{"id":"5f28df00-b7d8-4e60-b12e-bd6f89f7bf9c","arxiv_id":"2608.10122","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"TiMoCO2 is predicted to be a Z2 topological insulator while TiWCO2 is a trivial semimetal with a giant Rashba splitting and a very large Berry curvature dipole, tunable by strain.","lead":"Using density functional theory, the authors predict that two Janus MXene monolayers, TiMoCO2 and TiWCO2, host topologically nontrivial and strongly spin-orbit-coupled electronic states. The work suggests these 2D carbides could serve as a platform for Rashba spintronics and nonlinear Hall devices, with strain as a control knob.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Reported nonlinear Hall conductivities are computed from the peak Berry curvature dipole within an energy window, not at the equilibrium Fermi level; this can overstate the physical response and even vanishes for the undoped semiconductor.","rationale":"I agree with the reader that the nonmagnetic assumption is a real limitation, but I identify the use of peak BCD values rather than the equilibrium Fermi-level BCD as the more load-bearing concern for the central quantitative claim. The nonmagnetic assumption is explicitly scoped in the paper, and if the materials are nonmagnetic it does not affect the reported numbers. In contrast, the peak-vs-Fermi issue is present even within the stated nonmagnetic framework and directly affects the headline conductivity values. The manuscript's own Eqs. (1)-(2) show the BCD should be evaluated at the equilibrium Fermi level, yet Sec. III C and III D state that the 'largest value' or 'peak' within an energy window is used. For a metal this can overestimate the response; for a semiconductor it implicitly assumes a shifted chemical potential. My proposed test would settle whether the reported values correspond to physical equilibrium responses. If not, the main claim of a 'colossal nonlinear Hall effect' would need to be rescaled or recontextualized, while the Z2 topology and Rashba coefficients, which are band-structure properties, may survive. Therefore the CONDITIONAL verdict remains appropriate, with an added condition to report and discuss the Fermi-level BCD and any doping/gating assumptions.","tokens_in":14104,"tokens_out":10433,"duration_ms":110153,"concrete_test":"Recompute the Berry curvature dipole as a function of chemical potential for TWCO and for TMCO at 0%, 2%, and 3% tensile strain using WannierBerri with a 2000x2000 k-grid and a Fermi-Dirac smearing of 1 meV (or adaptive smearing). Extract the BCD at the self-consistent Fermi level (E=0 on the existing energy axis) and compare with the reported peak values (24-25 Å for TWCO; the values used to obtain 17x10^-4 G0 for strained TMCO). For unstrained TMCO, verify that the BCD at the intrinsic Fermi level in the gap is zero; if the code yields a nonzero value, check the occupation handling. If the at-E_F values are close to the peaks, the conclusions survive; if they are substantially smaller, the reported conductivities must be revised and the 'colossal' claim relative to WTe2 becomes unsupported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim, a nonlinear Hall conductivity of about 120x10^-4 G0 for TWCO and 17x10^-4 G0 for strained TMCO, is derived in Sec. III C and III D from the 'peak' or 'largest value' of the Berry curvature dipole within an energy window around E_F (e.g., ±0.4 eV for TWCO, ±200 meV for strained TMCO). However, Eq. (2) defines the BCD with the equilibrium Fermi function, so at T=0 only states at E_F contribute for a metal, and for an insulator with E_F in the gap the BCD is strictly zero. For the metallic TWCO, if the maximum of D(E) lies away from E_F, the reported 24-25 Å peak overestimates the equilibrium response. For the undoped semiconducting TMCO, the Fermi level lies in the gap, so the reported 'moderate nonlinear anomalous Hall conductivity' is not an equilibrium property unless a shifted chemical potential (doping or gating) is assumed, which the paper never states. The abstract and conclusion present these peak values as intrinsic material properties, making the 'colossal' comparison to WTe2 potentially overstated. The manuscript does not disclose the energy position of the BCD peak relative to E_F for TWCO, nor does it specify any doping/gating for TMCO. This is a direct threat to the headline numbers and is not addressed by the nonmagnetic assumption alone.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper uses DFT (PBE+SOC) and Wannier interpolation to study the structural stability and electronic properties of Janus o-MXene TiM''CO2 with M''=Mo and W. It reports that TiMoCO2 is a narrow-gap Z2 topological insulator, while TiWCO2 is a trivial metal with a strong Rashba effect (alpha_R up to 1.34 eV Å) and a very large Berry curvature dipole (24-25 Å), which the authors convert into a nonlinear anomalous Hall conductivity of about 120×10^-4 G0. The paper also reports that tensile strain drives TiMoCO2 from a topological insulator to a Z2 semimetal and modulates the sign and magnitude of the Berry curvature dipole. The work includes energetics for o-MXene versus i-MXene ordering, electrostatic potential differences, phonon/MD stability checks (in the SM), Wannier charge center Z2 invariants, surface spectral functions, and strain-dependent transport estimates.","tokens_in":14375,"tokens_out":3666,"duration_ms":38884,"significance":"If the results are correct, the paper identifies a new materials family—Janus bimetallic MXenes—with a rare combination of topological, Rashba, and nonlinear Hall properties, and it suggests strain as a control knob. The computational work is careful and follows standard practice: Wannier interpolation, WannierTools/WannierBerri usage, dense k-grids, and explicit checks of structural stability. The energetics comparison between o- and i-MXene configurations and the electrostatic potential analysis are thoughtful. The central claims are falsifiable predictions that could guide future experimental work on MXenes. However, the headline quantitative claim about the nonlinear Hall conductivity depends on assumptions about the Fermi level and on unverified nonmagnetic ordering, which limits the significance until those points are addressed.","major_comments":[{"comment":"All calculations are performed within a nonmagnetic PBE+SOC framework, and no spin-polarized total-energy comparison is reported. Ti, Mo, and W are transition metals, and MXenes are known to often have magnetic instabilities; without testing ferromagnetic or antiferromagnetic configurations, the time-reversal-symmetric Z2 classification and the Berry curvature dipole analysis rest on an unverified assumption. Please report spin-polarized total energies (for example, several collinear magnetic orders) for both TiMoCO2 and TiWCO2 and, if a magnetic state is lower in energy, re-evaluate the topological and transport conclusions.","section":"§II"},{"comment":"The nonlinear Hall conductivity is obtained using assumed values of τ = 10^-12 s and E = 10^3 V/m, and the quoted result scales linearly with τ. These parameters are not derived from the material or from experiment, so the 'colossal' 120 × 10^-4 G0 value is not an intrinsic property but a convoluted estimate. Please state explicitly that these are assumed and provide the dependence on τ (or a range of plausible values) so readers can assess the robustness of the claim.","section":"§III C, Eq. (1)"},{"comment":"The strain-dependent Berry curvature dipole for TiMoCO2 is again reported as a peak value within ±200 meV of E_F. The same Fermi-level issue as above applies here: for the unstrained semiconductor the equilibrium BCD is zero, and only after the strain-induced semimetal transition does a Fermi-surface contribution exist. The paper should report D(E_F) as a function of strain, not just the peak in an energy window, and specify the position of the chemical potential for the semi-metallic phases.","section":"§III D, Fig. 7"}],"minor_comments":[{"comment":"The abstract uses '120 x 0.0001 G0' and '17 X 0.0001 G0'; these should be written as 120 × 10^-4 G0 and 17 × 10^-4 G0 for consistency with the text.","section":"Abstract"},{"comment":"The conclusion contains the typo 'extraordinaryly'; it should be 'extraordinarily'.","section":"Conclusion"},{"comment":"The manuscript compares the TWCO nonlinear conductivity with 'WTe2 literature benchmarks' but does not give the quoted WTe2 value in the same units; please provide the specific benchmark numbers used for the two-orders-of-magnitude claim.","section":"§III C"},{"comment":"The Rashba parameter for TWCO is given as 1.06 eV Å below E_F and 1.34 eV Å above E_F, but the text later emphasizes only 1.34 (and the abstract says 1.35). Please reconcile these numbers and label the figure consistently.","section":"Fig. 4"},{"comment":"The language is occasionally promotional ('colossal', 'unprecedented', 'extraordinary'). While the results are interesting, please make the wording more measured and explicitly tie each superlative to the quantitative comparison with previous work.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is technically competent and addresses a timely topic, but the central quantitative claim about the nonlinear Hall effect is currently based on peak Berry-curvature-dipole values rather than the equilibrium response at the Fermi level, which is a load-bearing issue for the paper's headline. The nonmagnetic assumption is another significant gap that should be checked. The paper's comparison with WTe2 may be overstated if it relies on the peak values. I recommend major revision rather than rejection because the underlying methodology is sound and the issues are addressable with additional calculations and a more careful presentation of the transport results."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things up front. First, the headline NLAH conductivities (120×10^-4 G0 for TWCO, 17×10^-4 G0 for strained TMCO) are computed from the peak Berry curvature dipole within an energy window, not at the equilibrium Fermi level. For TMCO, which is a semiconductor with E_F in the gap, the equilibrium BCD is zero; the reported value implicitly assumes doping or gating that is never stated. For TWCO, the peak may not sit at E_F either, and the paper never shows D(E_F). So the 'colossal' numbers in the abstract are overstated as intrinsic properties. That is the main thing to know.\n\nSecond, the paper assumes a nonmagnetic ground state without testing spin-polarized configurations. If either compound is magnetic, the Z2 classification (which relies on TRS) and the BCD analysis would need to be redone. That is a standard check the authors skipped.\n\nWhat is genuinely new: the TiWCO2 case (trivial semimetal, strong Rashba, large BCD) and the strain-driven sign flip of the BCD in TMCO are not in the prior literature. The calculations are careful: standard PBE+SOC with VASP, Wannier interpolation, WannierTools for Z2 and edge states, and the numbers are internally consistent. The Z2 invariant for TMCO and the Rashba splittings are probably correct as reported.\n\nThe soft spots: aside from the two above, the TMCO baseline is heavily anticipated by the authors' own PRB 107, 075403 (ref 20), so the genuinely new content is a subset. The 0.1 eV PBE gap is small enough that hybrid functionals could change the topological classification, though this is less concerning because the Z2 invariant is often robust. The smearing parameters for the metallic BCD are not documented in the main text.\n\nWho is this for? People working on 2D materials, spintronics, and nonlinear Hall effects. The paper is a reasonable computational prediction, but the presentation of the headline numbers needs substantial revision. A serious referee should be engaged.\n\nRecommendation: send to peer review, with the expectation that the authors either report D(E_F) for the metal (and a labeled gated/doped value for the semiconductor) or soften the abstract accordingly, and add spin-polarized tests. As it stands, I would not cite the NLAH numbers, but the structural and Rashba data are useful.","headline":"Peak Berry curvature dipole values are presented as equilibrium NLAH conductivities, overstating the result for the semiconductor and likely the metal; the Rashba and Z2 parts are sound.","tokens_in":14933,"tokens_out":5881,"would_cite":false,"duration_ms":54037,"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":"Janus MXenes TiMoCO2 and TiWCO2 are predicted to be a topological insulator and a Rashba semimetal, respectively.","keywords":["MXene","Janus structure","spin-orbit coupling","Rashba effect","Z2 topological insulator","Berry curvature dipole","nonlinear anomalous Hall effect","strain engineering"],"falsifier":"A spin-polarized density-functional calculation (e.g., with PBE+U or hybrid functionals) that finds a magnetic ground state for TiMoCO2 or TiWCO2 would invalidate the $Z_2$ classification and the Berry curvature dipole analysis; alternatively, a nonlinear Hall transport measurement on a TiWCO2 monolayer could check whether the conductivity approaches the predicted $120 \\times 10^{-4} G_0$ scale after accounting for the relaxation time $\\tau$.","tokens_in":13877,"feed_emoji":"⚡","tokens_out":7840,"duration_ms":61920,"temperature":0.7,"pith_summary":"The paper predicts that two monolayer MXene compounds with a Janus (asymmetric) metal layer, TiMoCO2 and TiWCO2, turn the combination of broken inversion symmetry and strong spin-orbit coupling into distinct quantum functionalities. TiMoCO2 is predicted to be a $Z_2$ topological insulator with a narrow indirect gap and a Berry curvature dipole that can change sign under tensile strain, offering a strain-controlled nonlinear Hall switch. TiWCO2 is predicted to be a trivial semimetal with a giant Rashba coefficient of $1.34\\,\\mathrm{eV\\,\\AA}$ and a Berry curvature dipole of $24$–$25\\,\\mathrm{\\AA}$, yielding a nonlinear anomalous Hall conductivity of $120 \\times 10^{-4} G_0$, about two orders of magnitude above earlier Janus transition-metal dichalcogenide benchmarks. These results establish Janus MXenes as a tunable materials platform for spintronics and nonlinear Hall devices.","feed_headline":"TiWCO2 MXene predicted to show colossal nonlinear Hall effect","feed_subtitle":"One is a Z2 topological insulator; the other is a Rashba semimetal with a Hall response two orders larger.","key_machinery":"The central object is the Janus o-MXene structure — two distinct transition-metal layers (Ti on one side, Mo or W on the other) sandwiching a carbon layer, with oxygen passivation — which breaks inversion symmetry and produces an out-of-plane electric dipole. The mechanisms that carry the argument are (i) Rashba spin splitting from broken inversion symmetry plus strong spin-orbit coupling at the $4d/5d$ site, quantified by $\\alpha_R = 2E_R/k_R$; (ii) the Berry curvature dipole $D_{bd} = \\int_k f_0 \\, \\partial\\Omega_n^d/\\partial k_b$, whose first moment gives the nonlinear anomalous Hall conductivity; and (iii) the $Z_2$ invariant computed from the evolution of Wannier charge centers, which separates the topological insulator TiMoCO2 from the trivial semimetal TiWCO2.","core_discovery":"Within a nonmagnetic PBE+SOC framework, the authors find that the out-of-plane ordered Janus o-MXene structure of TiMoCO2 and TiWCO2 breaks inversion symmetry and creates a net electric dipole. TiMoCO2 is a $Z_2$ topological insulator: its Wannier charge centers show odd crossings, and a spectral function calculation reveals a conducting edge state at the $[010]$ surface. TiWCO2 is a trivial semimetal, but its strong W $5d$ spin-orbit coupling gives a Rashba coefficient $\\alpha_R = 1.34\\,\\mathrm{eV\\,\\AA}$ and a Berry curvature dipole of $24$–$25\\,\\mathrm{\\AA}$ that produce a nonlinear anomalous Hall conductivity of $120 \\times 10^{-4} G_0$ at an applied field of $10^3\\,\\mathrm{V/m}$ with $\\tau = 10^{-12}\\,\\mathrm{s}$, two orders of magnitude larger than that of known Janus transition-metal dichalcogenides. For TiMoCO2, $2$–$3\\%$ tensile strain induces a semiconductor-to-semimetal transition while preserving the $Z_2$ invariant, and the Berry curvature dipole flips sign with an enhanced peak value of $17 \\times 10^{-4} G_0$ at $2\\%$ strain.","pith_inferences":["Editorial inference: since PBE often underestimates gaps, the 0.1 eV gap of TiMoCO2 could close or open under hybrid functionals, but the $Z_2$ invariant is robust as long as the gap does not close.","Editorial inference: the predicted Berry curvature dipole of 24–25 Å is unusually large; if confirmed, it might be traced to the W $d$-orbital character near the Fermi level, suggesting a design rule: heavy $5d$ metals in Janus MXenes maximize the BCD.","Editorial inference: a natural experimental route would be selective etching of ordered MAX phases such as Mo2TiAlC2 to obtain the Janus monolayer, since these parent phases are already known.","Editorial inference: if the nonmagnetic assumption fails, the nonlinear Hall response could instead become magnetic-field-tunable, which would still be technologically useful but would change the theoretical framework."],"forward_implications":["TiWCO2 could be used as a metallic Rashba platform to induce spin-orbit coupling in graphene or TMDC monolayers via proximity.","The predicted nonlinear Hall conductivity makes TiWCO2 a candidate for frequency doubling and terahertz detection beyond the current WTe2 benchmark.","For TiMoCO2, tensile strain acts as a switch that reverses the sign of the nonlinear Hall current while keeping the $Z_2$ topology intact, enabling strain-gated Hall devices.","The 4d-to-5d substitution (Mo to W) at the Janus site is the control knob that turns a topological insulator into a Rashba semimetal."],"supporting_citations":[{"why":"Prior Mo-based Janus MXene study that showed giant Rashba effect and nonlinear anomalous Hall conductivity; this work extends the search to TiM''CO2 compounds.","marker":"[20]"},{"why":"Sodemann and Fu's theory of quantum nonlinear Hall effect induced by Berry curvature dipole, which supplies the formula for the nonlinear conductivity and dipole.","marker":"[24]"},{"why":"Soluyanov and Vanderbilt's method for computing topological invariants without inversion symmetry, used here to obtain the $Z_2$ invariant from Wannier charge centers.","marker":"[33]"},{"why":"WannierBerri code employed to compute the Berry curvature and Berry curvature dipole on a dense k-grid.","marker":"[34]"},{"why":"Acosta et al.'s definition of the 'Rashba scale' used to characterize TiWCO2 as a strong Rashba compound.","marker":"[38]"},{"why":"Du et al.'s quantum theory of the nonlinear Hall effect, providing the anomalous-velocity basis for the Berry curvature dipole response.","marker":"[42]"},{"why":"Janus TMDC monolayer calculations that provide the benchmark Berry curvature dipole values against which TiWCO2's large response is compared.","marker":"[44]"},{"why":"WTe2 nonlinear anomalous Hall study used as the conductivity benchmark showing TiWCO2 is about two orders of magnitude stronger.","marker":"[45]"}],"fun_headline_variants":["Janus MXenes: Z2 insulator vs Rashba semimetal","TiWCO2: strong Rashba and Berry-dipole Hall","Strain flips Berry dipole in topological Janus MXene","TiMoCO2: strain-switchable topological semimetal"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"All predictions rest on nonmagnetic PBE+SOC density-functional calculations, so if either compound has a lower-energy spin-polarized ground state, the time-reversal-symmetric $Z_2$ classification and Berry curvature dipole analysis would need to be redone.","fun_headline_variants_meta":{"raw":{"variants":["Janus MXenes: Z2 insulator vs Rashba semimetal","TiWCO2: strong Rashba and Berry-dipole Hall","Strain flips Berry dipole in topological Janus MXene","TiMoCO2: strain-switchable topological semimetal"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000845,"raw_usage":{"total_tokens":3768,"prompt_tokens":1121,"completion_tokens":2647,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":737,"completion_tokens_details":{"reasoning_tokens":2571}},"tokens_in":737,"tokens_out":2647,"duration_ms":20586,"temperature":1.0,"reasoning_tokens":2571,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T04:10:38.437516+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A spin-polarized density-functional calculation (e.g., with PBE+U or hybrid functionals) that finds a magnetic ground state for TiMoCO2 or TiWCO2 would invalidate the $Z_2$ classification and the Berry curvature dipole analysis; alternatively, a nonlinear Hall transport measurement on a TiWCO2 monolayer could check whether the conductivity approaches the predicted $120 \\times 10^{-4} G_0$ scale after accounting for the relaxation time $\\tau$.","supporting_citations":[{"cited_title":"Giant rashba effect and nonlinear anomalous hall conductivity in a two-dimensional molybdenum-based janus structure.Phys","cited_arxiv_id":null,"evidence_quote":"Prior Mo-based Janus MXene study that showed giant Rashba effect and nonlinear anomalous Hall conductivity; this work extends the search to TiM''CO2 compounds."},{"cited_title":"Quantum nonlinear hall effect induced by berry curvature dipole in time-reversal invariant materials.Physical review letters, 115(21): 216806, 2015","cited_arxiv_id":null,"evidence_quote":"Sodemann and Fu's theory of quantum nonlinear Hall effect induced by Berry curvature dipole, which supplies the formula for the nonlinear conductivity and dipole."},{"cited_title":"Computing topo- logical invariants without inversion symmetry.Physical Review B—Condensed Matter and Materials Physics, 83(23):235401, 10","cited_arxiv_id":null,"evidence_quote":"Soluyanov and Vanderbilt's method for computing topological invariants without inversion symmetry, used here to obtain the $Z_2$ invariant from Wannier charge centers."},{"cited_title":"The rashba scale: Emer- gence of band anti-crossing as a design principle for ma- terials with large rashba coefficient.Matter, 3(1):145– 165, 2020","cited_arxiv_id":null,"evidence_quote":"Acosta et al.'s definition of the 'Rashba scale' used to characterize TiWCO2 as a strong Rashba compound."},{"cited_title":"Quantum theory of the nonlinear hall effect.Nature communi- cations, 12(1):5038, 2021","cited_arxiv_id":null,"evidence_quote":"Du et al.'s quantum theory of the nonlinear Hall effect, providing the anomalous-velocity basis for the Berry curvature dipole response."},{"cited_title":"Tunable topology and berry curvature dipole in transition metal dichalcogenide janus monolayers.Materials Research Express, 8(12):124001, 2021","cited_arxiv_id":null,"evidence_quote":"Janus TMDC monolayer calculations that provide the benchmark Berry curvature dipole values against which TiWCO2's large response is compared."},{"cited_title":"Ferroelectric nonlinear anoma- lous Hall effect in few-layer WTe2.npj Computational Materi- als, 5(1):119, 2019","cited_arxiv_id":null,"evidence_quote":"WTe2 nonlinear anomalous Hall study used as the conductivity benchmark showing TiWCO2 is about two orders of magnitude stronger."}],"review_version":1}