{"id":"978d03f3-e294-47c6-ab65-d3bba4e6deb5","arxiv_id":"2505.14277","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"First-principles calculations show that Born effective charges jump at the topological transition in germanene and jacutingaite, making infrared spectra distinct markers of the two phases.","lead":"This paper predicts that infrared light absorption can tell apart the topological and trivial states of two quantum spin Hall insulators, germanene and jacutingaite. It calculates that the strength of infrared-active vibrations changes sharply across the phase transition, offering a possible non-contact way to identify topological phases.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The germanene infrared marker relies on model-only dynamical effective charges; the ab initio static Z* calculation is made in a regime where the static approximation is explicitly invalid, so the Fano-line shape prediction is not yet first-principles-validated.","rationale":"The reader's weakest assumption is close but not identical: I isolate the specific place where the first-principles support ends and the model begins. The static ab initio jump is real and well supported, and the model rationalization is plausible, but the experimental marker for germanene is the Fano profile, which is entirely determined by model dynamical Z*. The paper does benchmark static susceptibility, but not the frequency-dependent effective charge, so the central robustness claim rests on an unvalidated model quantity. This does not refute the paper; it identifies a concrete validation gap. A TDDFT calculation of Z*(ωph) would settle it. Since the reader already flagged the model dependence and recommended conditional acceptance, my assessment leaves the verdict unchanged. The paper deserves credit for the clean ab initio static calculations, the clear model derivation, and the explicit discussion of the static-approximation breakdown.","tokens_in":18108,"tokens_out":4559,"duration_ms":46831,"concrete_test":"Run first-principles TDDFT (as in Refs. [51,52]) to compute the complex frequency-dependent Born effective charge Z*_xx(ω) of germanene at the E-phonon frequency ω_ph, for the zero-field topological state (Δ0≈24 meV) and for a field above the critical field (trivial state). Compare Re Z*(ω_ph) and Im Z*(ω_ph) with the Kane-Mele values used in Fig. 4. If Im Z* changes sign between phases or |Z*(ω_ph)| differs by more than ~30% from the model, recompute the Fano parameters P and q; if the resulting lineshape difference between phases disappears, the dynamical marker is not robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing weak point is the germanene dynamical prediction. In Sec. 2.2 the ab initio Born effective charges are computed in the static limit, yet for the DFT gap of germanene Δ0 ≈ 24 meV the E-phonon frequency is ωph ≈ 35 meV, so the condition Z*(ωph) ≈ Z*(0) used to justify that calculation is violated. The paper acknowledges this and moves to the Kane-Mele model in Sec. 2.4, where frequency-dependent Z*(ω) and Fano parameters are derived analytically. However, the only ab initio check offered is for the static electric susceptibility (SI Fig. 12), not for the complex Z*(ωph) that enters Eqs. (10)-(11). The sign and magnitude of Im Z*(ωph) control the Fano asymmetry q = -Re Z*/Im Z*, and the model-specific gauge-field electron-phonon coupling from Ref. [50] is the sole source of this quantity. If the true dynamical effective charges differ—e.g., in the sign of Im Z* or in the size of the resonant enhancement—the predicted contrast between QSHI and trivial Fano profiles in Fig. 5 could weaken or invert, undermining the central claim that the marker is robust to dynamical effects.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"Using density functional perturbation theory, this paper studies the static Born effective charges (Z*) of germanene and jacutingaite monolayers as a function of a perpendicular electric field that drives a topological phase transition between a quantum spin Hall insulator (QSHI) and a trivial insulator. The authors find large discontinuous jumps in the in-plane Z* components across the transition (approximately 2 for germanene and approximately 2.5 for Hg in jacutingaite), consistent with the Kane-Mele relation Eq. (8), and use these jumps to predict a strong change in the infrared vibrational spectrum. For germanene, the DFT gap (24.3 meV) is smaller than the E phonon frequency (35.5 meV), so the static approximation is invalid; the authors therefore analyze dynamical effects within the Kane-Mele model, obtaining a complex frequency-dependent Z*(omega_ph) and predicting Fano line shapes for the phonon resonance that differ between the two phases. For jacutingaite, the large gap (about 0.15 eV) justifies the static treatment, and the ab initio spectrum shows large intensity changes of several IR-active phonon modes across the transition.","tokens_in":18363,"tokens_out":8740,"duration_ms":84936,"significance":"The proposal of an infrared fingerprint for the QSHI-to-trivial transition is timely and potentially useful, given the difficulty of transport and STM measurements. The static ab initio results for the Z* jumps in germanene and jacutingaite are concrete and directly computed, and the comparison with the Kane-Mele formula Eq. (8) is a valuable consistency test. The dynamical analysis in Sec. 2.4 is clearly presented and includes physically motivated ingredients, such as the experimental phonon linewidth and ab initio phonon frequency and electron-phonon coupling. However, the central claim that the marker is robust to dynamical effects rests on model calculations of the complex Z*(omega_ph) that have not been validated by first-principles methods; the sign of Im Z* is a delicate quantity that controls the Fano asymmetry. The work is therefore significant but incomplete in its present form.","major_comments":[{"comment":"The frequency-dependent complex Born effective charge Z*(omega_ph) that determines the Fano parameters q and P is computed entirely within the Kane-Mele model using the gauge-field electron-phonon coupling of Ref. [50]; the only ab initio comparison provided is the static electric susceptibility (SI Fig. 12), not Z*(omega_ph). Since Im Z*(omega_ph) sets the sign of the Fano asymmetry and its magnitude sets the strength, a different sign or a sizable trivial contribution from other bands could weaken or invert the predicted contrast between the QSHI and trivial phases in Fig. 5. Please provide an ab initio TDDFPT calculation of the dynamical Z*(omega_ph) for germanene, or, if that is not feasible, a systematic sensitivity analysis (e.g., varying the electron-phonon coupling xi and adding a k-independent background to Z*) that demonstrates the sign and shape of the Fano profile are robust.","section":"§2.4, Eqs. (10)-(11)"},{"comment":"The static infrared spectrum in Fig. 1(f) is presented without qualification, but the condition Z*(omega_ph) approximately equal to Z*(0) used to justify the static calculation is explicitly violated for the DFT gap of germanene (Delta_0 = 24.3 meV < omega_ph = 35.5 meV, as stated in Sec. 2.4). This spectrum therefore should not be read as the predicted IR response of germanene at its DFT gap; the authors should relabel it as the static-limit result and state clearly that dynamical corrections modify the prediction, including the apparent disappearance of the E mode in the QSHI phase.","section":"§2.2, Fig. 1(f)"},{"comment":"The 'excellent agreement' between the ab initio Z* and Eq. (8) in Fig. 1(d) is a consistency check rather than a fully parameter-free prediction: lambda_SO and the effective field E_tot^z are extracted from the same DFT gap via Eq. (7), and xi is computed from DFT electron-phonon matrix elements, so the model curve is constrained by the same first-principles input. This does not invalidate the direct DFPT computation of Z*, but the text should state explicitly which parameters are fitted and which are computed independently.","section":"§2.2 and Methods: Low energy model parameters"}],"minor_comments":[{"comment":"The phrase 'Kane-Male model' appears several times and should read 'Kane-Mele model'.","section":"§2.1"},{"comment":"The text says 'Even tough the intensity difference' and should read 'Even though the intensity difference'.","section":"§2.4"},{"comment":"The caption contains the fragment 'described in the nergy bands'; this appears to be a typo for 'energy bands'.","section":"Fig. 5 caption"},{"comment":"The Fano expression for sigma_ion is stated without derivation; please either derive it from Eq. (2) in the main text or provide an explicit reference to the Supplemental Material where the reduction is shown.","section":"§2.4, Eq. (10)"},{"comment":"The phonon-phonon linewidth gamma_ph-ph is taken from bulk Ge experiments; the authors should comment on the validity of this choice for a free-standing monolayer and on the sensitivity of the Fano profiles to this parameter.","section":"§2.4, after Eq. (11)"},{"comment":"The notation E_tot^z is used throughout; defining a shorthand (e.g., E_z) would improve readability and reduce the number of superscripts and subscripts.","section":"General notation"}],"recommendation":"major_revision","confidential_remarks":"The manuscript relies heavily on the authors' previous model paper (Ref. [50]) for the electron-phonon coupling and the Z* relation; this is not improper, but the dynamical predictions are essentially a test of that model rather than a fully first-principles result. The Supplemental Material is essential to verify Eq. (10) and the dynamical derivation, and the review was performed without access to it. The paper fits the journal's scope in condensed matter physics and materials science, and the topic is of current interest."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. The static part is real: for jacutingaite the in-plane Born effective charges on Hg jump by ~2.5 at the topological transition, and several IR-active modes change intensity sharply between phases. That is a concrete, falsifiable prediction worth having. The germanene dynamical line-shape prediction—the Fano asymmetry meant to distinguish the phases—comes entirely from the Kane-Mele model with the gauge-field electron-phonon coupling of their earlier paper. No first-principles complex Z*(ωph) is computed, and that quantity sets the Fano q. So the robustness claim in the abstract is only as good as that model.\n\nWhat they do well: they actually run DFPT for two real materials. The jacutingaite results are clean: the static approximation holds there (gap ~0.15 eV, phonons well below) and the spectral differences in Fig. 3 are stark. The germanene static calculation is careful, but as the authors themselves note, the DFT gap (24 meV) is smaller than the E phonon (35 meV), so the static IR spectrum in Fig. 1(f) is not quantitatively meaningful for real germanene. They switch to the model with the experimental gap (70 meV), which is a sensible move, but it means the germanene marker is not first-principles-validated.\n\nThe biggest soft spot is exactly what the stress test says: q = -Re Z*/Im Z* depends on the sign and magnitude of Im Z*(ωph), and that quantity has no ab initio check. The SI only compares the static susceptibility. If the real electron-phonon coupling deviates from the gauge-field form, the predicted contrast between the QSHI and trivial Fano profiles could weaken or even invert. That does not kill the jacutingaite result, but it should be stated in the paper. Also, the Discussion's claim that the change can be detected experimentally 'with the same sensitivity' is stronger than the simulations support—the linewidths are multiplied by an arbitrary factor and there is no noise estimate.\n\nWho is this for? People working on 2D topological insulators and optical probes, and experimentalists looking for a non-contact way to detect the transition. It deserves a serious referee. I would send it out, but ask the authors to add a first-principles dynamical Z* for germanene or explicitly label the Fano prediction as model-based and soften the robustness claim.","headline":"Useful first-principles extension of the BEC-jump idea, but the germanene Fano marker is model-only and should be read as a proposal, not a validated prediction.","tokens_in":18918,"tokens_out":5414,"would_cite":true,"duration_ms":49255,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Using first-principles calculations, the paper shows that infrared optical response can distinguish the topological and trivial phases of two-dimensional quantum spin Hall insulators because Born effective charges jump by up to about 2 at…","keywords":["quantum spin Hall insulator","Born effective charge","infrared spectroscopy","topological phase transition","Kane-Mele model","Fano resonance","germanene","jacutingaite"],"falsifier":"Measure the infrared reflectance of a gated germanene or jacutingaite monolayer while sweeping a perpendicular electric field through the critical value. The claim predicts an abrupt appearance of the in-plane phonon peak in germanene and a discontinuous reshuffling of mode intensities in jacutingaite at the transition, and, near resonance, a Fano profile whose asymmetry flips sign between phases; observing only smooth, continuous changes or no change at all would refute the marker.","tokens_in":17870,"feed_emoji":"📡","tokens_out":6740,"duration_ms":68142,"temperature":0.7,"pith_summary":"The paper proposes that infrared spectroscopy can serve as a bulk, contact-free marker of the topological phase transition in two-dimensional quantum spin Hall insulators. Using first-principles calculations for germanene and jacutingaite, it shows that the in-plane Born effective charges—the quantities setting the strength of infrared phonon absorption—are nearly zero in the topological phase and jump discontinuously to values of order 1–2.5 when an applied perpendicular electric field drives the system into the trivial phase. As a result, the phonon part of the optical conductivity changes abruptly across the transition: in germanene the in-plane peak almost disappears in the topological phase, while in jacutingaite several modes change intensity drastically. The paper also shows that including dynamical electron-phonon effects does not erase the marker: when the gap is comparable to the phonon frequency, the resonance becomes a Fano line whose shape and sign differ between the two phases.","feed_headline":"Infrared peaks tell topological from trivial 2D insulators","feed_subtitle":"A perpendicular electric field flips the phase, and phonon absorption changes abruptly—an optical test for quantum spin Hall states.","key_machinery":"The load-bearing object is the anomalous part of the Born effective charge $Z^{*,\\mathrm{an}}_{s,\\alpha\\beta}$, a Berry-phase quantity that measures the electronic polarization induced when an ion is displaced. In the low-energy Kane-Mele model it collapses to a topological identity, $$$Z^{{*,\\mathrm{an}}$}_{s,xx}=(1-|Z_2|)\\,\\xi\\, l_s\\, \\mathrm{sgn}(E_z)\\, A/\\pi,$$ so it vanishes in the topological phase ($|Z_2|=1$) and jumps to a finite value in the trivial phase ($|Z_2|=0$). The electron-phonon coupling enters the model as a gauge field, which is what ties this charge to the Berry curvature. The second piece of machinery is the frequency-dependent generalization: in the resonant regime the ionic conductivity takes the Fano form of Eq. (10) with strength $P$ and asymmetry parameter $q$ set by the complex dynamical effective charge $Z^*(\\omega_{\\mathrm{ph}})$, which is what turns the static jump into distinguishable line shapes.","core_discovery":"The paper establishes that the in-plane Born effective charges—the quantities that control how strongly lattice vibrations absorb infrared light—are effectively zero in the topological phase and jump discontinuously to large values (about 2 in germanene, up to about 2.5 on Hg in jacutingaite) when an applied perpendicular electric field drives the system through the transition into the trivial phase. This means the ionic contribution to the optical conductivity changes abruptly at the transition. In germanene, the in-plane phonon resonance nearly disappears in the topological phase and reappears strongly in the trivial phase; in jacutingaite, nine infrared-active phonon modes show large intensity changes, with the Hg-driven mode exhibiting a huge jump. The paper further argues that dynamical electron-phonon effects, which become relevant when the gap and phonon frequency are comparable, smooth but do not destroy the marker: the resonance then becomes a Fano line whose strength and asymmetry differ between the two phases, keeping the phases distinguishable.","pith_inferences":["The same charge-jump mechanism likely applies to other electric-field-tunable Kane-Mele-type monolayers such as silicene and stanene, where the size of the jump should scale with the electron-phonon coupling parameter.","A natural extension is a pump-probe measurement: because the topological transition is field-driven and the marker is optical, one could switch the phase on fast timescales and watch the infrared peak appear or disappear, offering an optical readout for a topological transistor.","The dynamical Fano rounding implies a practical guideline the authors do not state: for small-gap materials the largest contrast is achieved away from exact resonance, while at resonance the phase is read from the sign of the Fano asymmetry rather than from peak intensity.","If confirmed, infrared spectroscopy could be used as a screening tool for predicted two-dimensional topological insulators, since computing Born effective charges is cheaper than simulating edge transport."],"forward_implications":["Infrared spectroscopy becomes a bulk probe of the $Z_2$ transition, usable in the same field-effect geometry proposed for topological transistors.","In germanene the contrast is stark: the in-plane $E$ phonon peak is essentially absent in the topological phase and appears strongly in the trivial phase.","In jacutingaite, nine phonon modes show detectable changes, with the Hg-driven mode II displaying a huge intensity jump, so the spectrum identifies the phase even for comparable gaps.","Near resonance, dynamical effects convert the phonon resonance into a Fano profile; the sign and shape of the profile distinguish the phases even when the static jump is smoothed.","Because phonon frequencies themselves barely change across the transition, the effect is robust to structural details and should be reproducible in different samples."],"supporting_citations":[{"why":"Introduces the Kane-Mele model of the quantum spin Hall state that the paper uses as its low-energy framework.","marker":"[1]"},{"why":"Provides the experimental realization of germanene as a field-tunable QSHI, giving the measured gap used in the dynamical calculations.","marker":"[10]"},{"why":"Establishes the Kane-Mele description of monolayer jacutingaite and the electric-field-driven transition on which the ab initio results build.","marker":"[21]"},{"why":"Derives the topological formula for the anomalous Born effective charges in the Haldane and Kane-Mele models, including the gauge-field electron-phonon coupling that is the quantitative backbone of the marker.","marker":"[50]"},{"why":"Supplies the TDDFT expression for dynamical effective charges and the framework for phonon infrared spectra, including giant effective charges in gapped graphene.","marker":"[51]"},{"why":"Provides the first-principles theory of infrared vibrational spectroscopy with phonons coupled to electronic excitations, used for the Fano treatment.","marker":"[52]"},{"why":"Predicts and explains charged-phonon Fano lineshapes in graphene systems, the analogue used for the resonant phonon profiles here.","marker":"[64]"}],"fun_headline_variants":[],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The central prediction depends on the low-energy Kane-Mele model, with its gauge-field form of electron-phonon coupling, quantitatively reproducing the real frequency-dependent Born effective charges at the phonon resonance in germanene and jacutingaite; if that model misses details of the actual coupling, the predicted shape and intensity contrasts could change.","fun_headline_variants_meta":{"error":"Client error '402 Payment Required' for url 'https://api.deepseek.com/chat/completions'\nFor more information check: https://developer.mozilla.org/en-US/docs/Web/HTTP/Status/402"},"cache_creation_input_tokens":0},"created_at":"2026-08-07T15:37:06.530431+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the infrared reflectance of a gated germanene or jacutingaite monolayer while sweeping a perpendicular electric field through the critical value. The claim predicts an abrupt appearance of the in-plane phonon peak in germanene and a discontinuous reshuffling of mode intensities in jacutingaite at the transition, and, near resonance, a Fano profile whose asymmetry flips sign between phases; observing only smooth, continuous changes or no change at all would refute the marker.","supporting_citations":[{"cited_title":"Quantum spin hall states and topological phase transition in germanene,","cited_arxiv_id":null,"evidence_quote":"Provides the experimental realization of germanene as a field-tunable QSHI, giving the measured gap used in the dynamical calculations."},{"cited_title":"Prediction of a large-gap and switchable kane-mele quantum spin hall insulator,","cited_arxiv_id":null,"evidence_quote":"Establishes the Kane-Mele description of monolayer jacutingaite and the electric-field-driven transition on which the ab initio results build."},{"cited_title":"Nearly quantized born effective charges as probes for the topological phase transition in the haldane and kane-mele models,","cited_arxiv_id":null,"evidence_quote":"Derives the topological formula for the anomalous Born effective charges in the Haldane and Kane-Mele models, including the gauge-field electron-phonon coupling that is the quantitative backbone of the marker."},{"cited_title":"Giant effective charges and piezoelectricity in gapped graphene,","cited_arxiv_id":null,"evidence_quote":"Supplies the TDDFT expression for dynamical effective charges and the framework for phonon infrared spectra, including giant effective charges in gapped graphene."},{"cited_title":"First-principles theory of infrared vibrational spectroscopy of metals and semimetals: Application to graphite,","cited_arxiv_id":null,"evidence_quote":"Provides the first-principles theory of infrared vibrational spectroscopy with phonons coupled to electronic excitations, used for the Fano treatment."},{"cited_title":"Charged-phonon theory and fano effect in the optical spectroscopy of bilayer graphene,","cited_arxiv_id":null,"evidence_quote":"Predicts and explains charged-phonon Fano lineshapes in graphene systems, the analogue used for the resonant phonon profiles here."}],"review_version":1}