{"id":"6a6b3e5f-9166-402a-bbad-0c2a0a52af6f","arxiv_id":"2607.07199","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":3,"one_line_summary":"Circularly polarized light on Bi₂Se₃ generates four pairs of Floquet-Weyl points at one-photon resonance, with hole doping revealing a sharp anomalous Hall conductivity peak.","lead":"Shining circularly polarized light on the topological insulator Bi₂Se₃ creates Weyl points — special band crossings — through a one-photon resonance mechanism. This matters because it shows how to turn an ordinary insulator into a Weyl semimetal using light, with a characteristic threefold pattern dictated by crystal symmetry.","discovery_kind":"unclear","skeptic_critique":{"model":"glm-5.2","headline":"The sudden approximation (Eq. 11) for the nonequilibrium distribution is the weakest link: the Weyl-point topology is robust, but the 'sharp AHC peak' claim depends entirely on an equilibrium-derived occupation of Floquet states with no relaxation or dephasing.","rationale":"The reader correctly identified the sudden approximation as the weakest assumption. The Weyl-point topology (part 1 of the claim) is analytically and numerically well-supported and does not depend on the distribution function. The AHC peak claim (part 2) does depend on Eq. 11, and the paper does not quantify robustness to dissipation. This is a genuine soft spot but not a fatal one: the sudden approximation is standard in the Floquet literature, the paper is transparent about it, and the topological phase diagram and Weyl-point structure stand independently of the transport calculation. The CONDITIONAL verdict is appropriate — the paper substantively advances the field, but the AHC predictions await validation through more realistic nonequilibrium modeling or experiment. No adjustment to the reader's verdict is needed.","tokens_in":20781,"tokens_out":2212,"duration_ms":106408,"concrete_test":"Recompute the μ-dependent AHC in Fig. 6 using a Floquet-Green's function or Lindblad approach with a phenomenological dephasing rate γ corresponding to realistic scattering times τ = 100–500 fs in Bi₂Se₃. If the peak at μ ≈ −Ω/2 survives with height reduced by less than ~50% and width broadened by less than ~0.1 eV, the claim is robust. If the peak is washed out or shifted by more than ~0.05 eV, the experimental detectability claim needs revision.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's strongest claim has two parts: (1) four pairs of Floquet-Weyl points emerge with a C₃z-symmetric splitting pattern, and (2) hole doping to μ ≈ −Ω/2 yields a sharp AHC peak directly associated with these Weyl points. Part (1) is analytically sound — the effective two-band Hamiltonian (Eq. 4, derived in Appendix C via canonical transformation) and the Weyl-point positions (Eqs. 6–8) follow directly from the lattice symmetry, and the topological charges are verified numerically via Berry flux. This part does not depend on the distribution function and is robust.\n\nPart (2) is where the concern lies. The AHC (Eq. 9) is computed using the sudden approximation for f_n (Eq. 11), which populates Floquet eigenstates according to their overlap with equilibrium eigenstates |α⟩ at E₀ = 0. This assumes the system instantaneously projects onto Floquet eigenstates with no subsequent relaxation, dephasing, or reservoir coupling. In real driven Bi₂Se₃, electron-electron and electron-phonon scattering, as well as coupling to substrate/bath modes, will redistribute occupations on timescales of ~100–500 fs. The paper acknowledges this qualitatively (citing Refs. 20–22) but does not quantify how robust the peak at μ ≈ −Ω/2 is to any finite scattering rate. Since the peak's sharpness is a central part of the claim and is what makes it experimentally distinguishable from the broad HFE background (Fig. 7), this is load-bearing: if dissipation smears the peak significantly, the practical route to detecting the Weyl points via AHC weakens considerably. The sign-reversal feature around E₀ ≈ 6 MV/cm (Fig. 5) is similarly distribution-dependent.","agreement_with_reader":"agree"},"referee_report":{"model":"glm-5.2","summary":"This manuscript investigates Floquet-Weyl point generation in Bi2Se3-type three-dimensional topological insulators driven by circularly polarized light at one-photon resonance. The authors show that four pairs of Floquet-Weyl points emerge in the intermediate-frequency regime through hybridization between the original valence and photon-shifted conduction bands, with a characteristic threefold splitting pattern reflecting the C3z crystalline symmetry. They construct a topological phase diagram (gapped, Floquet-Weyl, Floquet-Chern states), derive an effective two-band Hamiltonian whose Weyl-point positions are determined analytically, and calculate the photo-induced anomalous Hall conductivity, showing that hole doping to mu ~ -Omega/2 yields a sharp peak associated with the Weyl points.","tokens_in":21476,"tokens_out":1271,"duration_ms":121097,"significance":"The work extends one-photon-resonant Floquet-Weyl physics from 3D Dirac semimetals (Hirai et al., Ref. 39) to spin-orbit-coupled topological insulators, which is a meaningful broadening of the mechanism. The analytical derivation of the effective two-band Hamiltonian (Eq. 4, Appendix C) is a genuine strength: the Weyl-point positions (Eqs. 6-8) follow from the lattice symmetry and Floquet Hamiltonian structure without fitting to the target result, and the threefold splitting pattern is a falsifiable, symmetry-dictated prediction distinct from the isotropic continuum double-Weyl result. The identification of hole doping as a practical route to expose the Weyl-point contribution to the AHC is a concrete, experimentally testable proposal, especially given that Ca substitution in Bi2Se3 can shift the Fermi level by ~0.3-0.4 eV (Ref. 55). The comparison with the high-frequency expansion (Appendix B) to disentangle resonant from off-resonant contributions is also valuable.","major_comments":[{"comment":"The AHC results (Figs. 5-6) and the claim of a 'sharp peak' at mu ~ -Omega/2 depend on the sudden approximation for the nonequilibrium distribution function f_n (Eq. 11), which populates Floquet eigenstates according to their overlap with equilibrium eigenstates without relaxation, dephasing, or reservoir coupling. The paper acknowledges this limitation qualitatively (citing Refs. 20-22) but does not quantify how robust the peak is to any finite scattering rate. Since the peak's sharpness relative to the broad HFE background (Fig. 7) is what makes it experimentally distinguishable, this is load-bearing for the transport claim. The authors should either (i) estimate the scattering timescales in Bi2Se3 and argue that the Floquet steady state is reached before significant relaxation, or (ii) show, even at a crude level (e.g., a phenomenological broadening parameter in the Kubo formula), how","section":null},{"comment":"The topological phase diagram in Fig. 4(a) shows three regions, but the criteria for the boundaries between the gapped, Floquet-Weyl, and Floquet-Chern states are described only qualitatively in the text (Sec. III C). The boundary between the Floquet-Weyl and Floquet-Chern states is stated to occur when Weyl points 'reach the BZ boundary and pair-annihilate,' but it is unclear whether this is determined by the Weyl points reaching a specific high-symmetry plane (e.g., the Z point) or by a Lifshitz-type transition. A more precise definition of the phase boundaries, ideally with the critical Omega or E0 values for the representative cuts in Figs. 4(b,c), would strengthen the phase diagram's utility.","section":null}],"minor_comments":[{"comment":"In Fig. 4(a), the color scale for Delta_k_z appears to saturate at the BZ boundary, but the distinction between Delta_k_z = 2*pi/c (Floquet-Chern) and Delta_k_z = 0 (gapped) is not visually clear in the dark-colored gapped region. A different colormap or an inset magnifying the small-Delta_k_z region would help.","section":null},{"comment":"The sign reversal of sigma_xy around E0 ~ 6 MV/cm (Sec. IV A) is attributed to the competition between positive off-resonant and negative resonant Berry-curvature contributions, but the physical origin of the negative sign of the resonant contribution is not explained. A brief comment on why the Berry curvature near the reduced gap is negative would improve the discussion.","section":null},{"comment":"In Eq. (11), the sum over alpha runs over the 0-photon bands in equilibrium, but the temperature T and chemical potential mu appear in the Fermi-Dirac factor. The text states T=0 and mu=0 for Fig. 5, but for Fig. 6 (mu dependence), it should be clarified whether the distribution function is re-evaluated at each mu or whether mu enters only the Kubo formula (Eq. 9) via the Berry curvature integral.","section":null},{"comment":"The phrase 'intermediate-frequency regime' is used throughout (e.g., abstract, Sec. III) without a precise definition relative to the band gap. A brief statement of the frequency range (e.g., Omega comparable to the gap) would help readers from the Floquet literature.","section":null},{"comment":"Reference [25] appears to have incomplete publication details (Nat. Mater., page numbers listed as '1'). Please update with final publication information if available.","section":null}],"recommendation":"minor_revision","confidential_remarks":"The reader's concern about the sudden approximation is valid but should not be over-weighted: the Weyl-point topology (the paper's primary contribution) is independent of f_n, and the AHC peak is a secondary, experimentally-motivated result. The paper is appropriate for the journal's scope. The main improvement needed is a more quantitative discussion of the transport claim's robustness, which can likely be addressed within the manuscript's existing framework without new calculations."},"author_rebuttal":null,"desk_editor":{"model":"glm-5.2","letter":"The main thing to know: this paper extends one-photon-resonant Floquet-Weyl physics from 3D Dirac semimetals (Hirai et al. 2024) to Bi2Se3, a topological insulator. The genuinely new result is the threefold Weyl splitting pattern — one node with charge −1 and three with charge +1 per half-BZ, reflecting C3z symmetry — which differs from the double-Weyl splitting in the isotropic continuum model. The effective two-band Hamiltonian (Eq. 4, derived carefully in Appendix C via canonical transformation) gives analytic Weyl-point positions (Eqs. 6–8) that match the numerical Berry-flux calculations. The topological phase diagram tracking pair creation, motion, and annihilation is well done. This part of the paper is parameter-free given the tight-binding model and is internally consistent. Credit earned there. The hole-doping proposal — shifting μ to −Ω/2 to place Weyl points at the Fermi level — is a practical and experimentally relevant idea, since Ca substitution in Bi2Se3 already achieves the needed ~0.3 eV shift. The HFE comparison in Appendix B, showing the AHC peak is absent in the off-resonant model, is a useful control. Now the soft spot. The AHC calculations use the sudden approximation (Eq. 11): Floquet eigenstates are populated by overlap with equilibrium eigenstates, with no relaxation, dephasing, or reservoir coupling. The paper acknowledges this qualitatively (citing Refs. 20–22) but never quantifies robustness. The sharpness of the peak at μ ≈ −Ω/2 and the sign reversal around E0 ≈ 6 MV/cm both depend on this distribution. Real experiments on Bi2Se3 will have electron-phonon and electron-electron scattering on 100–500 fs timescales that could smear the peak. This is a load-bearing assumption for the transport claims, though not for the topological structure itself. The reader's assessment is about right. The Weyl-point derivation is sound and novel; the AHC predictions need a grain of salt. The one-photon truncation is standard but its validity domain could be better characterized. This is a solid paper for Floquet engineering and topological materials researchers. The analytic work justifies a serious referee, who should push for at least a qualitative discussion of how dissipation would affect the AHC peak.","headline":"Solid Floquet-Weyl topology in Bi2Se3; the AHC peak claim leans on a sudden approximation that may not survive dissipation.","tokens_in":21976,"tokens_out":595,"would_cite":true,"duration_ms":89739,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["71.70.Ej","73.43.-f","78.20.Bh"],"model":"glm-5.2","headline":"Circular light creates Weyl points in Bi₂Se₃ at one-photon resonance","keywords":["Floquet engineering","Weyl semimetal","topological insulator","Bi₂Se₃","anomalous Hall effect","circularly polarized light","one-photon resonance","Berry curvature"],"falsifier":"If the anomalous Hall conductivity peak at μ ≈ −Ω/2 is absent or uncorrelated with the Weyl-point quasienergy in hole-doped Bi₂Se₃ under resonant circularly polarized light, the claim that resonant Weyl points produce a directly observable transport signal would fail.","tokens_in":21032,"feed_emoji":"💡","tokens_out":1412,"duration_ms":235025,"temperature":0.7,"pith_summary":"This paper claims that shining circularly polarized light on the three-dimensional topological insulator Bi₂Se₃, at a photon energy tuned to a one-photon resonance between the valence and conduction bands, creates four pairs of Weyl points — gapless band crossings that act as monopoles of Berry curvature in momentum space. The mechanism is the resonant hybridization between the original valence band and a photon-shifted copy of the conduction band, which occurs at an intermediate driving frequency too low for the usual high-frequency approximation to apply. Because Bi₂Se₃ has threefold rotational symmetry (C₃z), the Weyl points do not appear as simple double-Weyl nodes (as they would in an isotropic continuum model) but instead split into a characteristic pattern: one node with topological charge −1 on the rotation axis and three nodes with charge +1 arranged around it, in each half of the Brillouin zone. The authors construct a topological phase diagram showing gapped, Floquet-Weyl, and Floquet-Chern regimes as the light field and photon energy are varied. They further calculate the anomalous Hall conductivity and show that when the chemical potential is shifted by hole doping to the resonant quasienergy (approximately minus half the photon energy), a sharp peak in the Hall conductivity appears, directly attributable to the emergent Weyl points. This peak is absent in the high-frequency expansion, confirming its resonant origin.","feed_headline":"Circular light creates Weyl points in Bi₂Se₃ at one-photon resonance","feed_subtitle":"Four pairs of Floquet-Weyl nodes with a threefold symmetry pattern emerge in a 3D topological insulator, and hole doping reveals a predicted","key_machinery":"The one-photon-resonant Floquet Hamiltonian (Eq. 3), an 8×8 matrix coupling the 0-photon and −1-photon sectors; the effective 2×2 Hamiltonian (Eq. 4) obtained by projecting onto the two degenerate resonant states, whose off-diagonal terms contain both quadratic (q²₋) and linear (q±) in-plane momentum dependence, with the latter being symmetry-allowed by C₃z and responsible for splitting the double-Weyl point; the topological phase diagram in the (E₀, Ω) plane; and the Kubo formula for anomalous Hall conductivity with a sudden-approximation distribution function.","core_discovery":"The central discovery is that the crystalline C₃z symmetry of Bi₂Se₃ imprints a distinctive threefold splitting pattern on Floquet-Weyl points created at one-photon resonance: instead of the double-Weyl nodes (charge ±2) predicted by isotropic continuum models, the lattice model produces one node of charge −1 on the rotation axis and three nodes of charge +1 around it, per half of the Brillouin zone, totaling four pairs. This splitting is driven by linear-in-momentum terms (λ₁τ q±) in the effective two-band Hamiltonian, which are forbidden by continuous rotational symmetry but allowed by threefold crystal symmetry. The authors show that this resonant mechanism — distinct from off-resonant, H","pith_inferences":["The threefold splitting pattern is a direct crystallographic fingerprint: observing four pairs of Weyl points with the predicted 1:3 arrangement in momentum space would confirm that the resonant mechanism, rather than off-resonant band deformation, is operative.","The sign reversal of the anomalous Hall conductivity around E₀ ≈ 6 MV/cm, driven by Berry-curvature redistribution as the parent TI gap narrows, could serve as an independent diagnostic of the crossover from off-resonant to resonant regimes.","If dissipation and heating are strong enough to thermalize the distribution function away from the sudden approximation, the sharp AHC peak at μ ≈ −Ω/2 could broaden significantly, but the underlying Weyl-point topology in the Floquet band structure would persist — the band topology is a property of the Hamiltonian, not the distribution."],"forward_implications":["Hole-doped Bi₂Se₃ (already achieved experimentally via Ca substitution, shifting the Fermi level by ~0.3–0.4 eV) could serve as a direct platform for observing one-photon-resonant Floquet-Weyl physics through anomalous Hall measurements.","The photon energy controls the quasienergy of the Weyl points, so different resonant topological states can be probed within a single material by simply changing the laser frequency.","The symmetry-adapted splitting mechanism generalizes to other spin–orbit-coupled materials with different point-group symmetries, potentially producing Floquet topological defects with non-standard charge configurations.","Fermi-arc surface states connecting the surface projections of the resonant Weyl points are a natural experimental target for angle-resolved photoemission spectroscopy.","Replica-replica hybridization (between different Floquet-replica bands, not just original-replica) could provide additional Floquet-Weyl phases with more direct experimental signatures."],"fun_headline_variants":["Circular light splits Floquet-Weyl nodes along C3 symmetry in Bi2Se3","One-photon resonance yields four pairs of Floquet-Weyl nodes in Bi2Se3","Threefold crystal symmetry imprints splitting pattern on Floquet-Weyl points","Hole doping exposes anomalous Hall response from Floquet-Weyl nodes in Bi2Se3","Resonant Floquet-Weyl nodes in Bi2Se3 follow lattice symmetry not isotropic models"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The sudden approximation for the nonequilibrium electron distribution assumes that Floquet eigenstates are populated according to their overlap with equilibrium eigenstates, without accounting for relaxation, heating, or coupling to reservoirs. This determines the predicted anomalous Hall conductivity values and the sharpness of the doping-induced peak, which real experiments — with dephasing and dissipation — could smear or shift.","fun_headline_variants_meta":{"raw":{"variants":["Circular light splits Floquet-Weyl nodes along C3 symmetry in Bi2Se3","One-photon resonance yields four pairs of Floquet-Weyl nodes in Bi2Se3","Threefold crystal symmetry imprints splitting pattern on Floquet-Weyl points","Hole doping exposes anomalous Hall response from Floquet-Weyl nodes in Bi2Se3","Resonant Floquet-Weyl nodes in Bi2Se3 follow lattice symmetry not isotropic models"]},"model":"glm-5.2","effort":"low","cost_usd":0.0,"raw_usage":{"total_tokens":708,"prompt_tokens":606,"completion_tokens":102,"prompt_tokens_details":null},"tokens_in":606,"tokens_out":102,"duration_ms":44608,"temperature":1.0,"reasoning_tokens":null,"cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-09T17:27:59.725725+00:00","model_set":{"reader":"glm-5.2"},"falsifier":"If the anomalous Hall conductivity peak at μ ≈ −Ω/2 is absent or uncorrelated with the Weyl-point quasienergy in hole-doped Bi₂Se₃ under resonant circularly polarized light, the claim that resonant Weyl points produce a directly observable transport signal would fail.","supporting_citations":[],"review_version":1}