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Emblems of pair density waves: dual identity of topological defects and their transport signatures

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper argues that resistive switching in rhombohedral tetralayer graphene's SC1 state is driven by mobile topological defects of a pure pair density wave, each defect being at once a one-third vortex and a crystal dislocation.

desk verdict A credible, clearly-written mechanism proposal for the SC1 telegraph noise, built on a pure-PDW premise that is imported rather than established; the transport predictions are genuinely testable and the paper deserves peer review. read the letter →

arxiv 2506.08087 v1 pith:KTL3MS6Y submitted 2025-06-09 cond-mat.supr-con cond-mat.mes-hallcond-mat.str-el

Omri Lesser , Chunli Huang , James P. Sethna , Eun-Ah Kim This is my paper
classification cond-mat.supr-concond-mat.mes-hallcond-mat.str-el
keywords pairdensitywavefractionalvortextopologicaldefectsrhombohedraltetralayergrapheneresistiveswitchingBardeen-Stephenresistance5-7dislocationlineon
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 argues that the intermittent resistive switching seen in the SC1 superconducting state of rhombohedral tetralayer graphene is the transport signature of mobile topological defects in a pure pair density wave (PDW): a superconducting state in which Cooper pairs carry net momentum, so the pairing amplitude forms a periodic pattern instead of being uniform, arising naturally when a quarter-metal normal state (only one of four spin-valley flavors occupied) pairs within a single valley. In the three-component PDW expected there, each elementary defect has a dual identity: it winds the superconducting phase by a third of a turn, carrying fractional flux $\Phi_0/3 = h/6e$, and it simultaneously distorts the emergent triangular lattice into a 5-7 dislocation (a pair of sites with five and seven neighbors) with a Burgers vector. The crystalline facet lets charge disorder nucleate defect-antidefect pairs with no applied field, the vortex facet lets the bias current pull the pair apart, and the resulting stream of moving fractional vortices generates resistance through the standard Bardeen-Stephen mechanism, matching the abrupt resistive plateaus seen in the experiment. The same dual identity yields two sharp predictions: the resistive state should be strongly anisotropic and should exhibit a Hall angle $R_{xy}/R_{xx} = \cot\theta$ set by the angle between the current and the Burgers vector, while an out-of-plane field near 8 mT should block the defect stream and restore zero resistance. If confirmed, this would be the first clean experimental window into pure PDW physics and the first condensed-matter realization of lineon-like restricted motion.

What carries the argument

The central object is the topological defect of the three-component PDW: a composite excitation in which a $2\pi$ winding of one order-parameter component carries fractional flux $\Phi_0/3 = h/6e$ while the same winding deforms the emergent triangular lattice of pair-amplitude maxima into a 5-7 dislocation with Burgers vector $\mathbf b$. Its dual identity does all the work in the argument: the crystalline facet lets charge disorder nucleate defect pairs at zero field, the vortex facet lets the current drive them apart, and both facets together make field-induced vortices into roadblocks that stop the motion. The stability of these fractional vortices as textures of the PDW free energy is established in the Supplemental Material through a Ginzburg-Landau treatment cast as a nonlinear-$\sigma$ model, solved numerically for the order-parameter profiles.

What would settle it

Rotate the bias current in-plane while holding the sample fixed in the SC1 state and measure the longitudinal and transverse voltages: the theory predicts strong resistance anisotropy between perpendicular current directions and a Hall angle $R_{xy}/R_{xx} = \cot\theta$ that follows the angle between current and Burgers vector. Seeing nearly isotropic resistance with no angle-dependent Hall signal, or seeing the telegraph noise persist at perpendicular fields well above the estimated 8 mT blocking threshold, would rule out the mobile-defect mechanism. The paper's own blocking estimate at the observed threshold is only p about 0.1 and it deliberately declines to predict plateau heights or durations, so the directional signatures, not the plateau values or the field cutoff alone, are where the claim must stand or fall.

Watch

Extended reading notes

Core claim

Starting from a $\mathrm{C}_3$-symmetric three-component PDW order parameter $\Delta(\mathbf r) = \sum_{j=1}^3 \Delta_{q_j} e^{i(2K+q_j)\cdot \mathbf r}$, the paper establishes that winding the phase of only one component by $2\pi$ creates the elementary topological defect: a fractional vortex of vorticity $\frac{1}{3}(h/2e)$ that is at the same time a 5-7 dislocation of the triangular lattice formed by the pair-amplitude maxima. Because the defect's crystalline facet couples to charge disorder, an impurity can act as a continuous source of defect-antidefect pairs at zero magnetic field; because its vortex facet couples to the current, the two partners are driven in opposite directions and their motion produces a Bardeen-Stephen voltage that can sustain the resistive plateaus observed experimentally. The paper argues the same dual identity fixes the decisive observable consequences: the 5-7 dislocation glides easily but climbs only with difficulty, giving strongly anisotropic resistance; a current at angle $\theta$ to the Burgers vector produces a Hall angle $R_{xy}/R_{xx} = \cot\theta$; and full vortices introduced by a perpendicular field around 8 mT act as vacant sites that block the glide path, cutting off the defect stream and restoring zero resistance.

Load-bearing premise

The entire mechanism depends on the SC1 state actually being a pure pair density wave, a superconductor with no uniform component and with three equal-strength modulation directions; if it is an ordinary superconductor, a PDW mixed with a uniform component, or a PDW with broken $\mathrm{C}_3$ symmetry, the predicted transport signatures and the switching explanation do not follow.

Editorial extensions

If this is right

  • The resistive plateaus in the SC1 state can be explained without any uniform superconducting component: a fluctuating impurity source emitting topological defect pairs, with the defect stream sustaining a steady Bardeen-Stephen voltage, reproduces the abrupt appearance and disappearance of resistance.
  • Transport should be strongly direction-dependent: driving current along the easy (glide) direction versus the hard (climb) direction of the 5-7 dislocations should give markedly different resistances.
  • With current at angle $\theta = \pm 60^\circ$ to the Burgers vector, a transverse voltage should appear with Hall angle $R_{xy}/R_{xx} = \cot\theta$, giving a quantitative fingerprint of the defects' crystalline identity.
  • An out-of-plane magnetic field should kill the switching near 8 mT, where the roughly 108 field-induced vortices in the sample create enough vacancies to block the preferred defect path and restore zero resistance.
  • If these signatures are confirmed, rhombohedral tetralayer graphene would be the first genuine condensed-matter realization of lineon dynamics, with excitations whose motion is confined to a lower-dimensional subspace.

Reading between the lines

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

  • The cleanest test the paper leaves implicit is angular sweeping: rotating the in-plane current direction relative to the crystal axes should trace out the full $\cot\theta$ curve, whereas competing explanations for telegraph noise would give a different angular dependence, so a dedicated measurement of this curve would discriminate sharply between the mechanisms.
  • If the three PDW components are not exactly equal in amplitude, the elementary defect vorticity would shift from $\Phi_0/3$ toward other fractions, so the magnitude of the resistance steps and the blocking-field threshold could serve as a diagnostic of the PDW's internal symmetry rather than assuming it.
  • The paper notes that bound states inside the $1/3$ vortices remain largely unexplored; scanning tunneling spectroscopy across a pinned defect could reveal the subgap spectrum of a fractional vortex, giving a microscopic check independent of transport.
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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 proposes that the resistive telegraph noise observed in the SC1 superconducting state of rhombohedral tetralayer graphene is produced by mobile topological defects of a pure three-component pair density wave (PDW). Each defect is argued to be simultaneously a 1/3 vortex (fractional vorticity h/6e) and a 5-7 crystalline dislocation. Charge impurities are proposed as zero-field sources of such defect pairs, the bias current drives them via the Lorentz force, and their Bardeen-Stephen motion produces resistance with extreme anisotropy and a Hall angle set by the angle between the current and the Burgers vector. A perpendicular magnetic field is argued to block the motion by introducing vacancies in the emergent PDW lattice. The manuscript includes a Ginzburg-Landau/nonlinear-sigma-model analysis of fractional vortices in the supplemental material and uses experimental parameters from Ref. [1] for numerical estimates.

Significance. If correct, the paper would provide a concrete transport signature of a pure PDW without a uniform superconducting component, a state that has been difficult to realize and detect. The dual vortex-dislocation identification is conceptually appealing and leads to falsifiable predictions: strong transport anisotropy, a Hall angle Rxy/Rxx = cot(theta), and field-induced restoration of zero resistance. The authors are also commendably explicit about the quantities they cannot predict (effective viscosity, core size, plateau values, plateau duration). The main impact, however, is conditional on a load-bearing assumption — that SC1 is indeed a pure, equal-amplitude three-component PDW — and the supplemental stability analysis of the fractional vortex needs to be made rigorous. The paper ships no numerical data or code despite invoking a numerical solution for the vortex profile.

major comments (4)
  1. [Main text, Eq. (1) and following paragraph] The entire mechanism rests on the assumption that SC1 is a pure three-component PDW with no uniform pairing component: Eq. (1) contains only the three modulational components, and the text states that 'pure PDW, without a uniform component, is natural [14]'. This is an inference from the quarter-metal parent state, not an established property of SC1. If even a subdominant uniform pairing component is present, the fundamental topological excitations are conventional h/2e vortices, fractional vortices become confined by domain walls or strings, and the disorder-sourcing, telegraph-noise, and transport predictions do not follow. The manuscript should either provide experimental evidence or a concrete test for the pure-PDW premise, or explicitly reframe the paper as a conditional mechanism analysis and discuss how the conclusions are modified by a small uniform component.
  2. [Supplemental Material, SI, Eqs. (S19)-(S22)] The variational problem intended to establish the stability of the 1/3 vortex is not well posed. Substituting r = r0 e^t into Eq. (S19) gives Eq. (S20), whose integrand contains the term -e^{2t} cos^2(alpha) [sin^2(alpha) + (N-2)/(2(N-1))]. At the boundary condition alpha(infinity) = arcsin(1/sqrt(N)) from Eq. (S22), the bracket is positive, so the integral diverges to -infinity with the stated choice r0^2 = -kappa_bar/gamma_bar, or to +infinity if the sign is reversed. The uniform-PDW background free energy, which would remove this area divergence, is not subtracted. The claimed numerical solution is also not shown. As written, the SI does not demonstrate that a finite-energy fractional vortex exists; this is a load-bearing point for the paper's central claim.
  3. [Main text, field-blocking paragraph and SI Eq. (S23)] The quantitative estimate for the field-blocking threshold contains two inconsistencies. First, Eq. (S23) writes Nv = [Phi0/(B_perp Lx Ly)], which evaluates to roughly 0.01 for B_perp = 8 mT, Lx = 9.6 micrometers, and Ly = 2.9 micrometers; the correct relation is Nv = B_perp Lx Ly / Phi0, which gives about 108. Second, using the stated Nv = 108, a = 60 nm, and Lx = 9.6 micrometers in p = 1 - (1 - a/Lx)^{Nv} gives p approximately 0.49, not p = 0.1 as quoted in the main text. The blocking probability estimate should be recomputed and the equations made consistent.
  4. [Main text, Fig. 3 and paragraph following 'Having identified...'] The zero-field source of TD-antiTD pairs at charge impurities is the key ingredient for the telegraph-noise explanation, but no microscopic calculation or estimate is provided for how a charge impurity nucleates a 5-7 dislocation pair in the PDW lattice, nor for the nucleation rate or the proposed on/off switching by 'random thermal events' that reconfigure impurities. The statement that 'defects of the same topological charge logarithmically repel each other' does not explain why an oppositely charged TD and antiTD must travel a distance d before a new pair is generated; the steady-state spacing d remains a free parameter. The switching mechanism therefore rests on an assumed source behavior rather than a derived one.
minor comments (5)
  1. [Main text, sentence after Fig. 1] The phrase 'withina valley' is missing a space, and the sentence 'pure PDW, without a uniform component, is natural [14]' should be explicitly labeled as an assumption in the abstract or introduction, since it is central to the validity of the mechanism.
  2. [Supplemental Material, SI Eq. (S2)] The Ginzburg-Landau free energy in Eq. (S2) does not include the electromagnetic vector potential or inter-component Josephson-like couplings; as a result, the fractional flux quantum Phi0/3 is asserted rather than derived from the supercurrents of the coupled components. Please state the assumptions and provide the derivation.
  3. [Main text, Hall-angle paragraph] The prediction Rxy/Rxx = cot(theta) is stated without a derivation. Because this is one of the paper's main falsifiable signatures, a short derivation with the sign convention for theta and for the Hall angle should be included.
  4. [Supplemental Material, SI stability discussion] The text says the Euler-Lagrange equation 'can be solved numerically, yielding the order parameter profiles' but no profile plot, numerical method, or code is provided. The numerical evidence for stability should be presented or the claim softened.
  5. [Main text, Fig. 2 caption] The caption uses 'TD's' where 'TDs' is intended; similar apostrophe errors appear elsewhere. Please proofread the text.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation: transport predictions follow from the TD/dislocation geometry, and the observed switching threshold is used as a consistency check rather than a fitted output.

full rationale

The central derivation is not circular. The resistive-switching mechanism assumes, from external theory [14], that SC1 is a pure three-component PDW; this is an explicitly conditional premise (the abstract says 'suspected'), not a conclusion derived from the switching data. The Bardeen-Stephen resistance calculation is standard and is used only to estimate velocities; the paper explicitly declines to predict the plateau resistance values. The anisotropy and Hall-angle predictions (Rxy/Rxx = cot theta) follow from the geometric relation between the current and the Burgers vector once the 1/3-vortex/5-7-dislocation duality is accepted; no switching data enter. The field-blocking estimate p=0.1 uses the measured B_perp = 8 mT threshold, a, and Lx as inputs and asks whether blockage is plausible, so the threshold is not produced by the model; this is a post-hoc consistency check, not a fitted prediction. The only self-citation, Ref. [39] (Chung, Bluhm, Kim), is used as an analogy for half-quantum vortices in spin-triplet superconductors and carries no load in the derivation. The equal-amplitude C3 assumption in Eq. (1) and in the Supplemental Material before Eq. (S4) is stated as an assumption, not smuggled in through a citation. Overall, no claim reduces by construction to its input.

Assumptions & free parameters 3 free parameters · 8 assumptions · 0 invented entities

The central claim rests on the identification of SC1 as a pure, C3-symmetric three-component PDW, a GL energy functional borrowed from prior work, and the applicability of Bardeen-Stephen dynamics and dislocation glide to the fractional defects. Three parameters are left unconstrained by the theory (viscosity prefactor alpha, TD viscosity eta_eff, and source separation d), which is why the paper can explain the existence of resistive plateaus but not their magnitude or duration. No new microscopic entities are introduced.

free parameters (3)
  • TD effective viscosity eta_eff = unknown; assumed within ~10^3 of the standard vortex value
    The paper explicitly cannot calculate eta_eff because the defect core is not fully normal and the core radius is unknown (main text and SII.F). All quantitative resistance and timescale estimates inherit this uncertainty.
  • Viscosity prefactor alpha = 1 (chosen)
    In the Bardeen-Stephen estimate eta = alpha * Phi0^2 / (xi^2 * R_N), the text says alpha ~ O(1) is debatable, and the velocity estimate in SII.E effectively sets alpha = 1.
  • Source separation d = unknown; bounded by d > a > xi
    The steady-state number of moving defects is N_defects = L_y / d, and hence the plateau resistance magnitude depends on d, which is not measured or predicted (SII.F).
assumptions (8)
  • domain assumption The SC1 state in rhombohedral tetralayer graphene is a pure PDW with no uniform superconducting component.
    Inherited from cited theory [14]; the entire mechanism is conditional on this. The paper states 'pure PDW, without a uniform component, is natural [14]' in the introduction.
  • domain assumption The PDW modulation vectors q1, q2, q3 are incommensurate with the lattice, giving U(1) x U(1) x U(1) symmetry.
    Used in Eq. (1) and the paragraph immediately after; underpins the existence of fractional vortices that wind only one component.
  • domain assumption C3 symmetry is preserved in the uniform PDW, so the three order parameter components have equal amplitude away from defects.
    Stated in the SI before Eq. (S4): 'the assumption that the PDW state itself does not break the C3 symmetry.' This justifies the symmetric boundary conditions for the fractional vortex.
  • domain assumption The Ginzburg-Landau free energy (Eq. S2) captures the low-energy physics of the three-component PDW.
    Adopted from Ref. [47] without microscopic derivation; standard phenomenological modeling for PDWs.
  • domain assumption Bardeen-Stephen viscous vortex dynamics applies to fractional vortices carrying flux Phi0/3.
    Used in SII.A-C to derive force balance, terminal velocity, and resistance; no microscopic justification is given for fractional vortices moving through a PDW background.
  • domain assumption A field-induced vortex suppresses the pair amplitude at its core and creates a vacancy that blocks TD motion.
    Assumed in the section 'The effect of external magnetic field' and in footnote [46]; underlies the prediction that B_perp restores zero resistance.
  • ad hoc to paper Charge impurities can act as Frank-Read-like sources of TD-antiTD pairs at zero field.
    The paper argues by analogy to Frank-Read sources [32] and supercooled vapor nucleation, but offers no microscopic model or rate calculation for this source process.
  • ad hoc to paper Random thermal events can reconfigure impurities to turn the defect source on and off.
    Used to explain the abrupt onset and disappearance of resistive plateaus; no detailed mechanism or timescale is given.

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Cite this review

Pith. "Pith review of Emblems of pair density waves: dual identity of topological defects and their transport signatures." pith.science (2026). https://pith.science/paper/KTL3MS6Y

@misc{pith2026250608087,
  author       = {Pith},
  title        = {Pith review of: Emblems of pair density waves: dual identity of topological defects and their transport signatures},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KTL3MS6Y}},
  note         = {Machine review of arXiv:2506.08087}
}
abstract

The pair density wave (PDW) exemplifies intertwined orders in strongly correlated systems. A recent discovery of superconductivity in a quarter-metal state offers the first experimental system where a pure PDW without uniform superconductivity is suspected, offering a unique opportunity to examine the consequences of intertwined orders. A pure two-dimensional PDW supports an unusual fractional excitation as its topological defect (TD). A TD simultaneously winds the phase of the Cooper pair and distorts the amplitude modulation -- a dual role reflecting its intertwined character. As a vortex, a TD carries fractional vorticity of $\frac{1}{3} h/2e$, whose movement would cause resistance. As a crystalline defect, a TD can be sourced by charge disorder in the system. We show that experimentally observed resistive switching can originate from mobile TDs, while a small magnetic field will restore zero resistance by blocking their motion. The resulting resistive state exhibits extreme anisotropy and a Hall response, with the Hall angle determined by the angle between the current and the TD's Burgers vector. These features will serve as confirmation of the dual identity of topological defects as emblems of PDW order.

Figures

Figures reproduced from arXiv: 2506.08087 by the authors.

Figure 1
Figure 1. FIG. 1. (a) The Brillouin zone of (multilayer) graphene. In [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The PDW and its TDs. The colorscale indicates the [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The motion of defects in the pair density wave background and its associated resistance. (a)–(b) A weak spot [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The effect of an external magnetic field [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

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Reference graph

Works this paper leans on

48 extracted references · 33 canonical work pages · cited by 1 Pith paper

  1. [1]

    T. Han, Z. Lu, Z. Hadjri, L. Shi, Z. Wu, W. Xu, Y. Yao, A. A. Cotten, O. S. Sedeh, H. Weldeyesus, J. Yang, J. Seo, S. Ye, M. Zhou, H. Liu, G. Shi, Z. Hua, K. Watan- abe, T. Taniguchi, P. Xiong, D. M. Zumb¨ uhl, L. Fu, and L. Ju, Nature , 1 (2025)

    work page 2025

  2. [14]

    Han and S

    Z. Han and S. A. Kivelson, Physical Review B105, L100509 (2022)

    work page 2022

  3. [2]

    E. Berg, E. Fradkin, and S. A. Kivelson, Nature Physics 5, 830 (2009)

    2009

  4. [3]

    S. D. Edkins, A. Kostin, K. Fujita, A. P. Mackenzie, H. Eisaki, S. Uchida, S. Sachdev, M. J. Lawler, E.-A. Kim, J. C. S´ eamus Davis, and M. H. Hamidian, Science 364, 976 (2019)

    work page 2019

  5. [4]

    Choubey, S

    P. Choubey, S. H. Joo, K. Fujita, Z. Du, S. D. Edkins, M. H. Hamidian, H. Eisaki, S. Uchida, A. P. Mackenzie, J. Lee, J. C. S. Davis, and P. J. Hirschfeld, Proceedings of the National Academy of Sciences117, 14805 (2020)

    work page 2020

  6. [5]

    S. Wang, P. Choubey, Y. X. Chong, W. Chen, W. Ren, H. Eisaki, S. Uchida, P. J. Hirschfeld, and J. C. S. Davis, Nature Communications12, 6087 (2021)

    work page 2021

  7. [6]

    Dai, Y.-H

    Z. Dai, Y.-H. Zhang, T. Senthil, and P. A. Lee, Physical Review B97, 174511 (2018)

    work page 2018

  8. [7]

    Q. Gu, J. P. Carroll, S. Wang, S. Ran, C. Broyles, H. Sid- diquee, N. P. Butch, S. R. Saha, J. Paglione, J. C. S. Davis, and X. Liu, Nature618, 921 (2023)

    2023

Show all 48 references
  1. [8]

    Aishwarya, J

    A. Aishwarya, J. May-Mann, A. Almoalem, S. Ran, S. R. Saha, J. Paglione, N. P. Butch, E. Fradkin, and V. Mad- havan, Nature Physics20, 964 (2024)

    2024

  2. [9]

    H. Li, G. Fabbris, A. H. Said, J. P. Sun, Y.-X. Jiang, J.- X. Yin, Y.-Y. Pai, S. Yoon, A. R. Lupini, C. S. Nelson, Q. W. Yin, C. S. Gong, Z. J. Tu, H. C. Lei, J.-G. Cheng, M. Z. Hasan, Z. Wang, B. Yan, R. Thomale, H. N. Lee, and H. Miao, Nature Communications13, 6348 (2022)

    2022

  3. [10]

    H. Deng, H. Qin, G. Liu, T. Yang, R. Fu, Z. Zhang, X. Wu, Z. Wang, Y. Shi, J. Liu, H. Liu, X.-Y. Yan, W. Song, X. Xu, Y. Zhao, M. Yi, G. Xu, H. Hohmann, S. C. Holbæk, M. D¨ urrnagel, S. Zhou, G. Chang, Y. Yao, Q. Wang, Z. Guguchia, T. Neupert, R. Thomale, M. H. Fischer, and J....

    2024

  4. [11]

    Y.-M. Wu, R. Thomale, and S. Raghu, Physical Review B108, L081117 (2023)

    2023

  5. [12]

    Schwemmer, H

    T. Schwemmer, H. Hohmann, M. D¨ urrnagel, J. Potten, J. Beyer, S. Rachel, Y.-M. Wu, S. Raghu, T. M¨ uller, W. Hanke, and R. Thomale, Physical Review B110, 024501 (2024)

    2024

  6. [13]

    M. Yao, Y. Wang, D. Wang, J.-X. Yin, and Q.-H. Wang, Physical Review B111, 094505 (2025)

    2025

  7. [15]

    Y.-Z. Chou, J. Zhu, and S. Das Sarma, Physical Review B111, 174523 (2025)

    2025

  8. [16]

    Qin and C

    Q. Qin and C. Wu, Chiral finite-momentum su- perconductivity in the tetralayer graphene (2024), arXiv:2412.07145 [cond-mat]

    2024 arXiv

  9. [17]

    Yang and Y.-H

    H. Yang and Y.-H. Zhang, Topological incommen- surate Fulde-Ferrell-Larkin-Ovchinnikov superconductor and Bogoliubov Fermi surface in rhombohedral tetra- layer graphen (2024), arXiv:2411.02503

    2024 arXiv

  10. [18]

    Geier, M

    M. Geier, M. Davydova, and L. Fu, Chiral and topo- logical superconductivity in isospin polarized multilayer graphene (2024), arXiv:2409.13829 [cond-mat]

    2024 arXiv

  11. [19]

    M. Kim, A. Timmel, L. Ju, and X.-G. Wen, Physical Review B111, 014508 (2025)

    2025

  12. [20]

    C. Yoon, T. Xu, Y. Barlas, and F. Zhang, Quarter Metal Superconductivity (2025), arXiv:2502.17555 [cond-mat]

    2025

  13. [21]

    Parra-Martinez, A

    G. Parra-Martinez, A. Jimeno-Pozo, V. T. Phong, H. Sainz-Cruz, D. Kaplan, P. Emanuel, Y. Oreg, P. A. Pantaleon, J. A. Silva-Guillen, and F. Guinea, Band Renormalization, Quarter Metals, and Chiral Supercon- ductivity in Rhombohedral Tetralayer Graphene (2025), arXiv:2502.19474...

    2025

  14. [22]

    Daido, Y

    A. Daido, Y. Yanase, and K. T. Law, Current-induced Zero Resistance in Trigonal Fulde-Ferrell Superconduc- tors (2025), arXiv:2503.16923 [cond-mat]

    2025

  15. [23]

    Gil and E

    A. Gil and E. Berg, Charge and pair density waves in a spin and valley-polarized system at a Van-Hove singular- ity (2025), arXiv:2504.19321 [cond-mat]

    2025 arXiv

  16. [24]

    Christos, P

    M. Christos, P. M. Bonetti, and M. S. Scheurer, Finite- momentum pairing and superlattice superconductivity in valley-imbalanced rhombohedral graphene (2025), arXiv:2503.15471 [cond-mat]

    2025

  17. [25]

    Jahin and S.-Z

    A. Jahin and S.-Z. Lin, Spontaneous vortex lattice due to orbital magnetization in valley polarized superconductors (2025), arXiv:2505.22915 [cond-mat]

    2025 arXiv

  18. [26]

    K. S. Ralls, D. C. Ralph, and R. A. Buhrman, Physical Review B40, 11561 (1989)

    1989

  19. [27]

    J. M. Kosterlitz and D. J. Thouless, Journal of Physics C: Solid State Physics6, 1181 (1973)

    1973

  20. [28]

    J. V. Jos,40 Years of Berezinskii-Kosterlitz-Thouless Theory(World Scientific, 2013)

    2013

  21. [29]

    D. R. Nelson, Physical Review B18, 2318 (1978)

    1978

  22. [30]

    D. R. Nelson and B. I. Halperin, Physical Review B19, 2457 (1979)

    1979

  23. [31]

    Hayashi, Physica B: Condensed Matter324, 82 (2002)

    M. Hayashi, Physica B: Condensed Matter324, 82 (2002)

    2002

  24. [32]

    F. C. Frank and W. T. Read, Physical Review79, 722 (1950)

    1950

  25. [33]

    Nicolas, E

    A. Nicolas, E. E. Ferrero, K. Martens, and J.-L. Barrat, Reviews of Modern Physics90, 045006 (2018)

    2018

  26. [34]

    Baggioli, I

    M. Baggioli, I. Kriuchevskyi, T. W. Sirk, and A. Zaccone, Physical Review Letters127, 015501 (2021)

    2021

  27. [35]

    Z. W. Wu, Y. Chen, W.-H. Wang, W. Kob, and L. Xu, Nature Communications14, 2955 (2023)

    2023

  28. [36]

    D. F. Agterberg, M. Geracie, and H. Tsunetsugu, Phys- ical Review B84, 014513 (2011)

    2011

  29. [37]

    Gaggioli, D

    F. Gaggioli, D. Guerci, and L. Fu, Spontaneous vortex- antivortex lattice and Majorana fermions in rhombohe- dral graphene (2025), arXiv:2503.16384 [cond-mat]

    2025

  30. [38]

    D. F. Agterberg and H. Tsunetsugu, Nature Physics4, 639 (2008)

    2008

  31. [39]

    S. B. Chung, H. Bluhm, and E.-A. Kim, Physical Review Letters99, 197002 (2007)

    2007

  32. [40]

    A. P. Young, Physical Review B19, 1855 (1979)

    1979

  33. [41]

    Pretko and L

    M. Pretko and L. Radzihovsky, Physical Review Letters 120, 195301 (2018)

    2018

  34. [42]

    Radzihovsky and M

    L. Radzihovsky and M. Hermele, Physical Review Letters 124, 050402 (2020)

    2020

  35. [43]

    Gromov and L

    A. Gromov and L. Radzihovsky, Reviews of Modern Physics96, 011001 (2024)

    2024

  36. [44]

    M. J. Stephen and J. Bardeen, Physical Review Letters 6 14, 112 (1965)

    1965

  37. [45]

    A. J. Stone and D. J. Wales, Chemical Physics Letters 128, 501 (1986)

    1986

  38. [46]

    A vortex landing at locations away from the emergent lattice site will suppress more lattice sites, albeit more weakly

  39. [47]

    Rosales and E

    M. Rosales and E. Fradkin, Physical Review B110, 214508 (2024)

    2024

  40. [48]

    Tinkham,Introduction to Superconductivity, 2nd ed., International Series in Pure and Applied Physics (McGraw-Hill, New York, 1996)

    M. Tinkham,Introduction to Superconductivity, 2nd ed., International Series in Pure and Applied Physics (McGraw-Hill, New York, 1996). 7 Supplemental Material SI. FRACTIONAL VOR TICES IN A MUL TI-COMPONENT PDW Here we establish the existence of fractional vortices in the case ...

    1996

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