmion crystal and chiral soliton lattice phases.
  • In QCD under strong magnetic fields, the dislocations carry charged pion strings, so a closed dislocation loop would be an electrically charged superconducting object; the simulations here suggest how such loops form and reconnect dynamically.
  • The hopping motion of edge dislocations parallel to the external field is interpreted through the Peierls-Nabarro potential, and the configurations found here could be used to compute that potential explicitly.
  • The same framework might be extended to the chiral double sine-Gordon model or to higher domain-wall numbers, where a single dislocation could join several different types of domain walls.
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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

4 major / 5 minor

Summary. The paper studies dislocations in chiral soliton lattices (CSLs) and proposes a hierarchy of three field-theory models. Model I (chiral sine-Gordon) admits CSLs but has B-independent equations of motion and singular dislocations; Model II (axion model with a topological term) regularizes dislocations via vortices but still leaves the dynamics independent of the external field; Model III modifies the topological coupling to κ/v^2 j^μ S_μ with j^μ = ρ^2 ∂^μη, making the equations of motion depend on the external field. The authors then numerically study CSL formation from random initial states. In 2D they report spontaneous creation and annihilation of edge dislocation pairs leading to a final CSL; in 3D they report both edge and screw dislocations, reconnection events, and a stable double-helical screw dislocation resembling a DNA double helix. They also present relations between the external field strength and the final soliton density and formation speed. The central claim is that Model III provides a framework for studying dislocation dynamics in solitonic structures relevant to chiral magnets and QCD matter.

Significance. If the central claims hold, the paper would open a genuinely new direction: real-time crystallization dynamics of CSLs with explicit dislocation degrees of freedom, and a concrete field-theoretic realization of dislocations as endpoints of solitons. The topological classification in Sec. 3.1, the distinction between edge and screw dislocations in terms of DSG solitons and helicity, and the numerical observation of reconnection and dislocation-mediated growth are valuable and go beyond existing static treatments. The paper is also honest about numerical sensitivity and repeatedly cautions against over-reading single simulations. However, the significance is conditional on the physical status of Model III: the modified topological term is not derived from the anomaly-matched low-energy theory presented in Appendix A, and several headline claims (2D real-time formation, stability of the double helix) are established with dissipative or relaxation dynamics rather than Hamiltonian real-time evolution. These issues are fixable but currently limit the paper's reach.

major comments (4)
  1. [Sec. 2.3.1, Eq. (2.42)] The central claim rests on the modified topological term κ/v^2 j^μ S_μ, but this coupling is introduced ad hoc. Appendix A derives the anomaly-matched low-energy coupling for the claimed QCD applications in the Model II form κ S^μ ∂_μη, with a coefficient that is independent of the radial mode ρ. The two forms agree only on the constraint ρ = v, which is violated in vortex cores. Since edge and screw dislocations are precisely configurations with vortex cores, the B-dependent dynamics of Model III differ from the anomaly-matched theory exactly where the paper's central phenomena occur. Please either derive the ρ^2/v^2 coupling from a UV theory (chiral Lagrangian, Dzyaloshinskii-Moriya model, or an explicit integrating-out procedure) or clearly reframe the paper as a phenomenological model and correspondingly soften the claims about chiral magnets and QCD. A concrete test would be to repeat the dislocation-formation simulations with the anomaly-matched ρ-independent coupling and check whether the same qualitative dynamics survive.
  2. [Sec. 3.3, Eq. (3.14)] The 2D formation dynamics are simulated with an added diffusion term ϵ ∂_t φ on the right-hand side (ϵ = 0.05). This is not the equation of motion of Model III; it is a dissipative modification that can relax fluctuations toward a CSL. The abstract's 'real-time formation' claim for 2D therefore needs support. Please show that the dislocation-mediated formation persists as ϵ → 0, or at least for a sequence of decreasing ϵ, or explicitly characterize the 2D results as relaxation dynamics rather than real-time evolution.
  3. [Sec. 4.3.2, Figs. 26-28] The claimed stability of the double-helical screw dislocation is established by relaxation with a large diffusion coefficient ϵ = 1, i.e., by gradient flow, not by real-time evolution. Convergence under this relaxation shows local stationarity under a dissipative dynamics, but it does not establish dynamical stability of the Hamiltonian EOM (2.54). Please test the stability by evolving perturbed double-helix configurations with ϵ = 0, or state the weaker claim that the configuration is relaxation-stable.
  4. [Sec. 4.4, Fig. 33] The quantitative trends for the start and end times of CSL formation as functions of κ̃B are based on a single simulation per parameter value, despite the paper's own warning in Sec. 3.3 that results are sensitive to initial configurations, box size, boundary conditions, and the diffusion coefficient. For the claim that the external field controls formation speed and final soliton density, please provide an ensemble of initial conditions or at least error bars; otherwise these statements should remain qualitative.
minor comments (5)
  1. [Sec. 3.4 (heading)] The heading 'Dyamics of edge dislocations' contains a typo and should read 'Dynamics of edge dislocations'.
  2. [Sec. 5 (first paragraph)] The word 'crystalization' should be 'crystallization'.
  3. [Appendix A] The sentence containing 'taht' has a typo; it should read 'that'.
  4. [Sec. 2.3.1, after Eq. (2.42)] The phrase 'is not topological anymore' is imprecise; the term is no longer a total derivative, but it still has a topological flavor. Consider rephrasing to avoid confusion.
  5. [Sec. 2.3.2, Fig. 4 and Eq. (2.58)] The phase-boundary fit κ̃B_III = -a m̃^2 + (8/π) m̃ with a = 0.54 is presented without an uncertainty or fit range; please state the fitting interval and the fit quality.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central results are direct simulations of an explicitly defined model, and the fitted coefficients are descriptive parameters rather than inputs that force the claimed conclusions.

full rationale

The paper's central claim is that the explicitly written model III, defined by Eq. (2.42), has B-dependent equations of motion and, when evolved numerically from random initial states, spontaneously forms chiral soliton lattices with edge and screw dislocations. This is a direct numerical investigation of a stated model, not a derivation in which a target result is fed back as an assumption. The phase-boundary fit a = 0.54 in Eq. (2.58) and the vortex-trajectory fit alpha = 0.027 are descriptive parameterizations of data produced by solving the model's own equations; they are not fitted inputs used to generate the dislocation dynamics. The diffusion term added in Eq. (3.14) is disclosed as a numerical regularization, and the 3D real-time results use epsilon = 0, while the double-helix relaxation study is clearly labeled as a relaxation with epsilon = 1 rather than as a real-time prediction. The paper does cite prior work by the same authors in the introduction and in motivating CSL physics, but those citations are contextual and not load-bearing: no uniqueness theorem or ansatz is imported from same-author work to forbid alternatives or to make the numerical outcomes definitional. Appendix A derives the anomaly-matched form of model II, and the paper explicitly distinguishes model III rather than claiming it follows from that derivation; the ad hoc character of model III is a validity or UV-completion concern, not a circularity. The final CSL configurations are also reported to be robust by comparing with a different initial state in Appendix C, further showing that the formation results are not constructed into the initial data. I therefore find no step in which a prediction reduces to its own input by construction.

Assumptions & free parameters 3 free parameters · 4 assumptions · 1 invented entities

The counts here show that the paper's central results rest on one new ad hoc interaction term with no independent evidence, plus standard background results and a uniform-field assumption. The only fitted numerical coefficients (a and α) are auxiliary fits to phase boundaries and trajectories, not inputs to the central formation claim.

free parameters (3)
  • a = 0.54
    Coefficient in the phase boundary fit κB_III = -a m̃^2 + (8/π)m̃, shown in Eq. (2.58) and Fig. 4. It is fitted to numerical data points for the boundary between homogeneous and solitonic ground states.
  • α (vortex acceleration) = 0.027
    Acceleration parameter in the relativistic particle fit y±(t) = ±(1/α)√(1+(αt)^2) to the vortex positions in Fig. 6. It is fitted to a single trajectory with κB = 0.3.
  • ε (diffusion coefficient) = 0.05 (2D dynamics), 1 (relaxation)
    Chosen by hand to suppress random noise in the 2D simulations (Eq. 3.14) and to drive convergence in the relaxation method for static solutions. The results depend on this value, which is not part of the physical equations of motion.
assumptions (4)
  • standard math The chiral soliton lattice ground state is described by the elliptic amplitude solution η(x3;k) = 2am(mx3/k, k) + π (Eq. 2.13).
    This is a known solution of the sine-Gordon model and is used throughout Sec. 2.1 to compute CSL properties.
  • domain assumption The external current S^μ is a uniform constant background S^μ = (0,0,0,B).
    Stated in Eq. (2.7) and used for all simulations; it reduces the problem to a single direction and breaks parity in the z-direction.
  • ad hoc to paper Model III with the modified topological term κ/v^2 j^μ S_μ is a valid low-energy effective theory for chiral magnets and QCD matter.
    The model is proposed in Sec. 2.3.1 (Eq. 2.42) to solve the dynamical issues of Models I and II, but no UV completion or microscopic derivation is provided. The physical relevance of this term is an assumption.
  • domain assumption The vortex-soliton composites in model III can be represented by the amplitude-phase decomposition φ = ρ e^{iη}, and the phase windings (vortices) are identified with dislocations in the CSL background.
    Used throughout Secs. 3 and 4 to interpret the numerical solutions; the identification relies on the order parameter manifold argument in Sec. 3.1.
invented entities (1)
  • Modified topological term κ/v^2 j^μ S_μ in Model III
    purpose: Makes the equations of motion depend on the external field S^μ, allowing the chiral soliton lattice to form dynamically rather than being determined only by static energy arguments.
    The term is introduced in Eq. (2.42) as a modification of the axion model (Model II). The paper does not derive this term from a known UV theory, and no independent experimental or theoretical evidence is given for its presence in chiral magnets or QCD.

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Pith. "Pith review of Dislocations and crystallization dynamics of chiral soliton lattices." pith.science (2026). https://pith.science/paper/GVDRHEW5

@misc{pith2026250616354,
  author       = {Pith},
  title        = {Pith review of: Dislocations and crystallization dynamics of chiral soliton lattices},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GVDRHEW5}},
  note         = {Machine review of arXiv:2506.16354}
}
read the original abstract

Dislocations, as topological defects in crystal lattices, are fundamental to understanding plasticity in materials. Similar periodic structures also arise in continuum field theories, such as chiral soliton lattices (CSLs), which appear in condensed matter systems like chiral magnets and in high-energy contexts such as quantum chromodynamics in strong magnetic field or under rapid rotation. This work investigates whether dislocations can dynamically form within such emergent CSLs. The chiral sine-Gordon model, reduced from the aforementioned examples by certain truncations, is useful to determine the ground state but it cannot describe time evolution, lacks dynamical formation or leads to singular dislocations, because its equations of motion do not contain a topological term. We propose a field-theoretical model including the topological term coupled to external fields resolving these issues by modifying the topological term so it affects the dynamics. Using numerical simulations, we study the real-time formation of CSLs in two and three spatial dimensions. In 2D, edge dislocations emerge spontaneously, guiding soliton growth and later annihilating to leave a stable CSL. In 3D, both edge and screw dislocations form; the latter exhibits helical structure influenced by the external field. We find stable double helical screw dislocations looking like a double helix staircase or DNA. We then demonstrate the formation of helical dislocations and analyze how the external field strength affects CSL density and formation speed. Our results provide a novel theoretical framework for understanding dislocations in solitonic structures, connecting high-energy field theory with materials science phenomena.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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Works this paper leans on

106 extracted references · 42 canonical work pages · cited by 1 Pith paper

  1. [1]

    Volterra, Sur l’equilibre des corps elastiques multiplement connexes , Annales Scientifiques de l’Ecole Normale Superieure 24 (1907) 401–517

    V. Volterra, Sur l’equilibre des corps elastiques multiplement connexes , Annales Scientifiques de l’Ecole Normale Superieure 24 (1907) 401–517

    1907

  2. [2]

    Orowan, Zur kristallplastizitat

    E. Orowan, Zur kristallplastizitat. iii , Zeitschrift fur Physik 89 (1934) 634–659

    1934

  3. [3]

    Polanyi, ¨Uber eine art gitterstorung, die einen kristall plastisch machen k¨ onnte , Zeitschrift fur Physik 89 (1934) 660–664

    M. Polanyi, ¨Uber eine art gitterstorung, die einen kristall plastisch machen k¨ onnte , Zeitschrift fur Physik 89 (1934) 660–664

    1934

  4. [4]

    G. I. Taylor, The mechanism of plastic deformation of crystals. part i. theoretical , Proceedings of the Royal Society of London A. 145 (1934) 362–87

    1934

  5. [5]

    Hull and D

    D. Hull and D. J. Bacon, Introduction to dislocations (4th ed.) . Butterworth-Heinemann, 2001

    2001

  6. [6]

    P. M. Anderson, Theory of dislocations. Hirth, John Price, 1930-, Lothe, Jens (Third ed.), 2017

    1930

  7. [7]

    Frenkel, On the theory of plastic deformation and twinning , J

    J. Frenkel, On the theory of plastic deformation and twinning , J. Phys. 1 (1939) 137

    1939

  8. [8]

    Peierls, The size of a dislocation , Proceedings of the Physical Society 52 (1940) 34

    R. Peierls, The size of a dislocation , Proceedings of the Physical Society 52 (1940) 34

    1940

Show all 106 references
  1. [9]

    Nabarro, Dislocations in a simple cubic lattice , Proceedings of the Physical Society 59 (1947) 256

    F. Nabarro, Dislocations in a simple cubic lattice , Proceedings of the Physical Society 59 (1947) 256

    1947

  2. [10]

    O. M. Braun and Y. S. Kivshar, Nonlinear dynamics of the frenkel-kontorova model , Physics Reports 306 (1998) . – 51 –

    1998

  3. [11]

    Braun and Y

    O. Braun and Y. Kivshar, The Frenkel-Kontorova Model. Concepts, Methods and Applications. Springer, Berlin, 2004

    2004

  4. [12]

    J. M. Kosterlitz and D. J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems , J. Phys. C 5 (1972) L124

    1972

  5. [13]

    J. M. Kosterlitz and D. J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems , J. Phys. C 6 (1973) 1181

    1973

  6. [14]

    B. I. Halperin and D. R. Nelson, Theory of two-dimensional melting , Phys. Rev. Lett. 41 (1978) 121

    1978

  7. [15]

    D. R. Nelson and B. I. Halperin, Dislocation-mediated melting in two dimensions , Phys. Rev. B 19 (1979) 2457

    1979

  8. [16]

    A. P. Young, Melting and the vector coulomb gas in two dimensions , Phys. Rev. B 19 (1979) 1855

    1979

  9. [17]

    Nelson, Defects and geometry in condensed matter physics

    D. Nelson, Defects and geometry in condensed matter physics . Cambridge University Press, 2002

    2002

  10. [18]

    V. L. Berezinsky, Destruction of long range order in one-dimensional and two-dimensional systems having a continuous symmetry group. I. Classical systems , Sov. Phys. JETP 32 (1971) 493

    1971

  11. [19]

    V. L. Berezinsky, Destruction of long range order in one-dimensional and two-dimensional systems having a continuous symmetry group. II. Quantum systems , Sov. Phys. JETP 34 (1972) 610

    1972

  12. [20]

    F. C. Frank and W. T. Read, Multiplication processes for slow moving dislocations , Phys. Rev. 79 (1950) 722

    1950

  13. [21]

    Helfrich, Defect model of the smectic a-nematic phase transition , J

    W. Helfrich, Defect model of the smectic a-nematic phase transition , J. Phys. France 39 (1978) 1199

    1978

  14. [22]

    D. R. Nelson and J. Toner, Bond-orientational order, dislocation loops, and melting of solids and smectic- a liquid crystals , Phys. Rev. B 24 (1981) 363

    1981

  15. [23]

    Moreau, L

    P. Moreau, L. Navailles, J. Giermanska-Kahn, O. Mondain-Monval, F. Nallet and D. Roux, Dislocation-loop-mediated smectic melting, Europhysics Letters 73 (2005) 49

    2005

  16. [24]

    Pieranski, M

    P. Pieranski, M. Zeghal, M. H. Godinho, P. Judeinstein, R. Bouffet-Klein, B. Liagre et al., Topological metadefects: Tangles of dislocations, Phys. Rev. Lett. 131 (2023) 128101

    2023

  17. [25]

    Pieranski and M

    P. Pieranski and M. H. Godinho, Unknots, knots, links and necklaces made of dislocations in cholesterics , Liquid Crystals 51 (2024) 2144 [https://doi.org/10.1080/02678292.2024.2374948]

    2024

  18. [26]

    R. D. Kamien and R. A. Mosna, The topology of dislocations in smectic liquid crystals , New Journal of Physics 18 (2016) 053012

    2016

  19. [27]

    P. G. Severino, R. D. Kamien and B. Bode, Dislocations and fibrations: The topological structure of knotted smectic defects , 2024

    2024

  20. [28]

    Gromov and L

    A. Gromov and L. Radzihovsky, Colloquium: Fracton matter , Rev. Mod. Phys. 96 (2024) 011001 [2211.05130]

    2024 arXiv

  21. [29]

    Fulde and R

    P. Fulde and R. A. Ferrell, Superconductivity in a Strong Spin-Exchange Field , Phys. Rev. 135 (1964) A550. – 52 –

    1964

  22. [30]

    A. I. Larkin and Y. N. Ovchinnikov, Nonuniform state of superconductors , Zh. Eksp. Teor. Fiz. 47 (1964) 1136

    1964

  23. [31]

    Nitta, S

    M. Nitta, S. Sasaki and R. Yokokura, Spatially Modulated Vacua in a Lorentz-invariant Scalar Field Theory , Eur. Phys. J. C 78 (2018) 754 [ 1706.02938]

    2018 arXiv

  24. [32]

    Nitta, S

    M. Nitta, S. Sasaki and R. Yokokura, Supersymmetry Breaking in Spatially Modulated Vacua, Phys. Rev. D 96 (2017) 105022 [ 1706.05232]

    2017 arXiv

  25. [33]

    S. B. Gudnason, M. Nitta, S. Sasaki and R. Yokokura, Temporally, spatially, or lightlike modulated vacua in Lorentz invariant theories , Phys. Rev. D 99 (2019) 045011 [1810.11361]

    2019 arXiv

  26. [34]

    Bjarke Gudnason, M

    S. Bjarke Gudnason, M. Nitta, S. Sasaki and R. Yokokura, Supersymmetry breaking and ghost Goldstino in modulated vacua , Phys. Rev. D 99 (2019) 045012 [ 1812.09078]

    2019 arXiv

  27. [35]

    Machida and H

    K. Machida and H. Nakanishi, Superconductivity under a ferromagnetic molecular field , Phys. Rev. B 30 (1984) 122

    1984

  28. [36]

    Basar and G

    G. Basar and G. V. Dunne, Self-consistent crystalline condensate in chiral Gross-Neveu and Bogoliubov-de Gennes systems , Phys. Rev. Lett. 100 (2008) 200404 [ 0803.1501]

    2008 arXiv

  29. [37]

    Basar and G

    G. Basar and G. V. Dunne, A Twisted Kink Crystal in the Chiral Gross-Neveu model , Phys. Rev. D 78 (2008) 065022 [ 0806.2659]

    2008 arXiv

  30. [38]

    Casalbuoni and G

    R. Casalbuoni and G. Nardulli, Inhomogeneous superconductivity in condensed matter and QCD, Rev. Mod. Phys. 76 (2004) 263 [ hep-ph/0305069]

    2004 arXiv

  31. [39]

    Anglani, R

    R. Anglani, R. Casalbuoni, M. Ciminale, N. Ippolito, R. Gatto, M. Mannarelli et al., Crystalline color superconductors, Rev. Mod. Phys. 86 (2014) 509 [ 1302.4264]

    2014 arXiv

  32. [40]

    Togawa, T

    Y. Togawa, T. Koyama, K. Takayanagi, S. Mori, Y. Kousaka, J. Akimitsu et al., Chiral magnetic soliton lattice on a chiral helimagnet , Physical review letters 108 (2012) 107202

    2012

  33. [41]

    Togawa, Y

    Y. Togawa, Y. Kousaka, K. Inoue and J.-i. Kishine, Symmetry, structure, and dynamics of monoaxial chiral magnets , Journal of the Physical Society of Japan 85 (2016) 112001

    2016

  34. [42]

    Kishine and A

    J.-i. Kishine and A. S. Ovchinnikov, Chapter one - theory of monoaxial chiral helimagnet , vol. 66 of Solid State Physics , pp. 1–130, Academic Press, (2015), DOI

    2015

  35. [43]

    A. A. Tereshchenko, A. S. Ovchinnikov, I. Proskurin, E. V. Sinitsyn and J.-i. Kishine, Theory of magnetoelastic resonance in a monoaxial chiral helimagnet , Phys. Rev. B 97 (2018) 184303

    2018

  36. [44]

    Chovan, N

    J. Chovan, N. Papanicolaou and S. Komineas, Intermediate phase in the spiral antiferromagnet ba2cuge2o7, Phys. Rev. B 65 (2002) 064433

    2002

  37. [45]

    C. Ross, N. Sakai and M. Nitta, Exact ground states and domain walls in one dimensional chiral magnets, JHEP 12 (2021) 163 [ 2012.08800]

    2021 arXiv

  38. [46]

    Amari and M

    Y. Amari and M. Nitta, Chiral magnets from string theory , JHEP 11 (2023) 212 [2307.11113]

    2023 arXiv

  39. [47]

    Amari, C

    Y. Amari, C. Ross and M. Nitta, Domain-wall skyrmion chain and domain-wall bimerons in chiral magnets , Phys. Rev. B 109 (2024) 104426 [ 2311.05174]

    2024 arXiv

  40. [48]

    Amari and M

    Y. Amari and M. Nitta, Skyrmion crystal phase on a magnetic domain wall in chiral magnets, Phys. Rev. B 111 (2025) 134441 [ 2409.07943]. – 53 –

    2025 arXiv

  41. [49]

    Dzyaloshinskii, A Thermodynamic Theory of ‘Weak’ Ferromagnetism of Antiferromagnetics, J

    I. Dzyaloshinskii, A Thermodynamic Theory of ‘Weak’ Ferromagnetism of Antiferromagnetics, J. Phys. Chem. Solids 4 (1958) 241

    1958

  42. [50]

    Moriya, Anisotropic Superexchange Interaction and Weak Ferromagnetism , Phys

    T. Moriya, Anisotropic Superexchange Interaction and Weak Ferromagnetism , Phys. Rev. 120 (1960) 91

    1960

  43. [51]

    Chandrasekhar, Liquid Crystals (2nd ed.)

    S. Chandrasekhar, Liquid Crystals (2nd ed.) . Cambridge: Cambridge University Press, 1992

    1992

  44. [52]

    De Gennes, Calcul de la distorsion d’une structure cholesterique par un champ magnetique, Solid State Communications 6 (1968) 163

    P. De Gennes, Calcul de la distorsion d’une structure cholesterique par un champ magnetique, Solid State Communications 6 (1968) 163

    1968

  45. [53]

    D. T. Son and M. A. Stephanov, Axial anomaly and magnetism of nuclear and quark matter, Phys. Rev. D 77 (2008) 014021 [ 0710.1084]

    2008 arXiv

  46. [54]

    M. Eto, K. Hashimoto and T. Hatsuda, Ferromagnetic neutron stars: axial anomaly, dense neutron matter, and pionic wall , Phys. Rev. D 88 (2013) 081701 [ 1209.4814]

    2013 arXiv

  47. [55]

    Brauner and N

    T. Brauner and N. Yamamoto, Chiral Soliton Lattice and Charged Pion Condensation in Strong Magnetic Fields , JHEP 04 (2017) 132 [ 1609.05213]

    2017 arXiv

  48. [56]

    S. Chen, K. Fukushima and Z. Qiu, Skyrmions in a magnetic field and π0 domain wall formation in dense nuclear matter , Phys. Rev. D 105 (2022) L011502 [ 2104.11482]

    2022 arXiv

  49. [57]

    M. S. Grønli and T. Brauner, Competition of chiral soliton lattice and Abrikosov vortex lattice in QCD with isospin chemical potential , Eur. Phys. J. C 82 (2022) 354 [2201.07065]

    2022 arXiv

  50. [58]

    G. W. Evans and A. Schmitt, Chiral anomaly induces superconducting baryon crystal , JHEP 09 (2022) 192 [ 2206.01227]

    2022 arXiv

  51. [59]

    G. W. Evans and A. Schmitt, Chiral Soliton Lattice turns into 3D crystal , JHEP 2024 (2024) 041 [ 2311.03880]

    2024 arXiv

  52. [60]

    Qiu and M

    Z. Qiu and M. Nitta, Quasicrystals in QCD , JHEP 05 (2023) 170 [ 2304.05089]

    2023 arXiv

  53. [61]

    Huang, K

    X.-G. Huang, K. Nishimura and N. Yamamoto, Anomalous effects of dense matter under rotation, JHEP 02 (2018) 069 [ 1711.02190]

    2018 arXiv

  54. [62]

    Nishimura and N

    K. Nishimura and N. Yamamoto, Topological term, QCD anomaly, and the η ′ chiral soliton lattice in rotating baryonic matter , JHEP 07 (2020) 196 [ 2003.13945]

    2020 arXiv

  55. [63]

    M. Eto, K. Nishimura and M. Nitta, Phases of rotating baryonic matter: non-Abelian chiral soliton lattices, antiferro-isospin chains, and ferri/ferromagnetic magnetization , JHEP 08 (2022) 305 [ 2112.01381]

    2022 arXiv

  56. [64]

    M. Eto, K. Nishimura and M. Nitta, Non-Abelian chiral soliton lattice in rotating QCD matter: Nambu-Goldstone and excited modes , JHEP 03 (2024) 035 [ 2312.10927]

    2024 arXiv

  57. [65]

    D. T. Son and A. R. Zhitnitsky, Quantum anomalies in dense matter , Phys. Rev. D 70 (2004) 074018 [ hep-ph/0405216]

    2004 arXiv

  58. [66]

    Vilenkin, Macroscopic Parity Violating Effects: Neutrino Fluxes from Rotating Black Holes and in Rotating Thermal Radiation , Phys

    A. Vilenkin, Macroscopic Parity Violating Effects: Neutrino Fluxes from Rotating Black Holes and in Rotating Thermal Radiation , Phys. Rev. D 20 (1979) 1807

    1979

  59. [67]

    Vilenkin, Quamtum Field Theory at Finite Temperature in a Rotating System , Phys

    A. Vilenkin, Quamtum Field Theory at Finite Temperature in a Rotating System , Phys. Rev. D 21 (1980) 2260

    1980

  60. [68]

    D. T. Son and P. Surowka, Hydrodynamics with Triangle Anomalies , Phys. Rev. Lett. 103 (2009) 191601 [ 0906.5044]

    2009 arXiv

  61. [69]

    Brauner and S

    T. Brauner and S. V. Kadam, Anomalous low-temperature thermodynamics of QCD in strong magnetic fields , JHEP 11 (2017) 103 [ 1706.04514]. – 54 –

    2017 arXiv

  62. [70]

    Brauner and S

    T. Brauner and S. Kadam, Anomalous electrodynamics of neutral pion matter in strong magnetic fields , JHEP 03 (2017) 015 [ 1701.06793]

    2017 arXiv

  63. [71]

    Brauner, H

    T. Brauner, H. Koleˇ sov´ a and N. Yamamoto,Chiral soliton lattice phase in warm QCD , Phys. Lett. B 823 (2021) 136767 [ 2108.10044]

    2021 arXiv

  64. [72]

    Yamada and N

    A. Yamada and N. Yamamoto, Floquet vacuum engineering: Laser-driven chiral soliton lattice in the QCD vacuum , Phys. Rev. D 104 (2021) 054041 [ 2107.07074]

    2021 arXiv

  65. [73]

    Brauner, G

    T. Brauner, G. Filios and H. Koleˇ sov´ a,Chiral soliton lattice in QCD-like theories , JHEP 12 (2019) 029 [ 1905.11409]

    2019 arXiv

  66. [74]

    Brauner, G

    T. Brauner, G. Filios and H. Koleˇ sov´ a,Anomaly-Induced Inhomogeneous Phase in Quark Matter without the Sign Problem , Phys. Rev. Lett. 123 (2019) 012001 [ 1902.07522]

    2019 arXiv

  67. [75]

    Nitta and S

    M. Nitta and S. Sasaki, Solitonic ground state in supersymmetric theory in background , JHEP 10 (2024) 178 [ 2404.12066]

    2024 arXiv

  68. [76]

    M. Eto, K. Nishimura and M. Nitta, Domain-Wall Skyrmion Phase in Dense QCD at Strong Magnetic Fields Using Leading-Order Chiral Perturbation Theory , Phys. Rev. Lett. 134 (2025) 181902 [ 2304.02940]

    2025 arXiv

  69. [77]

    M. Eto, K. Nishimura and M. Nitta, Phase diagram of QCD matter with magnetic field: domain-wall Skyrmion chain in chiral soliton lattice , JHEP 12 (2023) 032 [ 2311.01112]

    2023 arXiv

  70. [78]

    Amari, M

    Y. Amari, M. Eto and M. Nitta, Domain-wall Skyrmion phase of QCD in magnetic field: gauge field dynamics , JHEP 05 (2025) 037 [ 2409.08841]

    2025 arXiv

  71. [79]

    Amari, M

    Y. Amari, M. Nitta and R. Yokokura, Spin statistics and surgeries of topological solitons in QCD matter in magnetic field , JHEP 02 (2025) 171 [ 2406.14419]

    2025 arXiv

  72. [80]

    Amari, M

    Y. Amari, M. Nitta and Z. Qiu, Phase Boundary of Nuclear Matter in Magnetic Field , 2504.08379

    arXiv

  73. [81]

    M. Eto, K. Nishimura and M. Nitta, Domain-wall Skyrmion phase in a rapidly rotating QCD matter , JHEP 03 (2024) 019 [ 2310.17511]

    2024 arXiv

  74. [82]

    Wang and S.-C

    Z. Wang and S.-C. Zhang, Chiral anomaly, charge density waves, and axion strings from weyl semimetals , Phys. Rev. B 87 (2013) 161107

    2013

  75. [83]

    Roy and J

    B. Roy and J. D. Sau, Magnetic catalysis and axionic charge-density-wave in Weyl semimetals, Phys. Rev. B 92 (2015) 125141 [ 1406.4501]

    2015 arXiv

  76. [84]

    Y. You, G. Y. Cho and T. L. Hughes, Response properties of axion insulators and weyl semimetals driven by screw dislocations and dynamical axion strings , Phys. Rev. B 94 (2016) 085102

    2016

  77. [85]

    Sehayek, M

    D. Sehayek, M. Thakurathi and A. A. Burkov, Charge density waves in weyl semimetals , Phys. Rev. B 102 (2020) 115159

    2020

  78. [86]

    Gooth, B

    J. Gooth, B. Bradlyn, S. Honnali, C. Schindler, N. Kumar, J. Noky et al., Axionic charge-density wave in the weyl semimetal (tase4)2i , Nature 575 (2019) 315–319

    2019

  79. [87]

    Schoenherr, J

    P. Schoenherr, J. M¨ uller and L. K¨ ohler et al.,Topological domain walls in helimagnets , Nature Phys 14 (2018) 465–468

    2018

  80. [88]

    Mukai and A

    N. Mukai and A. O. Leonov, Skyrmion and meron ordering in quasi-two-dimensional chiral magnets, Phys. Rev. B 106 (2022) 224428. – 55 –

    2022

  81. [89]

    Azhar, V

    M. Azhar, V. P. Kravchuk and M. Garst, Screw dislocations in chiral magnets , Phys. Rev. Lett. 128 (2022) 157204

    2022

  82. [90]

    I. I. Smalyukh, Review: knots and other new topological effects in liquid crystals and colloids, Rept. Prog. Phys. 83 (2020) 106601

    2020

  83. [91]

    P. G. Severino and R. D. Kamien, Escape from the second dimension: A topological distinction between edge and screw dislocations , Phys. Rev. E 109 (2024) L012701

    2024

  84. [92]

    R. D. Kamien and C. D. Santangelo, Smectic liquid crystals: Materials with one-dimensional, periodic order, Geometriae Dedicata 120 (2006) 229–240

    2006

  85. [93]

    D. F. Agterberg and H. Tsunetsugu, Dislocations and vortices in pair-density-wave superconductors, Nature Physics 4 (2008) 639–642

    2008

  86. [94]

    Shi and A

    A.-C. Shi and A. J. Berlinsky, Pinning and i-v characteristics of a two-dimensional defective flux-line lattice , Phys. Rev. Lett. 67 (1991) 1926

    1991

  87. [95]

    W¨ ordenweber and P

    R. W¨ ordenweber and P. H. Kes,Dimensional crossover in collective flux pinning , Phys. Rev. B 34 (1986) 494

    1986

  88. [96]

    E. H. Brandt, Range and strength of pins collectively interacting with the flux-line lattice in type-ii superconductors, Phys. Rev. Lett. 57 (1986) 1347

    1986

  89. [97]

    E. H. Brandt, Elastic and plastic properties of the flux-line lattice in type-ii superconductors, Phys. Rev. B 34 (1986) 6514

    1986

  90. [98]

    M. C. Marchetti and D. R. Nelson, Dislocation loops and bond-orientational order in the abrikosov flux-line lattice , Phys. Rev. B 41 (1990) 1910

    1990

  91. [99]

    M. J. W. Dodgson and M. A. Moore, Topological defects in the abrikosov lattice of vortices in type-ii superconductors, Phys. Rev. B 51 (1995) 11887

    1995

  92. [100]

    Shimizu and G.-W

    K. Shimizu and G.-W. Chern, Crystallization dynamics of magnetic skyrmions in a frustrated itinerant magnet, arXiv preprint arXiv:2305.16182 (2023)

    2023 arXiv

  93. [101]

    Eto and M

    M. Eto and M. Nitta, Quantum nucleation of topological solitons , JHEP 09 (2022) 077 [2207.00211]

    2022 arXiv

  94. [102]

    Higaki, K

    T. Higaki, K. Kamada and K. Nishimura, Formation of a chiral soliton lattice , Phys. Rev. D 106 (2022) 096022 [ 2207.00212]

    2022 arXiv

  95. [103]

    M. Eto, Y. Hamada and M. Nitta, Composite topological solitons consisting of domain walls, strings, and monopoles in O(N) models , JHEP 08 (2023) 150 [ 2304.14143]

    2023 arXiv

  96. [104]

    Vilenkin and E

    A. Vilenkin and E. P. S. Shellard, Cosmic Strings and Other Topological Defects . Cambridge University Press, 7, 2000

    2000

  97. [105]

    Yishi and Z

    D. Yishi and Z. Shengli, Topological structure of dislocation in the gauge field theory of dislocations and disclinations continuum , International Journal of Engineering Science 28 (1990) 689

    1990

  98. [106]

    A. J. Bray, Theory of phase-ordering kinetics , Advances in Physics 51 (2002) 481 [https://doi.org/10.1080/00018730110117433]. – 56 –

    2002 doi

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