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Exciton Alchemy: Chern Excitons from Trivial Bands

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Pith's one-line read This paper constructs a 2D model with topologically trivial electron bands whose lowest exciton band carries Chern number +1, showing interactions alone can generate exciton topology.

desk verdict A concrete, well-checked existence proof for Chern excitons from trivial bands, with a truncation caveat that is real but not disqualifying. read the letter →

arxiv 2608.07372 v1 pith:5JEUXKJK submitted 2026-08-07 cond-mat.mes-hall cond-mat.str-el

Yoonseok Hwang , Henry Davenport , Frank Schindler This is my paper · ORCID
classification cond-mat.mes-hallcond-mat.str-el
keywords Chernexcitontopologyinteraction-inducedinversionsymmetryWilsonloopenvelopewavefunctionreal-spacebasistrivialbands
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

Excitons are bound electron-hole pairs, and their topology is usually inherited from the topology of the underlying electron bands. This paper asks whether interactions alone can create a topological exciton when both participating bands are ordinary insulators, and answers yes by explicit construction. The authors build a two-dimensional inversion-symmetric model whose conduction and valence bands are topologically trivial, then show that the lowest exciton band carries Chern number $C_{\mathrm{exc}}=+1$, diagnosed by inversion eigenvalues, Wilson-loop winding, and chiral edge states in a ribbon. The topology lives in the exciton envelope wave function—the way the electron-hole separation is distributed—rather than in the bands. If correct, this is a microscopic existence proof and a recipe for engineering interaction-induced topological excitons.

What carries the argument

The load-bearing object is the projected exciton Hamiltonian $H_{\Delta,\Delta'}(\mathbf{p})$ in the real-space relative-distance basis $|\Delta,\mathbf{p}\rangle$, truncated to the five shortest electron-hole separations $\Delta\in\{0,\pm\hat{x},\pm\hat{y}\}$. Here $\Delta$ is the lattice vector separating the electron and hole and $\mathbf{p}$ is the total exciton momentum, so the eigenvectors $\phi_{n,\Delta}(\mathbf{p})$ are the exciton envelope wave functions. This finite-dimensional Hamiltonian reduces the exciton-topology question to a conventional band-topology problem on the envelope space, with inversion represented by $I=1_{1\times1}\oplus\sigma_x\oplus\sigma_x$; inversion eigenvalues at the four high-symmetry points then diagnose the Chern number modulo two. The second essential piece is the emergent spinless time-reversal symmetry: any projected Hamiltonian built from real hoppings and density-density interactions obeys $H_{\Delta,\Delta'}(\mathbf{p})=(H_{\Delta,\Delta'}(-\mathbf{p}))^*$, which protects nodal points and must be broken by the specifically designed complex interaction $V'$ to expose the Chern topology.

What would settle it

Enlarge the relative-coordinate cutoff from $|\Delta_x|,|\Delta_y|\le 10$ to systematically larger values and recompute the Wilson-loop winding of the lowest exciton band; if the winding ever departs from $C_{\mathrm{exc}}=+1$, or the bulk gap closes against the exciton continuum before the infinite-basis limit, the topological claim fails.

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Extended reading notes

Core claim

The paper's central discovery is that a gapped Chern exciton band can be manufactured from two topologically trivial bands through carefully chosen interactions. Starting from the atomic-limit Hamiltonian $H_0=-t_0\sum_{\mathbf{R}}(c_{\mathbf{R},A}^\dagger c_{\mathbf{R},B}+\mathrm{h.c.})$ on a two-sublattice lattice, the valence and conduction Wannier states are the even and odd sublattice combinations, with zero Chern number. Writing the projected exciton Hamiltonian in the relative-distance basis $\Delta\in\{0,\pm\hat{x},\pm\hat{y}\}$, the authors add repulsive density-density interactions $U_0,U_x,U_y$, then a symmetry-allowed interaction $V_x$ that induces a band inversion between the envelope states $\Phi_0$ and $\Phi_{-x}$ at the $M$ point. Because the projected Hamiltonian inherits a spinless time-reversal symmetry from ordinary hoppings and density-density terms, the inversion alone gives only nodal points; a further inversion-symmetric interaction $V'$ with a factor of $i$ breaks that emergent symmetry and opens a full gap. The resulting lowest exciton band has inversion eigenvalues $(+,+,+,-)$ at $\Gamma,X,Y,M$, giving $C_{\mathrm{exc}}=+1$; Wilson loops give $C_{\mathrm{exc}}=+1$ and $-1$ for the two lowest bands, and a ribbon calculation shows chiral edge states. The Chern number is carried entirely by the exciton envelope wave function, independent of the trivial electronic bands.

Load-bearing premise

The Chern number is computed after cutting the exciton's internal motion to the five shortest electron-hole separations, and the paper assumes this value survives when all larger separations are included.

Editorial extensions

If this is right

  • Interaction-induced Chern excitons are possible in principle: no topological parent bands are required, so trivial-band materials are not ruled out as hosts.
  • The inversion eigenvalues of the lowest exciton band, $(+,+,+,-)$, determine $C_{\mathrm{exc}}=+1$, while the second band carries $C_{\mathrm{exc}}=-1$, as confirmed by Wilson-loop winding.
  • Chiral exciton edge states traverse the bulk gap in a ribbon geometry, giving a concrete transport signature of the interaction-induced topology.
  • Any projected exciton Hamiltonian built from real hoppings and density-density interactions inherits spinless time-reversal symmetry, so achieving a Chern exciton requires an interaction term outside that class.
  • The construction recipe—atomic limit, inversion-guided band inversion, and breaking the emergent symmetry—provides a general route for designing topological excitons in other lattice settings.

Reading between the lines

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

  • This suggests that materials with tightly bound excitons and tunable interactions—such as moiré heterostructures or coupled quantum wells—could be screened for chiral exciton edge modes even when their single-particle bands are trivial.
  • One testable extension is to interpret the five-state envelope Hamiltonian as an effective tight-binding model on the relative-coordinate lattice; the Chern number would then be tunable by engineering envelope hoppings and phases instead of the electron bands.
  • The emergent spinless time-reversal symmetry may be a general obstruction: in any exciton projection from real hoppings and density-density terms, a nonzero exciton Chern number requires some term that acts on the envelope and breaks this effective symmetry, which narrows the search for realistic microscopic mechanisms.
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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

2 major / 4 minor

Summary. The paper constructs an explicit two-dimensional lattice model in which the electron and hole bands are topologically trivial, yet the lowest exciton band carries Chern number C_exc = +1 and the second band C_exc = -1. The construction works in a real-space exciton basis parameterized by relative electron-hole displacement Δ, starting from the atomic limit of a two-sublattice insulator. A sequence of density-density interactions, a pair-hopping interaction, and weak hoppings induces a band inversion in the five-state subspace Δ ∈ {0, ±x̂, ±ŷ}. The paper proves an emergent spinless time-reversal symmetry of the projected Hamiltonian for all inversion-preserving hoppings and density-density interactions, and shows that a correlated interaction term is required to break this symmetry. The nontrivial topology is diagnosed by inversion eigenvalues and confirmed by Wilson-loop winding and chiral edge states in a ribbon. The paper also presents an oblique-lattice realization and a route to multiband generalizations.

Significance. The central claim—an explicit microscopic existence proof for interaction-induced Chern excitons in trivial electronic bands—is important and, if correct, would resolve a question left open by the authors' earlier classification work. The paper is technically strong in several respects: the projected Hamiltonian is derived explicitly in the Supplemental Material; the emergent time-reversal obstruction is proven for a broad class of terms; and the topology is checked by three independent probes (inversion eigenvalues, Wilson loops, edge states). The construction recipe is concrete and transferable. The main caveat is the basis truncation, which does not yet have a rigorous or quantitative justification.

major comments (2)
  1. [Main text, 'Inversion-guided exciton band inversion'; SM Sec. S2 A4] The five-state truncation Δ ∈ {0, ±x̂, ±ŷ} is load-bearing for the existence proof. The Chern number is computed for this truncated basis, and the enlarged 441×441 basis is used only to verify that the bulk gap above the lowest band is preserved; no convergence test is provided for the Wilson-loop winding itself. The Supplemental Material (Sec. S2 A4) states that the truncation is justified 'provided that the additional terms introduced beyond the atomic limit are sufficiently small not to close this energy separation,' but no quantitative bound is given for the parameters used in the main text. Since the central claim concerns the full projected exciton Hamiltonian, an unobserved distant-envelope state that inverts with the lowest band at larger |Δ| would change C_exc. I request either a convergence test of the Wilson-loop winding for a sequence of cutoffs (e.g., |Δ_x|,|Δ_y| ≤ 5, 10, 15, 20) or a rigorous decay bound on the low-energy envelope wave functions in Δ that guarantees the winding is unchanged.
  2. [Full model definition, SM Eq. (S27)] The paper's headline claim is that the conduction and valence bands are topologically trivial. Although the construction starts from the atomic limit, the subsequent addition of t_x and t_{x+y} hoppings changes the non-interacting electronic Hamiltonian; the paper never explicitly verifies that both bands remain Chern-trivial in the full model. A one-sentence argument using the reality of the hoppings and the resulting spinless time-reversal symmetry would suffice, but without it the claim of interaction-induced topology is not fully closed.
minor comments (4)
  1. [Eq. (2)] The identity blocks in Eq. (2) are written as '1 1×1' and '1 2×2'; consider using standard notation such as I_1 and I_2 to avoid confusion with the inversion operator I.
  2. [Fig. 2(d)] The ribbon calculation is described as using the same parameters as the bulk, but the parameters are not restated in the figure caption; please list them for completeness.
  3. [SM Sec. S4 B] The inversion eigenvalues of the lowest band are given as (-1,-1,-1,+1) in the SM and as (+,+,+,-) in the main text, with the difference attributed to an absorbed overall sign; this notation shift is confusing and should be flagged explicitly at first use in each context.
  4. [Introduction, Note added] The 'Note added' mentions a very recent independent work (Ref. [56]); a brief sentence describing the difference between the two constructions would help the reader position this work.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the Chern exciton is computed directly from the model via explicit Wilson loops, and the self-citations are scaffolding rather than load-bearing inputs.

full rationale

The central claim is an existence proof: a fully specified microscopic model with topologically trivial conduction and valence bands whose lowest projected exciton band has nonzero Chern number. The derivation is self-contained. The microscopic Hamiltonian is given explicitly (Eq. S27), each contribution to the projected exciton Hamiltonian is evaluated term by term in the Supplemental Material, and the topological invariant is obtained from an explicit Wilson-loop calculation (Eq. 6, Fig. 2c) in an enlarged 441x441 basis. The inversion-eigenvalue pattern is used as a guide and as a consistency check, but the Wilson loop does not assume that pattern; it is an independent computation of the Chern number. The self-citations (Refs. 43, 44, 48) provide the real-space exciton framework and the symmetry classification, but the load-bearing result, the nonzero Chern number, is established in this paper by direct calculation. Even if the cited classification were set aside, the Wilson-loop winding and the chiral edge states in Fig. 2(c,d) remain explicit outputs of the model. No parameter is fitted to external data; the parameters are chosen to realize a band inversion, and the Chern number is then computed, not imposed. The one genuine limitation is the truncation of relative displacements: the Supplemental Material justifies the five-state truncation only 'provided that the additional terms introduced beyond the atomic limit are sufficiently small not to close this energy separation,' and the paper checks the bulk gap in a 441x441 basis but does not rigorously prove that the Wilson-loop winding is unchanged in the infinite-Delta limit. This is a mathematical-completeness gap, not a circular reduction of the prediction to its inputs. Overall, the derivation is independent and only minor self-citation is present.

Assumptions & free parameters 8 free parameters · 4 assumptions · 0 invented entities

The central claim depends on a standard symmetry-topology toolkit, the authors' own exciton classification, and the faithfulness of a truncated relative-coordinate basis. All numerical parameters are hand-chosen for the construction; none are fit to external data.

free parameters (8)
  • U_0 = 0.125
    Density-density interaction setting the energy of the flat doublets; chosen with U_x, U_y to place Φ0 lowest.
  • U_x = 0.10
    Density-density interaction along x; contributes to Φ0 dispersion and doublet energies.
  • U_y = 0.06
    Density-density interaction along y; sets the ordering of the Φ±y doublet.
  • V_x = 0.07
    Symmetry-allowed correlated hopping that drives the band inversion between Φ0 and Φ−x at M.
  • t_x = 0.025
    Hopping added to reduce the accidental nodal ring to nodal points on the X-M line.
  • V' = 0.03
    Imaginary-amplitude correlated hopping that breaks the emergent spinless TRS and gaps the remaining nodal points.
  • t_{x+y} = 0.02
    Hopping added to enlarge the bulk gap.
  • U'_x = 0.015
    Density-density interaction added to enlarge the bulk gap.
assumptions (4)
  • standard math Inversion-eigenvalue formula for Chern number mod 2 in the absence of TRS (Fu-Kane and follow-ups).
    Used to diagnose C_exc=1 mod 2 from the parity of odd inversion eigenvalues at HSMs (main text, second section).
  • domain assumption Excitonic generalization of the inversion-eigenvalue formula to envelope wave functions (Ref. 48).
    Self-cited theorem that the inversion eigenvalues of the projected exciton envelope function diagnose the exciton Chern number mod 2; used throughout.
  • standard math Exponentially localized Wannier functions exist for the trivial conduction and valence bands (Refs. 51,52).
    Justifies the real-space exciton basis; standard result for trivial bands.
  • ad hoc to paper The five-relative-displacement truncation Δ∈{0,±x̂,±ŷ} captures the low-energy exciton subspace and preserves the topological invariant.
    Needed to write a 5×5 model; verified numerically with a 441×441 basis but not proven rigorously.

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Cite this review

Pith. "Pith review of Exciton Alchemy: Chern Excitons from Trivial Bands." pith.science (2026). https://pith.science/paper/5JEUXKJK

@misc{pith2026260807372,
  author       = {Pith},
  title        = {Pith review of: Exciton Alchemy: Chern Excitons from Trivial Bands},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5JEUXKJK}},
  note         = {Machine review of arXiv:2608.07372}
}
read the original abstract

Exciton topology is commonly inherited from the topology of the underlying electronic bands. Recent theoretical work, however, has shown that the exciton Chern number can in general receive an additional contribution from the topology of the exciton envelope wave function, allowing, in principle, interaction-induced topological excitons even when the constituent electronic bands are topologically trivial. Here, we provide an explicit realization of this case by constructing a two-dimensional exciton model with topologically trivial conduction and valence bands that nevertheless hosts a Chern exciton diagnosed by inversion symmetry. Starting from a real-space limit of exponentially localized Wannier states for the conduction and valence bands, we identify the essential ingredients responsible for the emergent exciton topology and formulate a simple construction recipe. Our work demonstrates that interactions alone can generate nontrivial exciton topology, independent of the topology of the underlying electronic bands, and establishes a general framework for designing interaction-induced topological excitons.

Figures

Figures reproduced from arXiv: 2608.07372 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Unit cell and hopping geometry of the model with [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Exciton band structure of the minimal 5 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

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Works this paper leans on

68 extracted references · 25 canonical work pages

  1. [1]

    M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Reviews of Modern Physics82, 3045 (2010)

    2010

  2. [2]

    Qi and S.-C

    X.-L. Qi and S.-C. Zhang, Topological insulators and superconductors, Reviews of Modern Physics83, 1057 (2011)

    2011

  3. [3]

    C.-K. Chiu, J. C. Teo, A. P. Schnyder, and S. Ryu, Classi- fication of topological quantum matter with symmetries, Reviews of Modern Physics88, 035005 (2016)

    2016

  4. [4]

    Shiozaki, M

    K. Shiozaki, M. Sato, and K. Gomi, Topology of non- symmorphic crystalline insulators and superconductors, Physical Review B93, 195413 (2016)

    2016

  5. [5]

    Shiozaki, M

    K. Shiozaki, M. Sato, and K. Gomi, Topological crys- talline materials: General formulation, module structure, and wallpaper groups, Physical Review B95, 235425 (2017)

    2017

  6. [6]

    Kruthoff, J

    J. Kruthoff, J. De Boer, J. Van Wezel, C. L. Kane, and R.-J. Slager, Topological classification of crystalline in- sulators through band structure combinatorics, Physical Review X7, 041069 (2017)

    2017

  7. [7]

    Z. Wang, A. Alexandradinata, R. J. Cava, and B. A. Bernevig, Hourglass fermions, Nature532, 189 (2016). 5

    work page 2016

  8. [8]

    Bradlyn, J

    B. Bradlyn, J. Cano, Z. Wang, M. Vergniory, C. Felser, R. J. Cava, and B. A. Bernevig, Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals, Science353, aaf5037 (2016)

    work page 2016

Show all 68 references
  1. [9]

    B. J. Wieder, B. Bradlyn, Z. Wang, J. Cano, Y. Kim, H.- S. D. Kim, A. M. Rappe, C. L. Kane, and B. A. Bernevig, Wallpaper fermions and the nonsymmorphic Dirac insu- lator, Science361, 246 (2018)

    2018

  2. [10]

    Hwang, Y

    Y. Hwang, Y. Qian, J. Kang, J. Lee, D. Ryu, H. C. Choi, and B.-J. Yang, Magnetic wallpaper Dirac fermions and topological magnetic Dirac insulators, npj Compu- tational Materials9, 65 (2023)

    2023

  3. [11]

    Fu and C

    L. Fu and C. L. Kane, Topological insulators with inver- sion symmetry, Physical Review B76, 045302 (2007)

    2007

  4. [12]

    T. L. Hughes, E. Prodan, and B. A. Bernevig, Inversion- symmetric topological insulators, Physical Review B83, 245132 (2011)

    2011

  5. [13]

    A. M. Turner, Y. Zhang, R. S. Mong, and A. Vishwanath, Quantized response and topology of magnetic insulators with inversion symmetry, Physical Review B85, 165120 (2012)

    2012

  6. [14]

    C. Fang, M. J. Gilbert, and B. A. Bernevig, Bulk topolog- ical invariants in noninteracting point group symmetric insulators, Physical Review B86, 115112 (2012)

    2012

  7. [15]

    Alexandradinata, X

    A. Alexandradinata, X. Dai, and B. A. Bernevig, Wilson- loop characterization of inversion-symmetric topological insulators, Physical Review B89, 155114 (2014)

    2014

  8. [16]

    Bradlyn, L

    B. Bradlyn, L. Elcoro, J. Cano, M. G. Vergniory, Z. Wang, C. Felser, M. I. Aroyo, and B. A. Bernevig, Topological quantum chemistry, Nature547, 298 (2017)

    2017

  9. [17]

    J. Cano, B. Bradlyn, Z. Wang, L. Elcoro, M. G. Vergniory, C. Felser, M. I. Aroyo, and B. A. Bernevig, Building blocks of topological quantum chemistry: El- ementary band representations, Physical Review B97, 035139 (2018)

    2018

  10. [18]

    Elcoro, B

    L. Elcoro, B. J. Wieder, Z. Song, Y. Xu, B. Bradlyn, and B. A. Bernevig, Magnetic topological quantum chemistry, Nature Communications12, 5965 (2021)

    2021

  11. [19]

    Hwang, V

    Y. Hwang, V. Gupta, F. Schindler, L. Elcoro, Z. Song, B. A. Bernevig, and B. Bradlyn, Stable real-space invari- ants and topology beyond symmetry indicators, Nature Communications 10.1038/s41467-026-74844-w (2026)

    2026 doi

  12. [20]

    Hwang, V

    Y. Hwang, V. Gupta, A. Morales-P´ erez, C. Devescovi, M. Garc´ ıa-D´ ıez, J. L. Ma˜ nes, M. G. Vergniory, A. Garc´ ıa- Etxarri, and B. Bradlyn, Building blocks of topologi- cal band theory for photonic crystals, arXiv preprint arXiv:2601.06293 (2026)

    2026

  13. [21]

    H. C. Po, A. Vishwanath, and H. Watanabe, Symmetry- based indicators of band topology in the 230 space groups, Nature Communications8, 50 (2017)

    2017

  14. [22]

    Watanabe, H

    H. Watanabe, H. C. Po, and A. Vishwanath, Structure and topology of band structures in the 1651 magnetic space groups, Science Advances4, eaat8685 (2018)

    2018

  15. [23]

    Z. Song, T. Zhang, Z. Fang, and C. Fang, Quantitative mappings between symmetry and topology in solids, Na- ture Communications9, 3530 (2018)

    2018

  16. [24]

    Khalaf, H

    E. Khalaf, H. C. Po, A. Vishwanath, and H. Watan- abe, Symmetry indicators and anomalous surface states of topological crystalline insulators, Physical Review X 8, 031070 (2018)

    2018

  17. [25]

    N. F. Mott, The transition to the metallic state, Philo- sophical Magazine6, 287 (1961)

    1961

  18. [26]

    Yao and Q

    W. Yao and Q. Niu, Berry phase effect on the exciton transport and on the exciton Bose-Einstein condensate, Physical Review Letters101, 106401 (2008)

    2008

  19. [27]

    J. B. Haber, D. Y. Qiu, F. H. da Jornada, and J. B. Neaton, Maximally localized exciton Wannier functions for solids, Physical Review B108, 125118 (2023)

    2023

  20. [28]

    F. Wu, T. Lovorn, and A. H. MacDonald, Topological exciton bands in moir´ e heterojunctions, Physical Review Letters118, 147401 (2017)

    2017

  21. [29]

    Chen and R

    K. Chen and R. Shindou, Chiral topological excitons in a Chern band insulator, Physical Review B96, 161101 (2017)

    2017

  22. [30]

    Z. Gong, W. Luo, Z. Jiang, and H. Fu, Chiral topologi- cal excitons in the monolayer transition metal dichalco- genides, Scientific reports7, 42390 (2017)

    2017

  23. [31]

    Blason and M

    A. Blason and M. Fabrizio, Exciton topology and conden- sation in a model quantum spin Hall insulator, Physical Review B102, 035146 (2020)

    2020

  24. [32]

    Y. H. Kwan, Y. Hu, S. H. Simon, and S. Parameswaran, Exciton band topology in spontaneous quantum anoma- lous hall insulators: Applications to twisted bilayer graphene, Physical Review Letters126, 137601 (2021)

    2021

  25. [33]

    H.-Y. Xie, P. Ghaemi, M. Mitrano, and B. Uchoa, Theory of topological exciton insulators and condensates in flat Chern bands, Proceedings of the National Academy of Sciences121, e2401644121 (2024)

    2024

  26. [34]

    M. Xie, M. Hafezi, and S. Das Sarma, Long-lived topo- logical flatband excitons in semiconductor moir´ e het- erostructures: a bosonic Kane-Mele model platform, Physical Review Letters133, 136403 (2024)

    2024

  27. [35]

    Froese, T

    P. Froese, T. Neupert, and G. Wagner, Topological exci- tons in moir´ e MoTe2/WSe2 heterobilayers, Physical Re- view Research7, 023047 (2025)

    2025

  28. [36]

    Y. H. Kwan, Z. Wang, G. Wagner, S. H. Simon, S. Parameswaran, and N. Bultinck, Textured exciton in- sulators, Physical Review B112, 035129 (2025)

    2025

  29. [37]

    X. Cai, A. Consiglio, D. Di Sante, R. Thomale, and W. Hanke, Continuum theory for topological phase tran- sitions in exciton systems, Physical Review B113, 205121 (2026)

    2026

  30. [38]

    Eto and J

    R. Eto and J. Knolle, Odd-parity magnons in the Haldane-Hubbard model from topological exciton con- densation, arXiv preprint arXiv:2606.05837 (2026)

    2026 arXiv

  31. [39]

    Paiva, T

    C. Paiva, T. Holder, and R. Ilan, Shift and polariza- tion of excitons from quantum geometry, arXiv preprint arXiv:2408.10300 (2024)

    2024 arXiv

  32. [40]

    Lozano, H.-Y

    M. Lozano, H.-Y. Xie, and B. Uchoa, Optical selection rules of topological excitons in flat bands, Physical Re- view B112, 235417 (2025)

    2025

  33. [41]

    Qiu and F

    W.-X. Qiu and F. Wu, Quantum geometry probed by chi- ral excitonic optical response of Chern insulators, Phys- ical Review B111, L121104 (2025)

    2025

  34. [42]

    Davenport, Y

    H. Davenport, Y. Hwang, J. Knolle, and F. Schindler, Composite quantum geometry and semiclassical dynam- ics, arXiv preprint arXiv:2606.12525 (2026)

    2026 arXiv

  35. [43]

    Davenport, J

    H. Davenport, J. Knolle, and F. Schindler, Interaction- induced crystalline topology of excitons, Physical Review Letters133, 176601 (2024)

    2024

  36. [44]

    Davenport, J

    H. Davenport, J. Knolle, and F. Schindler, Exciton Berryology, Physical Review B113, 045125 (2026)

    2026

  37. [45]

    Davenport, F

    H. Davenport, F. Schindler, and J. Knolle, Berry curva- ture of low-energy excitons in rhombohedral graphene, Physical Review B113, 115102 (2026)

    2026

  38. [46]

    J. J. Thompson, W. J. Jankowski, R.-J. Slager, and B. Monserrat, Topologically enhanced exciton transport, Nature Communications16, 11448 (2025). 6

    2025

  39. [47]

    W. J. Jankowski, J. J. Thompson, B. Monserrat, and R.-J. Slager, Excitonic topology and quantum geometry in organic semiconductors, Nature Communications16, 4661 (2025)

    2025

  40. [48]

    Hwang, H

    Y. Hwang, H. Davenport, and F. Schindler, Stable wave- function zeros indicate exciton topology, arXiv preprint arXiv:2604.21643 (2026)

    2026 arXiv

  41. [49]

    Nalabothula, D

    M. Nalabothula, D. Sangalli, F. Paleari, S. Reichardt, and L. Wirtz, Symmetries of excitons, Physical Review B113, 205130 (2026)

    2026

  42. [50]

    See the Supplemental Material for details on real-space formalism, the projected Hamiltonian, the present model, emergent symmetry, the connection to momentum-space formalism, and the exciton Wilson loop

  43. [51]

    Brouder, G

    C. Brouder, G. Panati, M. Calandra, C. Mourougane, and N. Marzari, Exponential localization of Wannier functions in insulators, Physical Review Letters98, 046402 (2007)

    2007

  44. [52]

    Marzari, A

    N. Marzari, A. A. Mostofi, J. R. Yates, I. Souza, and D. Vanderbilt, Maximally localized Wannier functions: Theory and applications, Reviews of Modern Physics84, 1419 (2012)

    2012

  45. [53]

    Y. Kim, B. J. Wieder, C. L. Kane, and A. M. Rappe, Dirac line nodes in inversion-symmetric crystals, Physical Review Letters115, 036806 (2015)

    2015

  46. [54]

    Ono and H

    S. Ono and H. Watanabe, Unified understanding of sym- metry indicators for all internal symmetry classes, Phys- ical Review B98, 115150 (2018)

    2018

  47. [55]

    Z. Song, T. Zhang, and C. Fang, Diagnosis for nonmag- netic topological semimetals in the absence of spin-orbital coupling, Physical Review X8, 031069 (2018)

    2018

  48. [56]

    Zheng, K

    H. Zheng, K. Yang, T. Cao, and D. Xiao, Topo- logical charge-transfer excitons, arXiv preprint arXiv:2608.05308 (2026)

    2026 arXiv

  49. [57]

    Read, Compactly supported Wannier functions and algebraic K-theory, Physical Review B95, 115309 (2017)

    N. Read, Compactly supported Wannier functions and algebraic K-theory, Physical Review B95, 115309 (2017)

    2017

  50. [58]

    Rhim and B.-J

    J.-W. Rhim and B.-J. Yang, Classification of flat bands according to the band-crossing singularity of Bloch wave functions, Physical Review B99, 045107 (2019)

    2019

  51. [59]

    Graf and F

    A. Graf and F. Pi´ echon, Designing flat-band tight- binding models with tunable multifold band touching points, Physical Review B104, 1951128 (2021)

    2021

  52. [60]

    Hwang, J.-W

    Y. Hwang, J.-W. Rhim, and B.-J. Yang, General con- struction of flat bands with and without band crossings based on wave function singularity, Physical Review B 104, 085144 (2021)

    2021

  53. [61]

    Hwang, J.-W

    Y. Hwang, J.-W. Rhim, and B.-J. Yang, Flat bands with band crossings enforced by symmetry representa- tion, Physical Review B104, L081104 (2021)

    2021

  54. [62]

    Schindler and B

    F. Schindler and B. A. Bernevig, Noncompact atomic insulators, Physical Review B104, L201114 (2021). 7 Supplemental Material: Exciton Alchemy: Chern Excitons from Trivial Bands CONTENTS S1. Excitons in the relative distance basis 7 A. Wannier and exciton basis 7 B. Inversion s...

    2021

  55. [63]

    Therefore, ⟨GS|v† RvR|GS⟩=⟨GS|(1−v Rv† R)|GS⟩= 1,⟨GS|c † RcR|GS⟩= 0.(S30) It follows immediately that⟨GS| ˆh|GS⟩=−t 0 P R 1 =−t 0N

    Thet 0 term Thet 0 term is ˆh=−t 0 X R v† RvR−c† RcR .(S29) Since the reference ground state has the valence band completely filled,v † R|GS⟩= 0 andc R|GS⟩= 0. Therefore, ⟨GS|v† RvR|GS⟩=⟨GS|(1−v Rv† R)|GS⟩= 1,⟨GS|c † RcR|GS⟩= 0.(S30) It follows immediately that⟨GS| ˆh|GS⟩=−t 0...

  56. [64]

    Suppressing the hopping amplitude, we write ˆh= X R c† R+X,AcR,B +h.c

    Thet x andt x+y terms Thet x andt x+y terms have the same structure. Suppressing the hopping amplitude, we write ˆh= X R c† R+X,AcR,B +h.c. (S40) whereX=a 1 for thet x term anda 1 +a 2 for thet x+y term. Expressed in the Wannier basis, ˆh= 1 2 X R v† R+XvR−c† R+XcR + 1 2 X R c...

  57. [65]

    We simply list the results below

    Other terms The remaining terms can be evaluated in the same manner using Wick’s theorem. We simply list the results below. a. TheU 0,U x, andU y terms:The first three density-density interactions can be written in the unified form ˆh= X R nR+X,AnR,B,(S50) whereX=0,a 1,a 2 cor...

  58. [66]

    Here we explain why this truncation is justified when the terms introduced beyond the atomic limit are sufficiently small

    Continuum excitations beyond the truncated exciton basis In the main text, we constructed our model using a truncated exciton basis consisting of the five relative coordinates, ∆∈{0,+ˆx,−ˆx,+ˆy,−ˆy}. Here we explain why this truncation is justified when the terms introduced be...

  59. [67]

    For inter-sublattice hoppings, t X R c† R+X,AcR,B,(S70) whereXis a lattice vector and, for the moment,t∈C

    General hopping terms We next consider more general hopping processes. For inter-sublattice hoppings, t X R c† R+X,AcR,B,(S70) whereXis a lattice vector and, for the moment,t∈C. Under inversion, this term is mapped to t X R c† R,BcR+X,A.(S71) Including both terms and imposing ...

  60. [68]

    The most general inter-sublattice density-density interaction takes the form U X R nR+X,AnR,B,(S76) whereXis a lattice vector

    Density-density interactions We next consider density-density interactions. The most general inter-sublattice density-density interaction takes the form U X R nR+X,AnR,B,(S76) whereXis a lattice vector. Likewise, the most general intra-sublattice density-density interaction is...

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Reviewed August 15, 2026 · model on record in the stance chip above.