Intrinsic edge excitons in two-dimensional MoS$_2$

Andrea Ferretti; Daniele Varsano; Deborah Prezzi; Elisa Molinari; Marco Gibertini; Nicola Marzari; Pino D'Amico

REVIEW 2 major objections 5 minor 101 references

Intrinsic edge excitons in two-dimensional MoS$_2$

T0 review · 2 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read MoS2 ribbon edges host a 1.5 eV exciton below the bulk peaks

desk verdict Careful GW-BSE study predicting edge-localized excitons in MoS2 ribbons; the central prediction is plausible but rests on an unvalidated interpolation of W(q=0) that deserves sensitivity testing before I'd bet on it. read the letter →

arxiv 1909.01613 v1 pith:W4F4ADZO submitted 2019-09-04 cond-mat.mes-hall cond-mat.mtrl-sci

Pino D'Amico , Marco Gibertini , Deborah Prezzi , Daniele Varsano , Andrea Ferretti , Nicola Marzari , Elisa Molinari This is my paper · ORCID

classification cond-mat.mes-hallcond-mat.mtrl-sci

keywords edgeexcitonsMoS2transitionmetaldichalcogenideszigzagnanoribbonsGW-BSEBethe-Salpeterequationmany-bodyperturbationtheoryinmetallicsystems

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

Single-layer molybdenum disulfide, a semiconductor that absorbs light through tightly bound electron-hole pairs, is predicted to have additional excitons that belong to its edges rather than its interior. Using first-principles many-body calculations at the GW plus Bethe-Salpeter level, the paper finds two such excitons in zigzag nanoribbons, at roughly 0.55 eV and 1.49 eV, both well below the familiar A and B excitons of the two-dimensional sheet. The lower one binds electrons and holes on opposite edges and fades once ribbons exceed a few nanometres in width; the higher one lives on a single edge and is essentially unchanged as the ribbon widens. Because the same metallic edge states appear across edge terminations, orientations, and the whole family of group-VI transition-metal dichalcogenides, the authors argue this intra-edge exciton is a universal, intrinsic feature of edges rather than a ribbon-size artifact. If correct, it makes a naked edge optically visible at sub-gap energies in samples that range from nanoribbons to large flakes.

What carries the argument

The load-bearing object is the set of mid-gap, metallic edge states that arise from the polar discontinuity where the MoS2 sheet terminates; these states supply both the single-particle transitions that form the excitons and the metallic screening that the calculation must handle at q→0. The machinery is the GW-BSE scheme with a truncated Coulomb interaction, in which the poorly represented W(q=0) term is supplied by fitting the computed finite-q screening to a one-dimensional analytic form, introducing an inverse screening length and transverse ribbon size. The argument turns on classifying the BSE eigenstates by their spatial electron-hole distribution—inter-edge versus intra-edge—and on showing that the intra-edge distribution survives as the ribbon width grows.

What would settle it

Measure local optical absorption or photoluminescence on a MoS2 flake with straight zigzag edges, scanning across the edge at energies below the 1.88 eV A exciton: the central prediction fails if no width-independent, edge-localized peak near 1.5 eV appears. A calculation that recomputes the Bethe-Salpeter spectrum using an independent, non-fitted value for W(q=0) would also settle whether the edge excitons remain bound.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the metallic edge states of MoS2 nanoribbons—normally expected to screen Coulomb interactions so strongly that no excitons survive—still bind electron-hole pairs with substantial energy. Classifying the two lowest optical peaks, the authors identify an inter-edge exciton (E1) whose electron and hole sit on opposite ribbon edges, with binding energy about 0.21–0.25 eV and optical activity that vanishes with increasing width, and an intra-edge exciton (E2) whose electron and hole sit on the same edge, with binding energy about 0.39–0.42 eV that persists at larger widths. They show E2's position, binding, and character are nearly independent of edge termination (bare, S-monomer, S-dimer) and also appear for armchair ribbons, and they conclude that this intra-edge excitation is robust and universal—an intrinsic consequence of the edge's existence. The finite binding is attributed to screening being ineffective in one dimension, mirroring earlier findings on semimetallic carbon nanotubes.

Load-bearing premise

The load-bearing premise is that the fitted one-dimensional screening formula correctly gives the screened electron-hole attraction at the very long wavelength (zero momentum) that the calculation cannot sample directly; if that extrapolation is too attractive, the predicted edge excitons could fail to bind.

Editorial extensions

If this is right

The intra-edge E2 exciton should appear as a clear, edge-localized peak below the bulk A and B excitons in large MoS2 samples, not just in nanoribbons.
The inter-edge E1 exciton is a fingerprint of ultranarrow ribbons, and its disappearance with width tracks the vanishing wavefunction overlap between opposite edges.
Excitons can remain bound at metallic one-dimensional edges, so metallic screening does not automatically quench optical resonances in these systems.
Because edge mid-gap states are shared across edge terminations and orientations, similar sub-gap edge absorption is expected for armchair ribbons and for other group-VI TMDs such as MoSe2 and WS2.
Accurate quasiparticle corrections across the whole Brillouin zone are required; simplified scissor-style corrections would misplace the edge states relative to bulk bands.

Reading between the lines

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

If E2 is width-independent, edge-mapping optical techniques such as near-field photoluminescence on flakes with straight edges should see a sub-gap peak localized at the edge; this is a direct, testable consequence the paper does not itself propose.
The strong sensitivity to screening geometry suggests the edge-exciton energy should shift with the dielectric environment, such as substrate or capping layers; a systematic study of that shift could sharpen or falsify the predicted universality.
Because the fitted W(q=0) controls binding, the quantitative values of 0.21–0.42 eV carry an uncertainty not quantified here; recomputing the spectra with an independent treatment of metallic screening at q=0 would test whether the edge excitons are indeed bound.
If the intra-edge exciton proves real, it could seed sub-gap optical nonlinearities or low-threshold gain in TMD nanostructures, since the transition is spatially localized yet coupled to the metallic edge continuum.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

This is a solid computational paper with a genuinely new prediction: metallic zigzag MoS2 nanoribbons host edge excitons that sit well below the bulk A/B exciton peaks. The authors identify two classes, inter-edge (E1) and intra-edge (E2), and show across three edge terminations that E2 is stable and width-independent. If true, this gives experimentalists a non-invasive optical signature of edge quality, so the stakes are real.

What is done well: the GW-BSE calculations are careful. They check k-point convergence, number of bands, Tamm-Dancoff, and spin-orbit effects, and they are explicit that a scissor correction is inadequate. The termination study (bare, S-monomer, S-dimer) is a genuine robustness test. The binding energies (~0.2-0.4 eV) are reported per peak, and the exciton wavefunctions are consistent with the inter- vs intra-edge assignment. The comparison to semimetallic carbon nanotubes is apt. The referencing is honest; the authors cite their own prior work on polar-discontinuity edge states because that is the relevant antecedent.

The soft spot is the q=0 screened interaction. The SM says the q=0 point is not well represented and they fit W(q>0) to a 1D analytic form, then use the fitted W(0) in the BSE kernel. That is load-bearing: in a metallic 1D wire, whether a bound exciton appears at all depends on the long-wavelength head of W. The paper gives no fit parameters (q0, R) and no sensitivity analysis. The k-point convergence check refines q>0 sampling but does not validate the analytic continuation to q=0. I do not think the concern is fatal, because the fitting form is physically motivated and matches finite-q data, but the reader cannot check how robust the 0.4 eV binding energy is to the extrapolation. A sensitivity scan or an independent screening model would settle it.

The "universal" claim is also slightly beyond the directly computed parameter space: N=2 and N=3 ribbons, three ZZ terminations, and a citation for AC edges. The width-independence is plausible from the edge-state picture, but it is an extrapolation. This is a minor issue relative to the W(0) question.

Who this is for: anyone computing or measuring TMD edge states, and experimental groups doing low-temperature photoluminescence on flakes or ribbons. It deserves peer review. The question is well-posed, the methods are state-of-the-art, and the prediction is falsifiable. I would ask for the sensitivity analysis and a slightly softened "universal" phrasing, but this is not a desk reject. Engage with it.

Referee Report

2 major / 5 minor

Summary. Using G0W0 plus Bethe-Salpeter calculations on MoS2 zigzag nanoribbons (ZZ-NRs) with N=2 and N=3, and with S-dimer, S-monomer, and bare Mo-edge terminations, the authors predict two low-energy edge excitons below the bulk 2D exciton onset. E1 is an inter-edge exciton that becomes optically dark with increasing ribbon width; E2 is an intra-edge exciton that remains optically active and is claimed to be robust, universal, and observable in larger samples, with binding energies of about 0.2--0.4 eV attributed to ineffective screening of the metallic 1D edge states.

Significance. If correct, the predicted E2 peak would provide an experimentally accessible optical signature of edges in MoS2 and, plausibly, other group-VI TMDs, and it would be an interesting counterexample to the common expectation that metallic edges quench excitons. The manuscript has clear strengths: it uses a standard state-of-the-art G0W0-BSE framework, reports convergence tests (k-point sampling, number of bands, Tamm-Dancoff approximation), checks spin-orbit effects, and examines several edge terminations. The central quantitative prediction, however, depends on a fitted q=0 screened interaction whose parameters and sensitivity are not reported, and the 'universal' width-independent claim is extrapolated from only two ribbon widths. These issues affect the load-bearing parts of the paper and need to be addressed before the prediction can be fully accepted.

major comments (2)

[Supplemental Material, Sec. S4 (Eq. 1)] The treatment of the metallic q→0 limit is load-bearing for the central claim. As stated in SM S4, "the only point that is not well represented is the q=0 one," and the W(q=0) entering the BSE kernel is obtained by fitting the finite-q ab initio data to Eq. (1), with parameters q0 and R. The paper reports neither the fitted values (q0, R) nor the resulting W(0), and provides no sensitivity analysis. An overestimated W(0) would produce spurious bound excitons, while an underestimated value could artificially suppress or shift them; the k-point convergence test in Fig. S1 does not test this continuation. The authors should report the fit parameters and W(0) for each termination and width, and demonstrate that the existence and binding energies of E1 and E2 are stable when q0 and R are varied over the fitting uncertainty, or validate W(0) with an independent calculation that includes the intraband (1D metallic) contribution at small q.
[Main text, Fig. 2 and concluding paragraph] The "width-independent" and "larger samples" claim rests on calculations for only two widths, N=2 (1.11 nm) and N=3 (1.65 nm). While the physical reasoning (same-edge localization of electron and hole and weak width dependence of the edge bands) is plausible, it is an extrapolation to state that the intra-edge exciton is "expected in the optical spectrum not only of narrow ribbons, but also of larger samples." At least one additional width (e.g., N=4 or N=5) or a quantitative convergence model is needed to support this part of the conclusion; otherwise the statement should be weakened.

minor comments (5)

[Concluding paragraph] There is a typo in the conclusion: "width-indepedent" should be "width-independent."
[Supplemental Material, Sec. S5] In the description of Fig. S5, the text says the E1 transition has "an intra-edge character connecting left and right edges"; this should be "inter-edge character," because E1 connects states localized on opposite edges, consistent with the main text.
[Supplemental Material, Fig. S8 caption] In the Fig. S8 caption, "empy" should be "empty."
[Supplemental Material, Sec. S3] The spin-orbit check is performed only at the LDA and independent-particle level, not at the GW-BSE level; a brief statement on why the conclusion is expected to hold for the bound excitons would strengthen the argument.
[Main text, paragraph after Fig. 3] The claim that analogous edge-related excitons exist for armchair edges relies on a citation to Ref. [88] rather than on calculations in this work; specifying the level of theory used in that reference would help the reader assess the universality claim.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the GW-BSE edge-exciton prediction is self-contained, with the only fitted quantity (W(q=0)) matched to ab initio finite-q screening data rather than to the target peak energies.

full rationale

The central claim (E1/E2 edge excitons below the bulk onset) is obtained by a standard first-principles chain: LDA (Quantum ESPRESSO) to G0W0 (yambo) to BSE with RPA static screening. The only fitted quantity is W(q=0) in SM S4, obtained by fitting Eq. (1) to ab initio computed W(q>0) data shown in Fig. S4; it is not fit to the E1/E2 peak positions or binding energies, so the predicted exciton energies are not self-fitted. The metallic character of the ZZ edge, although contextualized by self-citations [51,53] for the polar discontinuity, is independently demonstrated in the paper's own LDA and G0W0 band structures (Fig. 2a,c), where three edge-localized bands cross the Fermi level. The universality claim across terminations is supported by explicit GW-BSE calculations for bare, S-monomer, and S-dimer edges (Table I), and the AC case is cited to external work [88]. The q=0 screening extrapolation in SM S4 is a numerical-sensitivity concern (the paper reports neither q0, R, nor a sensitivity analysis of the E2 binding energy to these parameters), but it is not circular: the extrapolation is anchored to ab initio finite-q data rather than to the predicted exciton features. No equation or parameter in the paper is equivalent by construction to the claimed edge-exciton prediction.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The central prediction imports standard many-body perturbation theory approximations and the earlier demonstration of polar-discontinuity edge states in MoS2 nanoribbons. The only parameters fitted to data are q0 and R of the 1D W(q) model in SM S4, which are matched to finite-q ab initio screening data rather than to the target exciton energies. No new physical entities are introduced.

free parameters (2)

q0 in 1D W(q) model = not reported
Used as the inverse screening length in Eq. (1) of SM S4; fitted to the ab initio W(q) at finite q to obtain W(q=0) for the BSE kernel.
R in 1D W(q) model = not reported
Effective transverse size of the ribbon in the same fit; this parameter together with q0 controls the long-wavelength screening that determines whether edge excitons bind.

assumptions (6)

domain assumption The G0W0 approximation and the Bethe-Salpeter equation provide reliable quasiparticle and optical spectra for these MoS2 nanoribbons.
Standard method for 2D semiconductors, but its accuracy is less established for metallic edge states; the paper provides convergence checks but no direct benchmark for edge excitons.
domain assumption The plasmon-pole approximation for the dynamic dielectric function is valid in these systems.
Used in the G0W0 self-energy; not separately validated for the nanoribbon edges (SM S1).
domain assumption The metallic edge states in zigzag MoS2 nanoribbons are correctly described by prior DFT calculations (Refs. [49,51]); they persist with the three terminations considered.
The existence of edge-localized states crossing the Fermi level is the foundation for the edge excitons; the paper reproduces this at LDA level and cites earlier work for the polar-discontinuity mechanism.
domain assumption The 1D analytic expression for the screened interaction (Eq. (1) in SM S4) accurately represents the q to 0 limit of the ribbon.
This model is fitted to finite-q ab initio data and then used to set W(q=0); the paper states the fit quality is good but does not report the fitted parameters.
domain assumption The Tamm-Dancoff approximation is sufficient for the BSE in these systems.
SM S1 states the antiresonant coupling correction is negligible after verification; this is a standard approximation.
domain assumption Spin-orbit coupling does not alter the qualitative conclusions.
SM S3 verifies this at the LDA independent-particle level, not at the GW-BSE level; the main text neglects SO.

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Pith. "Pith review of Intrinsic edge excitons in two-dimensional MoS$_2$." pith.science (2026). https://pith.science/paper/W4F4ADZO

@misc{pith2026190901613,
  author       = {Pith},
  title        = {Pith review of: Intrinsic edge excitons in two-dimensional MoS$_2$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/W4F4ADZO}},
  note         = {Machine review of arXiv:1909.01613}
}

abstract

Using accurate first-principles calculations based on many-body perturbation theory we predict that two-dimensional MoS$_2$ hosts edge excitons with universal character, intrinsic to the existence of edges and lying well below the onset of bulk features. These excitons are largely insensitive to edge terminations or orientation, persisting even in the presence of metallic screening at zigzag edges, with large binding energies of $\sim$0.4 eV. Additional excitons can also emerge in ultranarrow ribbons, or as a function of the chemical nature of the termination. The chemical, structural, and electronic similarities with Se- or W-based transition-metal dichalcogenides suggest that these optical features could be common in this class of materials.

Figures

Figures reproduced from arXiv: 1909.01613 by the authors.

**Figure 2.** FIG. 2. Electronic band-structures (a,c) and optical absorp [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** FIG. 3. Square modulus of the exciton wavefunctions for the [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

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