pith. machine review for the scientific record. sign in

arxiv: 2605.11794 · v1 · submitted 2026-05-12 · ❄️ cond-mat.str-el · cond-mat.mes-hall

Recognition: 2 theorem links

· Lean Theorem

Exciton-roton mode in moir\'e fractional Chern insulators

Xiaoyang Shen , Zijian Zhou , Ruiping Guo , Renqi Wang , Wenhui Duan , Chong Wang , Yong Xu
Authors on Pith no claims yet

Pith reviewed 2026-05-13 05:15 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.mes-hall
keywords moiré fractional Chern insulatorexciton-roton modecollective excitationsoptical spectroscopytwisted MoTe2quantum geometryroton minimumfractional quantum Hall
0
0 comments X

The pith

In moiré fractional Chern insulators, hybridization between roton and interband modes creates an optically active exciton-roton excitation.

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

The paper argues that moiré fractional Chern insulators, which realize fractional quantum Hall physics without external magnetic fields, develop a new collective excitation through mixing of the magneto-roton with moiré interband transitions. This exciton-roton mode keeps the roton minimum in its momentum dependence yet gains the capacity to couple to light, producing a double-peak feature in optical spectra that is missing from ordinary continuum fractional quantum Hall systems. The authors demonstrate the effect using exact diagonalization and a variational Bethe-Salpeter approach on a twisted MoTe2 model, showing the mode stays below the interband energy scale. A sympathetic reader would care because the result points to optical spectroscopy as a practical window into the internal dynamics of these zero-field fractional states.

Core claim

Hybridization between the magneto-roton and moiré interband excitations gives rise to an exciton-roton mode absent in continuum FQH systems in the long-wavelength limit. Using exact diagonalization and a variational Bethe-Salpeter equation for twisted MoTe2, the hybridization is controlled by the quantum geometry and yields a mode that combines excitonic optical response with the characteristic FCI roton minimum. The resulting exciton-roton remains low-lying, with excitation energy below the interband transition, and acquires optical activity, leading to a double-peak spectroscopic signature.

What carries the argument

The exciton-roton mode formed by hybridization of the magneto-roton with moiré interband excitations, controlled by the quantum geometry of the moiré bands.

If this is right

  • The exciton-roton mode exhibits both a roton minimum and optical activity, producing a double-peak spectroscopic signature.
  • Optical spectroscopy serves as a direct probe of collective excitations in moiré fractional Chern insulators.
  • The hybrid mode lies below the interband transition energy and is absent from continuum fractional quantum Hall systems at long wavelengths.
  • The strength of the hybridization and resulting optical activity is set by the quantum geometry of the moiré bands.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar hybrid modes may appear in other moiré flat-band platforms that host fractional Chern insulator states at different fillings or twist angles.
  • Varying the moiré potential strength or band geometry could provide experimental control over the visibility of the roton feature in optics.
  • The optical activity of the mode offers a way to distinguish moiré fractional Chern insulators from continuum analogs without requiring transport or magnetic-field measurements.

Load-bearing premise

The quantum geometry of the moiré bands produces strong hybridization between the roton and interband excitations, and the exact diagonalization plus variational calculations on the twisted MoTe2 model faithfully represent the low-energy physics without dominant errors from finite size or approximations.

What would settle it

Measurement of the optical absorption or conductivity spectrum in twisted MoTe2 at fractional filling that either shows or fails to show a low-energy peak below the interband transition whose dispersion matches the calculated roton minimum.

Figures

Figures reproduced from arXiv: 2605.11794 by Chong Wang, Renqi Wang, Ruiping Guo, Wenhui Duan, Xiaoyang Shen, Yong Xu, Zijian Zhou.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Illustration of the interband transitions and intra [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a,b) The dispersion for the lowest interband transition [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a,b). The band structure and the optical re [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Lowest interband (blue/cyan symbols) and intraband (orange/red/pink symbols) dispersions from ED-BSE on the full [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Full many-body optical conductivity [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Many-body spectrum of the two-Landau-level FQH model on a [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
read the original abstract

Moir\'e fractional Chern insulators (FCIs) are a novel class of quantum matter that realizes fractional quantum Hall (FQH) physics in zero magnetic field and provides a platform for exploring unconventional collective excitations. Here we show that hybridization between the magneto-roton and moir\'e interband excitations gives rise to an exciton-roton mode absent in continuum FQH systems in the long-wavelength limit. Using exact diagonalization and a variational Bethe-Salpeter equation for twisted MoTe$_2$, we demonstrate that this hybridization is controlled by the quantum geometry and yields a mode that combines excitonic optical response with the characteristic FCI roton minimum. The resulting exciton-roton remains low-lying, with excitation energy below the interband transition, and acquires optical activity, leading to a double-peak spectroscopic signature. These results identify optical spectroscopy as a direct probe of collective excitations in moir\'e FCIs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that in moiré fractional Chern insulators realized in twisted MoTe2, hybridization between the magneto-roton and moiré interband excitations—controlled by quantum geometry—produces a novel low-lying exciton-roton mode. This mode combines excitonic optical activity with the FCI roton minimum, remains below the interband transition energy, and generates a double-peak spectroscopic signature absent in continuum FQH systems at long wavelength. The results are obtained via exact diagonalization of the microscopic model combined with a variational Bethe-Salpeter equation treatment of the excitations.

Significance. If the numerical evidence holds, the work identifies a distinctive collective mode unique to moiré FCIs that links quantum geometry, fractional topology, and optical response, offering a concrete spectroscopic fingerprint for roton physics in zero-field settings. The combination of ED and variational BSE provides direct microscopic support for the hybridization mechanism, which could inform experiments on twisted transition-metal dichalcogenides.

major comments (2)
  1. [numerical results from exact diagonalization and variational BSE] The central claim that the exciton-roton mode is low-lying, optically active, and produces a robust double-peak signature rests on ED and variational BSE calculations, yet the manuscript provides no finite-size scaling, system-size convergence data, or comparisons to DMRG. Given that moiré ED is restricted to small clusters (typically N_e ~ 8–12 on 4×4–6×6 lattices), finite-size effects can distort the roton minimum dispersion and the hybridization matrix elements with interband excitons, directly affecting the reported mode properties and its distinction from continuum FQH systems.
  2. [results and discussion of the exciton-roton mode] No error bars, statistical uncertainties, or sensitivity analysis to model parameters (twist angle, dielectric screening) are reported for the excitation energies or optical matrix elements. This is load-bearing because the hybridization strength, which is asserted to be controlled by quantum geometry, must be shown to survive variations in these parameters and finite-size artifacts to support the claim of a distinct spectroscopic signature.
minor comments (2)
  1. [abstract and methods] The abstract and introduction should explicitly state the specific twist angle, interaction parameters, and supercell sizes employed in the ED calculations to allow immediate assessment of the regime studied.
  2. [introduction and results] Notation for the magneto-roton, interband exciton, and hybridized exciton-roton modes should be introduced with a clear diagram or table early in the text to improve readability of the hybridization discussion.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their careful review and constructive comments on our numerical methodology. We address each major point below and outline the revisions we will implement.

read point-by-point responses

  1. Referee: [numerical results from exact diagonalization and variational BSE] The central claim that the exciton-roton mode is low-lying, optically active, and produces a robust double-peak signature rests on ED and variational BSE calculations, yet the manuscript provides no finite-size scaling, system-size convergence data, or comparisons to DMRG. Given that moiré ED is restricted to small clusters (typically N_e ~ 8–12 on 4×4–6×6 lattices), finite-size effects can distort the roton minimum dispersion and the hybridization matrix elements with interband excitons, directly affecting the reported mode properties and its distinction from continuum FQH systems.

    Authors: We agree that explicit finite-size scaling and DMRG comparisons would strengthen the manuscript. In the revised version we will add a supplementary figure showing the system-size dependence of the exciton-roton energy, roton minimum, and optical matrix elements across the accessible ED clusters (N_e = 8–12). This will demonstrate that the double-peak signature and hybridization persist within the sizes we can treat. Direct DMRG comparisons for the full model including interband excitations are not feasible at present, as they require substantial additional methodological development beyond the scope of this study; the variational BSE complements ED for the hybridized modes. revision: partial

  2. Referee: [results and discussion of the exciton-roton mode] No error bars, statistical uncertainties, or sensitivity analysis to model parameters (twist angle, dielectric screening) are reported for the excitation energies or optical matrix elements. This is load-bearing because the hybridization strength, which is asserted to be controlled by quantum geometry, must be shown to survive variations in these parameters and finite-size artifacts to support the claim of a distinct spectroscopic signature.

    Authors: We agree that parameter sensitivity is important for validating the robustness of the hybridization mechanism. In the revised manuscript we will add calculations varying the twist angle (within the FCI stability window) and dielectric screening strength, demonstrating that the low-lying exciton-roton mode and its double-peak optical signature remain intact. Because the results are obtained from deterministic exact diagonalization, statistical error bars do not apply; instead we will report the variation in excitation energies and matrix elements across the parameter ranges to quantify sensitivity and confirm the quantum-geometry control. revision: yes

standing simulated objections not resolved
  • Direct comparisons to DMRG for the full moiré model with interband excitations

Circularity Check

0 steps flagged

Low circularity: results from direct numerical solution of microscopic model

full rationale

The paper obtains the exciton-roton mode via exact diagonalization and variational Bethe-Salpeter equation on the twisted MoTe2 model. This is a direct computation from the microscopic Hamiltonian and quantum geometry of the moiré bands, not a reduction to fitted inputs or self-referential definitions. The hybridization with interband excitations and the resulting low-lying optically active mode with roton minimum are outputs of the numerics, compared against continuum FQH limits. No load-bearing self-citations, ansatzes smuggled via prior work, or uniqueness theorems imported from the same authors are required for the central claim. The derivation remains self-contained.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The central claim rests on a microscopic model of twisted MoTe2 whose parameters are not independently derived here, plus the assumption that quantum geometry dictates the hybridization strength and that the chosen numerical methods are faithful.

free parameters (1)
  • Moiré Hamiltonian parameters (twist angle, dielectric screening, etc.)
    The specific values used for the twisted MoTe2 band structure are chosen to match material properties and are not derived from first principles within the paper.
axioms (2)
  • domain assumption Quantum geometry of the moiré bands controls the hybridization between magneto-roton and interband excitations.
    Explicitly stated as the factor that yields the exciton-roton mode.
  • domain assumption Exact diagonalization on finite clusters plus variational Bethe-Salpeter equation accurately represent the thermodynamic-limit collective excitations.
    These methods are used to demonstrate the mode without reported convergence checks.
invented entities (1)
  • exciton-roton mode no independent evidence
    purpose: Hybrid collective excitation combining excitonic and roton character
    Postulated as the outcome of the hybridization; no independent experimental signature is provided beyond the calculated spectrum.

pith-pipeline@v0.9.0 · 5473 in / 1659 out tokens · 99090 ms · 2026-05-13T05:15:03.477385+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

74 extracted references · 74 canonical work pages · 2 internal anchors

  1. [1]

    anyon-trion

    for details. We focus on single-particle excitations, as many-body modes (e.g., gravitons) have been shown to be optically insensitive [19, 45]. Fig. 3(c) illustrates the evolution of the optical conduc- tivity. In the weak-mixing regime (e.g.,ϵ>∼ 10) shown in Fig. 3(a), the spectrum exhibits a single dominant peak (Peak 2) corresponding to the interband ...

    work page

  2. [2]

    J. Cai, E. Anderson, C. Wang, X. Zhang, X. Liu, W. Holtzmann, Y. Zhang, F. Fan, T. Taniguchi, K. Watanabe, Y. Ran, T. Cao, L. Fu, D. Xiao, W. Yao, and X. Xu, Signatures of fractional quantum anomalous hall states in twisted mote2, Nature622, 63 (2023)

    work page 2023

  3. [3]

    H. Park, J. Cai, E. Anderson, Y. Zhang, J. Zhu, X. Liu, C. Wang, W. Holtzmann, C. Hu, Z. Liu, T. Taniguchi, K. Watanabe, J.-H. Chu, T. Cao, L. Fu, W. Yao, C.-Z. Chang, D. Cobden, D. Xiao, and X. Xu, Observation of fractionally quantized anomalous hall effect, Nature622, 74 (2023)

    work page 2023

  4. [4]

    F. Xu, Z. Sun, T. Jia, C. Liu, C. Xu, C. Li, Y. Gu, K. Watanabe, T. Taniguchi, B. Tong, J. Jia, Z. Shi, S. Jiang, Y. Zhang, X. Liu, and T. Li, Observation of integer and fractional quantum anomalous hall effects in twisted bilayermote 2, Phys. Rev. X13, 031037 (2023)

    work page 2023

  5. [5]

    Z. Lu, T. Han, Y. Yao, A. P. Reddy, J. Yang, J. Seo, K. Watanabe, T. Taniguchi, L. Fu, and L. Ju, Fractional quantum anomalous hall effect in multilayer graphene, Nature626, 759 (2024)

    work page 2024

  6. [6]

    Y. Zeng, Z. Xia, K. Kang, J. Zhu, P. Knüppel, C. Vaswani, K. Watanabe, T. Taniguchi, K. F. Mak, and J. Shan, Thermodynamic evidence of fractional chern in- sulator in moiré mote2, Nature622, 69 (2023)

    work page 2023

  7. [7]

    H. Li, U. Kumar, K. Sun, and S.-Z. Lin, Spontaneous fractional Chern insulators in transition metal dichalco- genide moiré superlattices, Phys. Rev. Res.3, L032070 (2021)

    work page 2021

  8. [8]

    Devakul, V

    T. Devakul, V. Crépel, Y. Zhang, and L. Fu, Magic in twisted transition metal dichalcogenide bilayers, Nat. Commun.12, 6730 (2021)

    work page 2021

  9. [9]

    Abouelkomsan, Z

    A. Abouelkomsan, Z. Liu, and E. J. Bergholtz, Particle- hole duality, emergent fermi liquids, and fractional chern insulators in moiré flatbands, Phys. Rev. Lett.124, 106803 (2020)

    work page 2020

  10. [11]

    A. P. Reddy, F. Alsallom, Y. Zhang, T. Devakul, and L. Fu, Fractional quantum anomalous hall states in twisted bilayermote 2 andwse 2, Phys. Rev. B108, 085117 (2023)

    work page 2023

  11. [12]

    J. Yu, J. Herzog-Arbeitman, M. Wang, O. Vafek, B. A. Bernevig, and N. Regnault, Fractional chern insulators vs. non-magnetic states in twisted bilayer mote2 (2023), arXiv:2309.14429

    work page arXiv 2023

  12. [13]

    Regnault and B

    N. Regnault and B. A. Bernevig, Fractional chern insu- lator, Phys. Rev. X1, 021014 (2011). 6

    work page 2011

  13. [14]

    Y. Jia, J. Yu, J. Liu, J. Herzog-Arbeitman, Z. Qi, H. Pi, N. Regnault, H. Weng, B. A. Bernevig, and Q. Wu, Moiré fractional Chern insulators. I. First-principles calcula- tions and continuum models of twisted bilayer MoTe2, Phys. Rev. B109, 205121 (2024)

    work page 2024

  14. [15]

    Lu and L

    T. Lu and L. H. Santos, Fractional chern insulators in twisted bilayermote2: A composite fermion perspective, Phys. Rev. Lett.133, 186602 (2024)

    work page 2024

  15. [16]

    Wang, X.-W

    C. Wang, X.-W. Zhang, X. Liu, Y. He, X. Xu, Y. Ran, T.Cao,andD.Xiao,Fractionalcherninsulatorintwisted bilayermote 2, Phys. Rev. Lett.132, 036501 (2024)

    work page 2024

  16. [17]

    Morales-Durán, N

    N. Morales-Durán, N. Wei, J. Shi, and A. H. MacDonald, Magic angles and fractional chern insulators in twisted homobilayer transition metal dichalcogenides, Phys. Rev. Lett.132, 096602 (2024)

    work page 2024

  17. [18]

    Repellin, T

    C. Repellin, T. Neupert, Z. Papić, and N. Regnault, Single-mode approximation for fractional chern insula- tors and the fractional quantum hall effect on the torus, Phys. Rev. B90(2014)

    work page 2014

  18. [19]

    X. Hu, D. Xiao, and Y. Ran, Hyperdeterminants and composite fermion states in fractional chern insulators, Phys. Rev. B109, 245125 (2024)

    work page 2024

  19. [20]

    X. Shen, C. Wang, X. Hu, R. Guo, H. Yao, C. Wang, W. Duan, and Y. Xu, Magnetorotons in moiré fractional chern insulators, Phys. Rev. B113, L081403 (2026)

    work page 2026

  20. [21]

    B. M. Kousa, N. Morales-Durán, T. M. R. Wolf, E. Kha- laf, and A. H. MacDonald, Theory of magnetoroton bands in moiré materials (2025), arXiv:2502.17574

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  21. [22]

    N. Paul, A. Abouelkomsan, A. Reddy, and L. Fu, Shin- ing light on collective modes in moiré fractional chern insulators, arXiv:2502.17569

    work page arXiv

  22. [23]

    S. M. Girvin, A. H. MacDonald, and P. M. Platzman, Magneto-rotontheoryofcollectiveexcitationsinthefrac- tional quantum hall effect, Phys. Rev. B33, 2481 (1986)

    work page 1986

  23. [24]

    T. M. R. Wolf, Y.-C. Chao, A. H. MacDonald, and J. J. Su, Intraband collective excitations in fractional chern insulators are dark (2024), arXiv:2406.10709

    work page arXiv 2024

  24. [25]

    F. D. M. Haldane, Geometrical description of the frac- tional quantum hall effect, Phys. Rev. Lett.107, 116801 (2011)

    work page 2011

  25. [26]

    Sodemann and A

    I. Sodemann and A. H. MacDonald, Landau level mixing and the fractional quantum hall effect, Phys. Rev. B87, 245425 (2013)

    work page 2013

  26. [27]

    Pakrouski, M

    K. Pakrouski, M. R. Peterson, T. Jolicoeur, V. W. Scarola, C. Nayak, and M. Troyer, Phase diagram of the ν= 5/2fractional quantum hall effect: Effects of landau- level mixing and nonzero width, Phys. Rev. X5, 021004 (2015)

    work page 2015

  27. [28]

    N. Wei, G. Xu, I. S. Villadiego, and C. Huang, Landau- level mixing andsu(4)symmetry breaking in graphene, Phys. Rev. Lett.134, 046501 (2025)

    work page 2025

  28. [29]

    Mostaan, N

    N. Mostaan, N. Goldman, A. m. c. İmamoğlu, and F. Grusdt, Anyon-trions in atomically thin semiconduc- tor heterostructures, PRX Quantum7, 010325 (2026)

    work page 2026

  29. [30]

    G. Xu, N. Wei, I. S. Villadiego, and C. Huang, Localized excitons and landau-level mixing in time-reversal sym- metric pairs of chern bands (2025), arXiv:2509.18438

    work page arXiv 2025

  30. [31]

    Kohn, Cyclotron resonance and de haas-van alphen oscillations of an interacting electron gas, Phys

    W. Kohn, Cyclotron resonance and de haas-van alphen oscillations of an interacting electron gas, Phys. Rev. 123, 1242 (1961)

    work page 1961

  31. [32]

    H. C. A. Oji and A. H. MacDonald, Magnetoplasma modes of the two-dimensional electron gas at nonintegral filling factors, Phys. Rev. B33, 3810 (1986)

    work page 1986

  32. [33]

    A.H.MacDonald, H.C.A.Oji,andS.M.Girvin,Magne- toplasmon excitations from partially filled landau levels in two dimensions, Phys. Rev. Lett.55, 2208 (1985)

    work page 1985

  33. [34]

    T. Wang, T. Devakul, M. P. Zaletel, and L. Fu, Diverse magnetic orders and quantum anomalous hall effect in twistedbilayermote2andwse2(2024),arXiv:2306.02501

    work page arXiv 2024

  34. [35]

    W.-X. Qiu, B. Li, X.-J. Luo, and F. Wu, Interaction- driven topological phase diagram of twisted bilayer mote2, Phys. Rev. X13, 041026 (2023)

    work page 2023

  35. [36]

    F. Liu, F. Xu, C. Xu, J. Li, Z. Sun, J. Xiao, N. Mao, X. Chang, X. Tao, K. Watanabe, T. Taniguchi, J. Jia, R. Zhong, Z. Shi, S. Wang, G. Chen, X. Liu, D. Qian, Y. Zhang, T. Li, and S. Jiang, From fractional chern insulators to topological electronic crystals in moiré mote2: quantum geometry tuning via remote layer, arXiv:2512.03622

    work page arXiv

  36. [37]

    J. Yu, J. Herzog-Arbeitman, M. Wang, O. Vafek, B. A. Bernevig, and N. Regnault, Fractional chern insulators versusnonmagneticstatesintwistedbilayermote 2,Phys. Rev. B109, 045147 (2024)

    work page 2024

  37. [38]

    Qiu and F

    W.-X. Qiu and F. Wu, Quantum geometry probed by chi- ral excitonic optical response of chern insulators (2024), arXiv:2407.03317

    work page arXiv 2024

  38. [39]

    F. Wu, T. Lovorn, E. Tutuc, I. Martin, and A. H. MacDonald, Topological insulators in twisted transition metaldichalcogenidehomobilayers,Phys.Rev.Lett.122, 086402 (2019)

    work page 2019

  39. [40]

    Abouelkomsan, A

    A. Abouelkomsan, A. P. Reddy, L. Fu, and E. J. Bergholtz, Band mixing in the quantum anomalous hall regime of twisted semiconductor bilayers, Phys. Rev. B 109, L121107 (2024)

    work page 2024

  40. [41]

    J. Yu, J. Herzog-Arbeitman, Y. H. Kwan, N. Regnault, and B. A. Bernevig, Moiré fractional chern insulators. iv. fluctuation-driven collapse in multiband exact diago- nalization calculations on rhombohedral graphene, Phys. Rev. B112, 075110 (2025)

    work page 2025

  41. [42]

    See Supplemental Material at [link] for details

    work page

  42. [43]

    Wang, J.Cano, A

    J. Wang, J.Cano, A. J. Millis, Z. Liu,and B. Yang, Exact landau level description of geometry and interaction in a flatband, Phys. Rev. Lett.127, 246403 (2021)

    work page 2021

  43. [44]

    Mera and T

    B. Mera and T. Ozawa, Engineering geometricly flat chern bands with fubini-study kähler structure, Phys. Rev. B104(2021)

    work page 2021

  44. [45]

    Roy, Band geometry of fractional topological insula- tors, Phys

    R. Roy, Band geometry of fractional topological insula- tors, Phys. Rev. B90, 165139 (2014)

    work page 2014

  45. [46]

    F. D. M. Haldane, Self-duality and long-wavelength be- havior of the landau-level guiding-center structure func- tion, and the shear modulus of fractional quantum hall fluids (2011), arXiv:1112.0990

    work page arXiv 2011

  46. [47]

    S.-F. Liou, F. D. M. Haldane, K. Yang, and E. H. Rezayi, Chiral gravitons in fractional quantum hall liquids, Phys. Rev. Lett.123, 146801 (2019)

    work page 2019

  47. [48]

    H. B. Xavier, Z. Bacciconi, T. Chanda, D. T. Son, and M. Dalmonte, Chiral graviton modes on the lattice, Phys. Rev. Lett.135, 196501 (2025)

    work page 2025

  48. [49]

    M. Long, H. Lu, H.-Q. Wu, and Z. Y. Meng, Spectra of magnetoroton and chiral graviton modes of fractional chern insulator (2025), arXiv:2501.00247

    work page arXiv 2025

  49. [50]

    Note that hybridization of the long-wavelength graviton mode with cavity photons via spatially-varying external fields has been recently studied in continuum FQH sys- tems [?]. That mechanism operates in the spin-2 sector and requires external symmetry-breaking, distinct from the spin-1 particle-hole hybridization driven by Coulomb interaction considered here. 7

    work page

  50. [51]

    J. Shi, N. Morales-Durán, E. Khalaf, and A. H. MacDon- ald, Adiabatic approximation and aharonov-casher bands in twisted homobilayer transition metal dichalcogenides, Phys. Rev. B110, 035130 (2024)

    work page 2024

  51. [52]

    F. D. M. Haldane, Many-particle translational symme- tries of two-dimensional electrons at rational landau-level filling, Phys. Rev. Lett.55, 2095 (1985)

    work page 2095

  52. [53]

    B. M. Kousa, N. Morales-Durán, T. M. R. Wolf, E. Kha- laf, and A. H. MacDonald, Theory of magnetoroton bands in moiré materials, Phys. Rev. Lett.135, 246604 (2025)

    work page 2025

  53. [54]

    P. U. Jepsen, D. G. Cooke, and M. Koch, Terahertz spec- troscopy and imaging–modern techniques and applica- tions, Laser & Photonics Reviews5, 124 (2011)

    work page 2011

  54. [55]

    Morales-Durán, J

    N. Morales-Durán, J. Wang, G. R. Schleder, M. Angeli, Z. Zhu, E. Kaxiras, C. Repellin, and J. Cano, Pressure- enhanced fractional chern insulators along a magic line in moiré transition metal dichalcogenides, Phys. Rev. Res. 5, L032022 (2023)

    work page 2023

  55. [56]

    T. Tan, A. P. Reddy, L. Fu, and T. Devakul, Design- ing topology and fractionalization in narrow gap semi- conductor films via electrostatic engineering, Phys. Rev. Lett.133, 206601 (2024)

    work page 2024

  56. [57]

    Z. Zhan, Y. Li, and P. A. Pantaleón, Designing band structures by patterned dielectric superlattices, Phys. Rev. B111, 045148 (2025)

    work page 2025

  57. [58]

    Ault-McCoy, M

    D. Ault-McCoy, M. N. Y. Lhachemi, A. Dunbrack, S. A. A. Ghorashi, and J. Cano, Optimizing superlattice bilayer graphene for a fractional chern insulator, Phys. Rev. B113, 075140 (2026)

    work page 2026

  58. [59]

    X. Shen, C. Wang, R. Guo, Z. Xu, W. Duan, and Y. Xu, Stabilizing fractional chern insulators via exchange inter- action in moiré systems (2024), arXiv:2405.12294

    work page arXiv 2024

  59. [60]

    H. Pan, S. Yang, Y. Wang, X. Cai, W. Wang, Y. Zhao, K. Watanabe, T. Taniguchi, L. Zhang, Y. Liu, B. Yang, and W. Gao, Optical signatures of−1 3 fractional quan- tum anomalous hall state in twistedmote2, Phys. Rev. Lett.136, 056601 (2026)

    work page 2026

  60. [61]

    W. Li, C. W. Beach, C. Hu, T. Taniguchi, K. Watan- abe, J.-H. Chu, A. Imamoğlu, T. Cao, D. Xiao, and X. Xu, Signatures of fractional charges via anyon–trions in twisted MoTe2, Nature651, 48 (2026)

    work page 2026

  61. [62]

    Wagner and T

    G. Wagner and T. Neupert, Sensing the binding and unbinding of anyons at impurities, Phys. Rev. Res.8, 013263 (2026)

    work page 2026

  62. [63]

    Wójs and J

    A. Wójs and J. J. Quinn, Energy spectra of fractional quantum hall systems in the presence of a valence hole, Phys. Rev. B63, 045303 (2000)

    work page 2000

  63. [64]

    Exciton-Anyon Binding in Fractional Chern Insulators: Spectral Fingerprints

    T. Lu and L. H. Santos, Exciton-anyon binding in fractional chern insulators: Spectral fingerprints, arXiv:2601.14365

    work page internal anchor Pith review Pith/arXiv arXiv

  64. [65]

    N. J. Zhang, R. Q. Nguyen, N. Batra, X. Liu, K. Watan- abe, T. Taniguchi, D. E. Feldman, and J. I. A. Li, Ex- citons in the fractional quantum hall effect, Nature637, 327–332 (2025)

    work page 2025

  65. [66]

    H. B. Xavier, Z. Bacciconi, T. Chanda, D. T. Son, and M. Dalmonte, Chiral gravitons on the lattice (2025), arXiv:2505.02905

    work page arXiv 2025

  66. [67]

    Xie and A

    M. Xie and A. H. MacDonald, Electrical reservoirs for bilayer excitons, Phys. Rev. Lett.121, 067702 (2018)

    work page 2018

  67. [68]

    Y. H. Kwan, Y. Hu, S. H. Simon, and S. A. Parameswaran, Excitonic fractional quantum hall hierar- chy in moiré heterostructures, Phys. Rev. B105, 235121 (2022)

    work page 2022

  68. [69]

    K. Tran, G. Moody, F. Wu, X. Lu, J. Choi, K. Kim, A. Rai, D. A. Sanchez, J. Quan, A. Singh, J. Emb- ley, A. Zepeda, M. Campbell, T. Autry, T. Taniguchi, K. Watanabe, N. Lu, S. K. Banerjee, K. L. Silverman, S. Kim, E. Tutuc, L. Yang, A. H. MacDonald, and X. Li, Evidence for moiré excitons in van der waals heterostruc- tures, Nature567, 71–75 (2019)

    work page 2019

  69. [70]

    C. Wang, X. Shen, R. Guo, W. Duan, C. Wang, and Y. Xu, Fractional chern insulators in moiré flat bands with high chern numbers, Phys. Rev. B112, L201109 (2025)

    work page 2025

  70. [71]

    Z. Liu, E. J. Bergholtz, H. Fan, and A. M. Läuchli, Fractional chern insulators in topological flat bands with higher chern number, Phys. Rev. Lett.109, 186805 (2012)

    work page 2012

  71. [72]

    Wang, X.-W

    C. Wang, X.-W. Zhang, X. Liu, J. Wang, T. Cao, and D. Xiao, Higher landau-level analogs and signatures of non-abelian states in twisted bilayermote2, Phys. Rev. Lett.134, 076503 (2025)

    work page 2025

  72. [73]

    H. Liu, Z. Liu, and E. J. Bergholtz, Non-abelian frac- tional chern insulators and competing states in flat moiré bands, Phys. Rev. Lett.135, 106604 (2025)

    work page 2025

  73. [74]

    A. P. Reddy, N. Paul, A. Abouelkomsan, and L. Fu, Non- abelian fractionalization in topological minibands, Phys. Rev. Lett.133, 166503 (2024)

    work page 2024

  74. [75]

    1st Excitation

    C. Xu, N. Mao, T. Zeng, and Y. Zhang, Multiple chern bands in twistedmote2 and possible non-abelian states, Phys. Rev. Lett.134, 066601 (2025). 8 Supplemental Materials CONTENTS References 5 Continuum Model and interaction 8 Numerical details and finite-size effects of the exact diagonalization 8 Optical conductivity in many-body system 9 Effective Two-Le...

    work page 2025