{"id":"e0334ab2-48b2-4b71-9403-efbba4ced536","arxiv_id":"2607.20000","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"In discrete Kekulé-modulated photonic lattices, the initial modulation phase shifts the Dirac-vortex mode center and, with a sublattice-antisymmetric perturbation, tunes its frequency across nearly the full bandgap.","lead":"This paper shows that in a discrete photonic lattice with constant-amplitude Kekulé modulation, the global initial phase of the modulation, normally a redundant gauge choice, physically moves the vortex mode's center. Adding a sublattice-antisymmetric perturbation converts this motion into continuous frequency tuning across most of the topological bandgap, demonstrated in simulation and microwave experiments.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Quantitative frequency-tuning prediction rests on a fitted displacement r0 and hand-set phase ϕc, with no microscopic derivation from the discrete lattice; the model is thus partly circular.","rationale":"I read the paper in good faith and find the core physical insight compelling: in the α=0 constant-amplitude regime, the discrete lattice breaks the continuous rotational symmetry that makes ϕ0 a pure gauge in the continuum Jackiw–Rossi model, and the observed center displacement and frequency response are consistent with that idea. The experimental data, though limited to four phases and without error bars, show a clear resonance shift that matches the sinusoidal-like trend. My stress-test pass therefore does not overturn the reader's conditional verdict. However, the weakest point is indeed the quantitative model: Eq. (8) postulates a rigid displacement, Eq. (10) uses r0 fitted to simulations, and ϕc is chosen by hand. The manuscript even describes the CUC as a 'lever' without deriving its effect. This is not an internal inconsistency, but it means the model's predictive power is limited and the agreement in Fig. 3(d) is partially circular. A first-principles derivation of rc(ϕ0) from the discrete lattice would settle whether the displacement picture is correct and whether r0 is robust. The reader flagged the same assumption, so I agree. No new concern beyond the reader's weakest assumption was found.","tokens_in":9284,"tokens_out":6414,"duration_ms":71500,"concrete_test":"Independently derive rc(ϕ0) from a tight-binding or coupled-mode model of the discrete Kekulé lattice, including the central-unit-cell phase ϕc, without fitting to full-wave simulations. Compare the predicted trajectory and r0 with the fitted circle in Fig. 3(b). Then use the derived r0 to recompute Eq. (10) for ΔR = 0.3 mm (an intermediate perturbation not used in the paper) and compare with a fresh full-wave simulation. If the derived radius deviates by more than ~20% or the predicted frequency shift disagrees with simulation, the fitted-parameter model is substantively circular and the quantitative tuning claim is not independently validated.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—that initial phase ϕ0 becomes physically observable and can continuously tune the DVM frequency—is qualitatively supported by simulations and experiments. However, the quantitative prediction Eq. (10) depends critically on Eq. (8), which models all discreteness effects as a rigid displacement of the ideal Jackiw–Rossi wavefunction by rc(ϕ0). The trajectory rc(ϕ0) in Fig. 3(b) is not derived from the discrete lattice Hamiltonian; it is extracted from full-wave simulations and fitted to a circle of radius r0. Eq. (10) is directly proportional to r0, and the stated agreement in Fig. 3(d) therefore partly validates a fit against the same class of simulations used to obtain r0. Furthermore, the central-unit-cell phase ϕc is assigned by hand (fixed to 0° to maximize the effect), and the paper states that this phase 'dictates the radius of this motion' via the CUC. No theory predicts r0 or the dependence on ϕc from the microscopic lattice parameters. The derivation of Eq. (10) is relegated to SI Note 5, which is not included, making the key step unverifiable from the manuscript alone. If the rigid-displacement form is only approximate—or if r0 differs in the presence of the sublattice-antisymmetric perturbation—the claimed quantitative agreement would be fortuitous.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports that the global initial phase ϕ₀ of the Kekulé modulation, which is a gauge degree of freedom in the continuum Jackiw–Rossi model, becomes physically observable in discrete lattices when the modulation profile approaches a constant amplitude (α→0, Eq. (1)). The authors show that the energy-weighted mode center r_c of the Dirac-vortex mode shifts with ϕ₀. By introducing a sublattice-antisymmetric radius perturbation (Eq. (4)), they convert this displacement into a continuous, sinusoidal-like frequency response spanning nearly the entire topological bandgap. Full-wave simulations and four-phase microwave experiments, including real-space field maps and FFT spectra, support the qualitative behavior. A 'revised continuum model' (Eqs. (7)–(10)) is proposed, in which the discreteness effect is absorbed into a rigid displacement r_c(ϕ₀) of the ideal wavefunction, with r_c fitted to a circular trajectory of radius r₀; the resulting frequency shift Δf ∝ r₀ sin ϕ₀ is compared with simulations and experiments.","tokens_in":9710,"tokens_out":13274,"duration_ms":170055,"significance":"The work identifies a concrete mechanism by which lattice discreteness goes beyond the continuum Jackiw–Rossi description and promotes a formerly redundant phase variable into a useful tuning knob. If supported by a quantitative theory, this would be a valuable contribution to reconfigurable topological photonics. The paper combines full-wave simulations, a simplified semi-analytic model, and microwave experiments, which is commendable. However, the predictive power of the semi-analytic model is limited because its key input, the displacement radius r₀, is extracted from the same simulations it is later compared with. The claims of quantitative agreement should therefore be calibrated against this limitation.","major_comments":[{"comment":"The quantitative validation is partly circular: the prediction of Eq. (10) is proportional to r₀, which is the radius of a circle fitted to the mode-center trajectory extracted from full-wave simulations (Fig. 3b). The rigid-displacement assumption in Eq. (8) and the circular form of the trajectory are not derived from the discrete lattice Hamiltonian. Thus, the 'excellent agreement' in Fig. 3(d) is substantially a refitting of the same simulations. Please provide a microscopic derivation or at least a scaling argument for r₀(ϕ_c, α, d₀) from a lattice model, or explicitly state that Eq. (10) is a phenomenological parametrization rather than an ab initio prediction. Also report the fit residuals for the circular trajectory.","section":"§3, Eq. (10), Fig. 3(b,d)"},{"comment":"The central unit cell (CUC) phase ϕ_c is introduced in §1 as a 'lever' controlling the radius of the mode-center motion, and then fixed to ϕ_c = 0° in §3 'to maximize the mode-center motion'. This means that the amplitude of the predicted tuning in Eq. (10) depends on a hand-chosen, explicitly optimized parameter. Without a measurement or scaling of r₀(ϕ_c), the tuning range is not predicted independently of this choice. Please provide numerical scans over ϕ_c to demonstrate how the lever works and to show that the main conclusions are robust to this choice.","section":"§1 and §3 (CUC phase ϕ_c)"},{"comment":"The derivation of Eq. (10) is deferred to SI Note 5, which was not included with this manuscript. The key step is therefore not verifiable from the manuscript alone. In addition, the printed Eq. (10) appears to contain a factor 'sgn(sin ϕ₀)' inside an integral, which would produce a non-smooth cusp at ϕ₀ = 0 and π, inconsistent with the smooth sinusoidal curves shown in Fig. 3(d). Please include the full derivation in the main text or in the SI, define all integration variables, and clarify the smoothness of the result at ϕ₀ = 0 and π.","section":"Eq. (10) / SI Note 5"}],"minor_comments":[{"comment":"The α→0 limit is not explicitly defined. The displayed tanh factor is singular at α = 0 unless the limit is taken carefully; the text says 'constant profile', but the precise limiting form should be stated.","section":"Eq. (1)"},{"comment":"Please quantify the tuning range, e.g., as the ratio of the maximum frequency shift to the width of the topological bandgap of the unperturbed lattice. Also clarify whether 'bandgap' refers to the unperturbed lattice or the lattice with ΔR ≠ 0.","section":"§2, 'nearly the entire bandgap'"},{"comment":"For ΔR = 0.5 mm, deviations between the semi-analytic result and full-wave simulations appear substantial over part of the phase range. Please provide a residual plot or error bars, and discuss whether the deviations arise from higher-order terms or from a change in r_c when the perturbation is finite.","section":"Fig. 3(d)"},{"comment":"The value of β used in the fabricated samples is not stated. Since the simulations fix β = 0.01, please specify the experimental β or comment on the sensitivity of the measured response to fabrication details of the transition region.","section":"§4, experimental methods"},{"comment":"Reference [32] is cited to support the claim that changing ϕ₀ shifts the Kekulé bonding texture and thereby affects the mode distribution, but that reference concerns fractional charge and does not directly address mode-center motion in photonic crystals. Please consider citing a more directly relevant lattice model.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The main concern is the phenomenological nature of the quantitative model, which weakens the claimed predictive power. If the authors can provide a microscopic derivation of r₀ or explicitly label the model as an effective parametrization, the paper will be suitable for publication. Please ensure that SI Note 5 is included in the submission package; it is essential for verifying the central derivation."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line up front: this paper shows something real — in discrete Kekulé lattices the initial phase is not a gauge redundancy; it moves the Dirac-vortex mode center, and with a sublattice-antisymmetric perturbation that motion becomes a sinusoidal frequency shift covering nearly the whole bandgap. The four-phase microwave experiment and the COMSOL simulations are consistent, and the field maps plus FFTs confirm a coherent K/K′ superposition throughout. That is a genuine advance over the continuum Jackiw-Rossi picture and beyond the qualitative observation in Ref. [32].\n\nWhat is new is the tuning mechanism and the revised continuum model. The model is honest: it takes the mode-center trajectory as input rather than deriving it. That is also its limit. Equation (10) is proportional to r0, a radius fitted to the displacement extracted from the same class of full-wave simulations, so the agreement in Fig. 3(d) is to some extent a consistency check, not an independent prediction. The hand-set central-unit-cell phase φc and the missing SI Note 5 make it harder to verify the derivation. The experimental points have no error bars and only four phases. None of this guts the central claim, but it does mean the quantitative part is semi-phenomenological.\n\nThe paper deserves a serious referee. It is a solid, well-executed advance in topological photonics, and the experimental demonstration grounds the claim. A referee should ask for SI Note 5, error estimates, and a discussion of whether r0 can be estimated from lattice parameters. The authors are not overclaiming; they explicitly say the displacement is extracted from simulations. I would send it out.","headline":"Discreteness turns a gauge phase into a real frequency-tuning knob for Dirac-vortex cavities, with an honest but partly fitted quantitative model; the experimental demonstration is solid and deserves peer review.","tokens_in":10086,"tokens_out":3196,"would_cite":true,"duration_ms":34009,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["42.70.Qs"],"model":"deepseek-v4-flash","headline":"This paper shows that in discrete lattices the global initial phase of a Kekulé modulation—redundant in the continuum Jackiw–Rossi model—becomes observable and drives a displacement of the Dirac-vortex mode center, which can be converted in","keywords":["Dirac-vortex modes","Kekulé modulation","Jackiw-Rossi model","photonic crystals","topological bandgap","frequency tuning","mode center displacement","gauge redundancy"],"falsifier":"Measure the mode-center trajectory in full-wave simulations for a central-cell phase different from 0° (e.g., 90°) and compare the radius and the resulting frequency shift to the model's prediction; if the trajectory is not circular or the tuning range changes in a way not captured by the rigid-displacement formula, the ansatz is falsified. Alternatively, compute the mode displacement directly from the discrete lattice Hamiltonian and check whether it matches the fitted circle.","tokens_in":9239,"feed_emoji":"🌀","tokens_out":7251,"duration_ms":64959,"temperature":0.7,"pith_summary":"The paper establishes that in discrete lattices the global initial phase of the periodic Kekulé modulation, which is a redundant gauge degree of freedom in the continuum Jackiw–Rossi model, becomes physically observable when the modulation amplitude is constant (α = 0). In this regime the phase drives a rotation-like displacement of the Dirac-vortex mode center by up to a lattice constant, comparable to the mode's own radius. By adding a sublattice-antisymmetric perturbation across a mirror axis, the paper converts this spatial motion into a continuous, approximately sinusoidal frequency shift of the mode across nearly the entire topological bandgap. A revised continuum model, which inserts a phase-dependent rigid displacement into the ideal zero-mode wavefunction, predicts this spectral response and matches both full-wave simulations and microwave measurements. The result turns the initial phase from an inert choice into a practical control knob for reconfigurable photonic devices.","feed_headline":"Rotating a hidden phase retunes vortex light modes","feed_subtitle":"Rotating the initial phase sweeps the mode frequency across nearly the entire bandgap.","key_machinery":"The load-bearing ansatz is a displaced Jackiw–Rossi zero-mode wavefunction: Ψ(φ0, r) = Ψ0(r − rc(φ0)), where rc (energy-density-weighted center) moves on a fitted circular trajectory of radius r0 as φ0 varies. This displacement, driven by the central unit cell's fixed Kekulé phase φc, converts the gauge phase into a physical perturbation probe. Evaluated against the sublattice-antisymmetric staggered mass mΔ tanh(y/β) sgn(y) σz⊗I in first-order perturbation theory, it yields a closed-form frequency shift Δf(1)(φ0) proportional to r0 and roughly to sin φ0, matching the simulated and measured tuning.","core_discovery":"The ideal Jackiw–Rossi model treats the initial phase φ0 as a gauge choice with no observable effect; the paper shows this breaks down in discrete lattices in the constant-amplitude Kekulé regime. There, lattice discreteness makes the initial phase physically felt as a lattice-scale displacement of the DVM center, which traces a phase-dependent trajectory around the vortex core. With a sublattice-antisymmetric perturbation, this displacement causes the mode to sample contrasting sublattice biases, producing a first-order frequency shift that depends sinusoidally on φ0 and can span nearly the entire topological bandgap. The authors capture this by re-centering the ideal zero-mode wavefunction","pith_inferences":["If the center-displacement mechanism holds in other wave platforms, the same phase-controlled tuning should appear in acoustic, elastic, and mechanical Kekulé lattices, making it a generic design principle rather than a photonic-specific effect.","The central unit cell's phase φc is effectively a second control knob: adjusting it should change the trajectory radius and therefore the tuning range, which could be tested experimentally by fabricating samples with different φc values.","The phase-driven center motion itself could be used as a spatial switch or a way to adiabatically transport the mode around the vortex core, without any dynamical perturbation, since the static tuning mechanism implies strong phase-sensitivity of the mode position.","A full tight-binding derivation of rc(φ0) from the discrete Hamiltonian—rather than a fitted circle—would extend the model beyond the constant-modulation regime and may reveal corrections to the rigid-displacement ansatz."],"forward_implications":["In the constant-modulation regime, changing the global initial phase shifts the mode center by about a lattice constant; the effect is largest when the central unit cell's phase is set to 0° and the modulation profile is flat.","A sublattice-antisymmetric radius perturbation converts the center motion into frequency tuning; at ΔR = 0.5 mm the tuning range nearly fills the original topological bandgap.","The tuning curve is approximately sinusoidal in φ0, a direct consequence of the circular center trajectory; at φ0 = 0° and 180° the shift vanishes.","The effect is a qualitative departure from the continuum Jackiw–Rossi model, which predicts no phase-dependent spectral response; experiments and numerics agree with the corrected model.","Initial-phase engineering becomes a viable route for reconfigurable devices such as tunable topological cavities and filters."],"fun_headline_variants":["Lattice discreteness turns vortex phase into a tunable dial","Hidden phase becomes a real control knob for vortex modes","Discrete lattice makes vortex phase matter for frequency","Phase shift now tunes vortex modes across the bandgap","Lattice effects turn phase into a bandgap-tuning switch"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The model assumes that the entire effect of lattice discreteness on the mode is a rigid circular displacement of the ideal Jackiw–Rossi wavefunction, with radius r0 taken from simulation fits and the central cell phase set by hand to 0°; the frequency-shift prediction is directly proportional to that fitted r0.","fun_headline_variants_meta":{"raw":{"variants":["Lattice discreteness turns vortex phase into a tunable dial","Hidden phase becomes a real control knob for vortex modes","Discrete lattice makes vortex phase matter for frequency","Phase shift now tunes vortex modes across the bandgap","Lattice effects turn phase into a bandgap-tuning switch"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00021,"raw_usage":{"total_tokens":1241,"prompt_tokens":731,"completion_tokens":510,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":475,"completion_tokens_details":{"reasoning_tokens":432}},"tokens_in":475,"tokens_out":510,"duration_ms":5884,"temperature":1.0,"reasoning_tokens":432,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T11:03:11.626527+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the mode-center trajectory in full-wave simulations for a central-cell phase different from 0° (e.g., 90°) and compare the radius and the resulting frequency shift to the model's prediction; if the trajectory is not circular or the tuning range changes in a way not captured by the rigid-displacement formula, the ansatz is falsified. Alternatively, compute the mode displacement directly from the discrete lattice Hamiltonian and check whether it matches the fitted circle.","supporting_citations":[],"review_version":1}