{"id":"bffab40c-8d2b-4364-959f-a3d901b8ac9e","arxiv_id":"2608.02040","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"PLE spectroscopy resolves the 2s, 3s, and 4s excited states of interlayer excitons in MoSe2/WSe2 heterostructures across several twist angles.","lead":"This paper reports photoluminescence excitation measurements that reveal a Rydberg-like series of excited interlayer exciton states in MoSe2/WSe2 stacks. The result gives a new experimental window on weakly emitting exciton states in 2D materials.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 56° sample's stated IX2/IX3/IX4 energies give successive spacings of 59 and 78 meV — increasing with n — contradicting the Rydberg-like claim on which the central assignment rests.","rationale":"The reader's weakest assumption focused on the PLE-to-absorption energy mapping. That is a legitimate methodological concern, but the paper contains a more direct, internal quantitative problem: the 56° state energies reported in Section IV violate the decreasing-spacing property that is the defining feature of a Rydberg-like series and that the paper itself asserts. This does not depend on external assumptions about PLE offsets or dielectric modeling; it is a checkable inconsistency in the paper's own numbers. Since the central claim is that the observed peaks are a Rydberg-like 2s/3s/4s series, this concern is load-bearing. The proposed digitization/refit test would settle it. I keep the reader's conditional verdict: the paper should not be treated as settled until this check is done and the energies are reconciled with the Rydberg progression.","tokens_in":13179,"tokens_out":10104,"duration_ms":96619,"concrete_test":"Digitize the 56° baseline-subtracted PLE spectrum in Fig. 3(b) (or rerun the multi-Gaussian fit on the raw integrated-intensity data) and extract the three peak centers with uncertainties. Compute r = (E_IX4 − E_IX3)/(E_IX3 − E_IX2). The text values give r ≈ 78/59 ≈ 1.32; a Rydberg-like series requires r < 1 in all standard models. If the reanalysis confirms r > 1, the n=2,3,4 assignment is falsified as stated; if the reanalysis yields different centers (e.g., E_IX3 > 1.59 eV) or additional peaks, the claim may survive with corrected energies.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section IV reports for the 56° HS: IX2s = 1.464 eV, IX3s = 1.523 eV, IX4s = 1.601 eV. The successive spacings are E3−E2 = 59 meV and E4−E3 = 78 meV, i.e., the spacing increases with principal quantum number. Every model invoked in the paper — hydrogenic, 2D-hydrogenic, and the screened Wannier ladder shown in Fig. 1(d) — has spacings that decrease as n increases; the text itself states this expectation immediately after giving these numbers. The extracted peaks therefore do not exhibit the defining signature of the claimed Rydberg-like series, so the n=2,3,4 labels cannot be correct as assigned. If the numbers are accurate, the central claim is internally inconsistent; if they are a typo or a fitting artifact, the assignment must be rederived from the raw PLE data before the claim can be evaluated. This is independent of the separate question of whether PLE peak energies map one-to-one to IX absorption energies.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports photoluminescence excitation (PLE) measurements on MoSe2/WSe2 heterostructures with twist angles of 1°, 14°, and 56°, claiming to resolve a Rydberg-like series of excited interlayer exciton states (IX2, IX3, IX4) below the intralayer exciton energies. The states are assigned to the 2s, 3s, and 4s excitons by comparison with Wannier-exciton calculations that incorporate screened Coulomb interactions and dielectric environment effects. The authors argue that the excited-state ladder is robust against twist-angle variation, and that PLE provides direct experimental access to these high-energy interlayer exciton states.","tokens_in":13509,"tokens_out":2965,"duration_ms":30153,"significance":"If the assignment is correct, the paper would provide a new experimental window onto excited interlayer exciton states, which have been difficult to access experimentally due to weak oscillator strength. The use of PLE rather than reflection contrast is a sensible strategy, and the comparison of three twist angles is a strength. The Wannier-exciton calculations are based on parameters from earlier literature (Refs. [33,34]) and are not fitted to the IX2–IX4 data, so the theoretical predictions are independent to a degree. The manuscript also includes supporting evidence from linewidth and emission-energy modulations in the SI. These elements make the claim potentially important if the assignment withstands scrutiny.","major_comments":[{"comment":"The reported IX2/IX3/IX4 energies for the 56° sample are (1.464±0.002) eV, (1.523±0.002) eV, and (1.601±0.001) eV. The successive spacings are E3−E2 = 59 meV and E4−E3 = 78 meV, i.e., the spacing increases with n. This contradicts the very next sentence in the same paragraph ('As expected for a Rydberg-like series, the spacing between successive states decreases with increasing principal quantum number') and also contradicts all models invoked in the paper, including the 2D-hydrogenic and Wannier ladders. If these numbers are accurate, the n=2,3,4 assignment is internally inconsistent. If they are a typo or a fitting artifact, the assignment must be rederived from the raw data before the central claim can be evaluated. This is load-bearing and cannot be left as is.","section":"Section IV"},{"comment":"The paper documents that PLE resonance energies are offset from absorption energies by 43 meV (XWSe2) and 15 meV (XMoSe2), and states that PLE resonances need not coincide with absorption resonances. Nevertheless, the assignment of IX2/IX3/IX4 relies on 'excellent agreement' between the measured PLE energies and the calculated absorption spectrum (Fig. 1d). Since the PLE offset for interlayer states is unconstrained and could be tens of meV, the absolute-energy comparison is not a valid test. The analysis should either use the energy separations between excited states and the ground state, which are insensitive to a common offset, or independently calibrate the PLE offset for interlayer excitons.","section":"Section III"},{"comment":"The PLE resonances used to extract IX2/IX3/IX4 are weak modulations on a log-scale after subtraction of an exponentially decaying baseline (Fig. 3b). The manuscript does not report the uncertainty in the baseline model or the statistical significance of the fitted Gaussians. Given that the resonances are weak and are the sole experimental evidence for the central claim, the paper should present quantitative measures of fit robustness (e.g., residuals, confidence intervals, or replicate measurements) to rule out baseline-fitting artifacts. The linewidth modulations in SI Fig. S2 are qualitative and do not by themselves establish the peak energies.","section":"Methods B and Figure 3"}],"minor_comments":[{"comment":"There are numerous typos and proofreading errors: 'assembaly', 'continues wave', 'on the the MoSe2', 'wavlength', 'close-cycle cryostat', 'Manthai' in the SI author list, and '3H type stacking' in SI. These should be corrected.","section":"Throughout"},{"comment":"The caption describes panel (d) as showing 'two additional PLE resonances corresponding to IX2, IX3 and IX4'—the wording is inconsistent (two vs three). Please clarify.","section":"Figure 2 caption and text"},{"comment":"The energy axis in SI Fig. S2(a) appears mislabeled: the values 1.3225–1.3375 eV are far below the XWSe2/XMoSe2 range discussed in the caption. Check the axis units.","section":"SI Fig. S2"},{"comment":"The choice of Lorentzian broadening parameters Γ1=1.5 meV and Γ2=Γ3=20 meV is stated but not justified. A brief explanation or reference would help the reader assess the calculated spectra.","section":"Methods C"}],"recommendation":"major_revision","confidential_remarks":"The internal inconsistency in the 56° energy spacings is the most serious issue: if the numbers are correct, the central assignment fails; if they are not, the raw-data analysis must be repeated. The PLE-offset issue reinforces the need for a relative-energy comparison. I recommend major revision rather than rejection because the experimental approach and the multi-twist dataset are valuable and the problems may be fixable within the manuscript's scope. The editor may wish to ask for the raw data and fit residuals to be included in the revised version."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nYou should know two things up front. The paper reports what would be a nice result — the first PLE-based Rydberg ladder for interlayer excitons in MoSe2/WSe2 — and the Wannier model is a genuine forward calculation. But the reported peak energies contradict the central assignment, and the paper doesn't appear to notice.\n\nThe novelty is real. PLE has been used for intralayer Rydberg excitons, but extending it to interlayer excitons and seeing resonances below the intralayer transitions in three samples with different twist angles is a step forward. The theory uses parameters from prior literature rather than fitting to the new data, so on that axis the paper is honest.\n\nThe soft spots are not minor. In Section IV the authors give, for the 56° sample, IX2 = 1.464 eV, IX3 = 1.523 eV, IX4 = 1.601 eV. The successive spacings are 59 meV and 78 meV — the spacing increases with n. Every model they invoke, including their own Figure 1(d), has spacings that shrink with n. The text even says Rydberg spacings should decrease, immediately before reporting numbers that don't. That is a load-bearing inconsistency. Either the labels are wrong or the peak picking is off, but as written the central claim is not supported by the paper's own data.\n\nThe second problem is the mapping between PLE peaks and absorption. The paper itself shows PLE resonances are redshifted by 15–43 meV relative to reflection-contrast absorption for the intralayer excitons. The offset for the interlayer states is unconstrained, so the identification of the observed modulations with specific n states relies on an assumption that the paper elsewhere shows is unreliable.\n\nThere are also weaker concerns: the resonances are weak modulations on a log-scale after exponential baseline subtraction, and the twist-angle robustness conclusion rests on three samples in possibly different dielectric environments. Those I'd treat as minor relative to the spacing problem.\n\nWho is this for? Researchers working on TMDC excitonics and PLE spectroscopy. It deserves a serious referee, but the verdict should be 'major revision,' not acceptance. The experimental approach is worth engaging with; the analysis needs to be redone and the energies checked against the raw PLE data.\n\nMy recommendation: send it to referees, but with a note that the internal consistency of the extracted energies is the first thing to check.","headline":"Novel PLE experiment, but the reported IX2/IX3/IX4 spacings increase with n, contradicting the central Rydberg assignment.","tokens_in":14033,"tokens_out":2647,"would_cite":false,"duration_ms":24449,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Photoluminescence excitation spectroscopy resolves a Rydberg-like series of excited interlayer exciton states in MoSe2/WSe2 heterostructures.","keywords":["interlayer excitons","Rydberg series","photoluminescence excitation spectroscopy","MoSe2/WSe2 heterostructures","twist angle","dielectric screening","Wannier exciton model","high-energy exciton states"],"falsifier":"Measure the PLE spectrum while detecting emission from a different recombination channel (e.g., a trion or a localized state) or perform linear absorption spectroscopy (reflection contrast) on the same high-quality sample with enhanced sensitivity; if the PLE 'resonances' shift or disappear when the detection energy changes, or if reflection contrast shows no corresponding absorption features at those energies, the one-to-one absorption interpretation would be falsified.","tokens_in":13129,"feed_emoji":"🔬","tokens_out":1778,"duration_ms":20626,"temperature":0.7,"pith_summary":"The paper claims that photoluminescence excitation (PLE) spectroscopy can directly observe the previously hidden high-energy excited states of interlayer excitons in MoSe2/WSe2 heterostructures. It reports multiple PLE resonances below the intralayer exciton energies and assigns them to the 2s-, 3s-, and 4s-like states of the interlayer exciton. These resonances appear consistently across samples with twist angles of 1°, 14°, and 56°, suggesting the excited-state spectrum is nearly independent of twist angle. Wannier-exciton calculations with screened Coulomb interactions reproduce the overall energy scale and trends, supporting the assignment. A sympathetic reader would care because this opens a direct experimental window into the high-energy Rydberg ladder of interlayer excitons, which is key for understanding many-body interactions and nonlinear optics in van der Waals heterostructures.","feed_headline":"PLE resolves Rydberg ladder of interlayer excitons","feed_subtitle":"Photoluminescence excitation directly sees the excited 2s, 3s, 4s states of interlayer excitons in MoSe2/WSe2 stacks.","key_machinery":"The central experimental tool is photoluminescence excitation (PLE) spectroscopy, where the integrated intensity of the ground-state IX emission is recorded as the excitation laser is tuned across the high-energy region. The central theoretical tool is a Wannier-exciton model based on an effective Bethe-Salpeter equation with parabolic bands and a screened Coulomb potential, solved on a 2D k-grid; this model produces a calculated Rydberg-like IX series (1s, 2s, 3s, 4s) with momentum-space wavefunctions shown in the paper. The PLE resonances are the load-bearing observable, and the Wannier-exciton calculation supplies the labeling of the peaks.","core_discovery":"The core claim is that PLE spectroscopy resolves a Rydberg-like series of excited interlayer exciton states in MoSe2/WSe2 heterostructures. The authors observe multiple PLE resonances below the intralayer exciton energies, which they assign to the 2s-, 3s-, and 4s-like states of the interlayer exciton (denoted IX2, IX3, IX4). These resonances are found in three heterostructures with different twist angles (1°, 14°, 56°), indicating that the excited-state spectrum is only weakly affected by twist angle, in contrast to the ground-state IX energy. Wannier-exciton calculations incorporating screened Coulomb interactions reproduce the overall energy scale and qualitative trends of the measured se","pith_inferences":["An implicit corollary is that the same PLE approach could resolve excited states of interlayer excitons in other TMDC heterobilayers (e.g., MoS2/WSe2 or MoSe2/WS2), provided the intralayer exciton is higher in energy than the interlayer Rydberg series.","A testable extension would be to measure PLE on samples with a continuous range of twist angles, especially near small angles where moiré reconstruction is strongest, to see whether the claimed twist-angle robustness survives in the moiré-localized regime.","The paper's logic suggests that the observed PLE modulations might also arise from phonon-assisted absorption or continuum-edge effects rather than bound 2s/3s/4s states; a decisive check would be comparing PLE spectra with two-photon absorption or nonlinear spectroscopy that directly probes even-parity exciton states.","If the assignment holds, the excited IX states could serve as sensitive local probes of dielectric disorder, since their large Bohr radii make them more affected by spatial variations in screening than the 1s state."],"forward_implications":["If correct, PLE spectroscopy becomes a routine direct probe of the high-energy interlayer exciton spectrum, complementing reflection contrast which cannot resolve these weak states.","The near-independence of the excited-state ladder from twist angle implies that dielectric screening, disorder, and hybridization with intralayer excitons dominate over moiré potential effects in setting the high-energy IX state energies.","The non-hydrogenic spacing of the series (deviating from 1/n²) provides a quantitative constraint on the screened Coulomb interaction and dielectric environment of the heterostructure.","The strong calculated sensitivity to dielectric screening suggests that encapsulating or suspending the heterostructure can tune the entire Rydberg ladder, offering a design knob for experiments.","The demonstration that PLE resonances can be offset from absorption resonances (shown for intralayer excitons) implies that PLE-based energy assignments for interlayer states should be calibrated against a direct absorption measurement when possible."],"fun_headline_variants":["Interlayer excitons show Rydberg ladder in PLE","PLE exposes excited states of interlayer excitons","High-energy IX states seen via PLE spectroscopy","Twist angle barely shifts IX Rydberg series","2s,3s,4s interlayer excitons resolved by PLE"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The assignment of the weak PLE features to specific 2s, 3s, and 4s interlayer exciton states presumes that each PLE enhancement peak corresponds one-to-one to an interlayer exciton absorption resonance, an assumption the paper does not directly calibrate for these states.","fun_headline_variants_meta":{"raw":{"variants":["Interlayer excitons show Rydberg ladder in PLE","PLE exposes excited states of interlayer excitons","High-energy IX states seen via PLE spectroscopy","Twist angle barely shifts IX Rydberg series","2s,3s,4s interlayer excitons resolved by PLE"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000259,"raw_usage":{"total_tokens":1425,"prompt_tokens":751,"completion_tokens":674,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":495,"completion_tokens_details":{"reasoning_tokens":606}},"tokens_in":495,"tokens_out":674,"duration_ms":6320,"temperature":1.0,"reasoning_tokens":606,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T16:09:48.755974+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the PLE spectrum while detecting emission from a different recombination channel (e.g., a trion or a localized state) or perform linear absorption spectroscopy (reflection contrast) on the same high-quality sample with enhanced sensitivity; if the PLE 'resonances' shift or disappear when the detection energy changes, or if reflection contrast shows no corresponding absorption features at those energies, the one-to-one absorption interpretation would be falsified.","supporting_citations":[],"review_version":1}