{"id":"a66d586b-c2b4-4178-8310-19943d8d63f0","arxiv_id":"2501.05980","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Hydrostatic pressure drives 1T'-WS2 from a superconducting state into a normal state with an anomalous Hall effect, then into a reentrant superconducting state coexisting with the anomalous Hall effect.","lead":"Researchers find that squeezing a 12-layer crystal of 1T'-WS2 with pressure first kills its superconductivity and switches on an anomalous Hall effect, then brings back a different superconducting state that coexists with that Hall effect. The result offers a single tunable material platform for studying how superconductivity, topology, and possible magnetic order interact.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The coexistence claim rests on the AHE identification; because the extraction assumes a linear-in-field background in exactly the pressure range where DFT predicts a Lifshitz transition, ordinary two-band Hall nonlinearity is a live alternative that the paper does not exclude.","rationale":"The reader's weakest assumption is correctly identified: the anomalous Hall component is the most fragile premise for the coexistence claim. My reading of the manuscript supports this. The paper is otherwise strong in several respects: the superconducting phase diagram is built from multiple samples, the pressure cycling shows reversibility, and the DFT/RPA/phonon calculations are extensive and internally consistent. But the AHE identification has no control experiment. In particular, the authors' own band-structure calculations show a Lifshitz transition in the same pressure interval where the AHE appears (P = 1.63 GPa), so a conventional multi-band Hall contribution is not a generic hypothetical alternative but a concrete one. The linear-subtraction procedure in Methods IV removes only a linear-in-field term; if the ordinary Hall coefficient itself becomes field-dependent from two-carrier conduction, the residual 'anomalous' loop would be an artifact of the fit. The observed disappearance around 25–28 K is consistent with a magnetic origin, but it is also consistent with a transport anomaly tied to the 30 K resistance feature, which the authors themselves state requires structural analysis to interpret. Therefore the coexistence claim is conditional on a missing control, and the paper's own conditional verdict is appropriate. I do not see grounds to reject the paper or to accept it outright; the CONDITIONAL verdict should stand until the Hall analysis is tested against a multi-carrier model or an independent magnetic probe.","tokens_in":17990,"tokens_out":4171,"duration_ms":44785,"concrete_test":"Re-fit the raw Hall traces at P = 1.63 and 2.3 GPa, together with the Extended Fig. 3 data at 1.15 and 1.8 GPa, using a two-band or mobility-spectrum model constrained by the measured longitudinal magnetoresistance and the 18 T high-field Hall slope. If the best-fit multi-carrier Hall contribution fully accounts for the low-field nonlinearity, leaving a residual within noise or independent of temperature, then the anomalous Hall attribution is unsupported and the coexistence claim collapses. If a temperature-dependent residual with the reported Rxy^AHE amplitude survives the multi-carrier fit, the AHE identification is strengthened and the claim stands.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that SC2 coexists with an anomalous Hall effect is load-bearing, and it depends entirely on extracting Rxy^AHE by subtracting a linear-in-field baseline (Methods IV; Fig. 3d,f; Fig. 4b,d). The text itself states 'no hysteresis is observed' and no magnetization or muSR probe is presented, so the low-field nonlinearity is not independently established as AHE. This is especially concerning because the same pressure range hosts a Lifshitz transition in the authors' own DFT (Fig. 5e,f): merging electron pockets and changing carrier balance can produce a nonlinear, temperature-dependent ordinary Hall signal from two-band/multi-pocket transport that would survive a linear subtraction and could masquerade as AHE. The near-vanishing of the extracted signal by 25–28 K is suggestive of magnetic order, but it could equally reflect a mobility or carrier-density anomaly tied to the 30 K resistance feature (Extended Fig. 4), which the authors explicitly defer for future structural analysis. Thus the coexistence premise is not secured: if the AHE attribution fails, the reentrant SC2 phase is just a second superconducting dome in a band-structure-tuned metal, not superconductivity coexisting with broken time-reversal symmetry.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript reports pressure-dependent electrical transport measurements on few-layer (12-layer) 1T'-WS2 Hall bars, showing a first superconducting dome (SC1) that is suppressed by P≈1.15 GPa, the emergence of a low-field nonlinear Hall component at the same pressure, and a reentrant superconducting dome (SC2) at P≥1.8 GPa with a larger in-plane/out-of-plane Hc2 anisotropy. The authors combine these data with DFT, tight-binding, RPA susceptibility, and electron-phonon calculations to argue for a pressure-induced topological transition and a possible magnetic instability, and they interpret the reentrant SC2 state as coexisting with a broken-time-reversal-symmetry-like anomalous Hall response.","tokens_in":18222,"tokens_out":8125,"duration_ms":77061,"significance":"The potential significance is high if the central claim holds: 1T'-WS2 would be a rare tunable system in which superconductivity reappears out of a state exhibiting an anomalous Hall effect, with a possible unconventional pairing. The experimental work includes data from three samples with reversible pressure behavior, and the theory section is unusually complete, with machine-checkable band-structure, symmetry-indicator, EPW, and RPA calculations. The paper is also transparent about its limitations, explicitly noting the absence of hysteresis and the need for future structural and muSR studies. However, the fragility of the AHE identification is the main factor limiting confidence in the coexistence claim.","major_comments":[{"comment":"The extraction of Rxy^AHE by subtracting a linear-in-field baseline is the sole experimental basis for the anomalous Hall effect claim, but the paper never specifies the field range over which the linear fit is performed, nor does it compare the residual against a two-band or multi-band ordinary Hall model. This is a live alternative because the authors' own band-structure calculations locate a Lifshitz transition in exactly this pressure range (Fig. 5e,f), which can produce a temperature-dependent, nonlinear ordinary Hall signal of the same shape. The absence of hysteresis (stated in the main text) and the lack of any magnetization or muSR data mean that the broken-time-reversal-symmetry interpretation is not independently secured. To make the coexistence claim convincing, the authors should show the raw Rxy(B) data with the chosen linear fit overlaid, test whether a two-band fit with pressure- and temperature-dependent densities/mobilities can reproduce the observed nonlinearity, and either provide a magnetic probe or explicitly soften the language from 'anomalous Hall effect' to 'anomalous Hall-like nonlinearity'.","section":"Fig. 3 and Methods IV"},{"comment":"The assumption that 1T'-WS2 remains structurally stable under pressure is supported only by transport reversibility and phonon calculations (Extended Fig. 7), with no in-situ structural characterization. This is a load-bearing assumption because the 30 K resistance anomaly (Extended Fig. 4) and the appearance of the low-field nonlinear Hall component at 1.15 GPa could both reflect a pressure-induced structural distortion rather than a purely electronic transition. If the structure changes, the topological and Fermi-surface calculations at P = 2.3 GPa (Fig. 5) would not describe the measured state. The authors should either provide high-pressure X-ray diffraction or Raman data, or explicitly state that the topological interpretation is conditional on the untested stability of the 1T' phase.","section":"Main text, 'The wealth of pressure-tunable electronic states...'"},{"comment":"The proposed competition between superconductivity and the anomalous Hall effect in SC2 rests on the observation that the saturated value of the extracted Rxy^AHE slightly decreases below Tc. Since the extraction procedure itself assumes a particular form for the ordinary Hall background, this decrease could be an artifact of the superconducting transition modifying that background (e.g., through changes in the carrier scattering rate or in the magnetoresistance). The authors should demonstrate that the decrease is robust across a range of linear-subtraction windows and reproducible in all three samples before interpreting it as evidence for competition between the two orders.","section":"Fig. 4c,d"}],"minor_comments":[{"comment":"The symmetry indicator lists contain a typo: 'z2w2 = 0, z2w2 = 0' should read 'z2w2 = 0, z2w3 = 0' in the P = 2.3 GPa case (Methods V and Fig. 5a caption).","section":"Methods V and Fig. 5 caption"},{"comment":"The pressure phase diagrams in Fig. 1e-g show data from three samples without any error bars or individual data-point identification; given that the SC2 dome is defined by only two pressures, the authors should add error bars or at least specify the sample-to-sample spread in Tc and Hc2.","section":"Fig. 1e-g"},{"comment":"The notation for the in-plane upper critical field is inconsistent: the text says 'μ0Hc2||bc' for fields oriented 'along the c-axis' in one place, while the caption says 'fields directed along the bc plane' (Fig. 1g). Please standardize the field-orientation nomenclature.","section":"Main text, Fig. 1 caption"},{"comment":"In the paragraph describing the Wannier basis, 's-orbitals of S' appears to be a typo for 'p-orbitals of S', since the text elsewhere states that the basis is W d-orbitals and S p-orbitals.","section":"Methods V"},{"comment":"Reference 35 duplicates Reference 31 (both cite Yang et al., 'Giant, unconventional anomalous Hall effect in the metallic frustrated magnet candidate, KV3Sb5') with slightly different journal formatting; one should be removed or the citation should be consolidated.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the journal's scope and the experimental dataset is interesting, but the central claim of coexistence with an anomalous Hall effect hinges on a subtraction procedure that is not sufficiently validated. The manuscript can be made publishable by adding the requested controls or by reframing the claim with the appropriate caveats."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my read. The genuinely new result is the pressure phase diagram of few-layer 1T'-WS2: a first superconducting dome that dies near 1.15 GPa, then a reentrant dome above roughly 1.8 GPa with markedly different anisotropy. That part looks convincing. The transport is consistent across three samples, pressure cycling is reversible, and the upper-critical-field analysis is careful. The theory section is serious: band structure with symmetry indicators, Lifshitz transitions, RPA susceptibility, and EPW calculations. It does not feed back into the measured claims, so there is no circularity.\n\nThe soft spot is the anomalous Hall effect, and it carries much of the weight of the \"coexistence\" story. The AHE is extracted by subtracting a linear-in-field baseline from Hall traces. No hysteresis is reported, no magnetization or muSR data are shown, and the pressure interval where the signal appears is exactly where their own DFT finds a Lifshitz transition merging electron pockets. Ordinary two-band/multi-pocket Hall can be nonlinear and temperature-dependent; the linear subtraction would leave a residual that looks like an AHE. The suppression of the extracted signal around 25-28 K and the weak 30 K resistance anomaly are suggestive, but they do not eliminate a mobility-driven ordinary Hall feature. So the coexistence of SC2 with broken time-reversal symmetry is not established. The reentrant superconductivity itself stands; the AHE attribution does not.\n\nSmaller concerns: no error bars on the phase diagram, and the structural-stability assumption rests on phonon calculations and transport reversibility rather than in-situ diffraction. The Hubbard U in the RPA is hand-chosen, but since it is not fit to the transport data, that is acceptable.\n\nThis is a paper for people working on TMD superconductivity and pressure-tuned topology; it will generate good discussion. I would bring it to reading group.\n\nRecommendation: send it to peer review, but make sure the referees push hard on the Hall analysis. The authors are explicit about the missing structural data, so they may engage seriously. If the AHE survives a proper multi-band analysis and magnetic probes, this becomes a significant result. If it does not, you still have a solid transport study of a reentrant superconducting dome.","headline":"Pressure-tuned reentrant superconductivity in 1T'-WS2 looks solid; the anomalous Hall effect that the coexistence claim rides on is not yet properly established.","tokens_in":18881,"tokens_out":3170,"would_cite":true,"duration_ms":31752,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Hydrostatic pressure drives few-layer 1T'-WS2 through two superconducting phases, the second coexisting with an anomalous Hall effect.","keywords":["1T'-WS2","reentrant superconductivity","anomalous Hall effect","hydrostatic pressure","topological phase transition","Lifshitz transition","transition metal dichalcogenides","unconventional superconductivity"],"falsifier":"A muon spin rotation or magnetic torque measurement on 1T'-WS2 near 1.63 GPa and below 30 K could settle the broken-symmetry claim: if no static or slowly fluctuating internal field emerges in that regime, the proposed magnetic order is ruled out and the transport anomaly would require another explanation.","tokens_in":17796,"feed_emoji":"⚡","tokens_out":9938,"duration_ms":83230,"temperature":0.7,"pith_summary":"Applying hydrostatic pressure to twelve-layer 1T'-WS2 produces a cascade of electronic ground states in one material. The ambient-pressure superconducting phase (SC1) is suppressed at $P = 1.15$ GPa exactly where a nonlinear anomalous Hall component appears in the normal-state Hall resistance. Above $P = 1.8$ GPa superconductivity returns as a second phase (SC2) with a lower $T_c$, a different upper-critical-field anisotropy, and a still-present but subdued anomalous Hall effect. The paper argues that SC2 is a distinct superconducting state, possibly with unconventional pairing symmetry, emerging from a normal state with broken-time-reversal-symmetry-like transport signatures. If correct, this makes 1T'-WS2 a clean single-parameter platform for studying the interplay of superconductivity, topology, and magnetic order.","feed_headline":"Pressure revives superconductivity inside 1T'-WS2's Hall state","feed_subtitle":"A higher-pressure superconducting phase with distinct anisotropy hints at unconventional pairing.","key_machinery":"The load-bearing object is the pressure-tuned electronic structure of 1T'-WS2. The argument traces how a band inversion at the $Y$ point (around 1 GPa) switches the system from a topological crystalline insulator into a strong topological phase, while a Lifshitz transition reconstructs the Fermi surface. These changes are connected to the experiments through first-principles band structures, Wannier tight-binding models, random-phase-approximation susceptibility calculations (which find a magnetic divergence at an incommensurate wave vector), and electron-phonon coupling estimates that weaken with pressure. The symmetry analysis of the $C_{2h}$ point group, giving four one-dimensional pairing irreps ($A_g$, $B_g$, $A_u$, $B_u$), is what lets the authors argue that the reentrant phase could realize a distinct, possibly triplet, pairing channel in the presence of the anomalous-Hall normal state.","core_discovery":"The central claim is that pressure reentrantly induces a second superconducting state in few-layer 1T'-WS2 that coexists with an anomalous Hall effect. At ambient pressure the material superconducts (SC1); its critical temperature falls with pressure and vanishes at $P = 1.15$ GPa, at which point the Hall resistance develops a low-field nonlinear component attributed to an anomalous Hall effect. Increasing pressure further, superconductivity reappears at $P = 1.8$ GPa (SC2) with a smaller $T_c$, a smaller out-of-plane upper critical field (and smaller $\\mu_0 H_{c2\\perp bc}/T_c$), but a comparable in-plane upper critical field, yielding nearly twice the $\\mu_0 H_{c2\\parallel bc}/T_c$ ratio and a markedly larger superconducting anisotropy $\\gamma$. The authors take the enhanced anisotropy, together with the persistence of the anomalous Hall effect in the normal state, as evidence that SC2 has a different pairing symmetry from SC1, potentially involving triplet pairing. First-principles calculations show that the same pressure range hosts a band inversion at $Y$ that changes the topological classification from a topological crystalline insulator to a strong topological phase, along with Lifshitz transitions and a calculated magnetic (incommensurate spin-density-wave-like) susceptibility divergence, supporting a magnetic-fluctuation origin for the anomalous Hall effect and the unconventional pairing scenario.","pith_inferences":["A direct extension not pursued in the paper: if the anomalous Hall component is confirmed as intrinsic, 1T'-WS2 would join a small family of superconductors in which pairing nucleates from a time-reversal-symmetry-broken normal state; a Josephson-interferometry or polar-Kerr measurement could determine whether the superconducting order itself breaks time-reversal symmetry.","The coincidence of the ~30 K resistance anomaly with the vanishing of the anomalous Hall effect suggests a genuine phase transition; specific-heat or thermal-expansion measurements under pressure could test this without relying on transport.","Because the calculated topological surface cone lies only ~50 meV above the Fermi level, electron doping (via gating or intercalation) might bring it to the Fermi energy and make the surface states participate in transport, which the paper does not explore.","The computed rise in spin susceptibility with pressure and the drop in electron-phonon coupling suggest that still higher pressures could further tip the balance toward magnetic order or another superconducting dome, but the paper's data stop at 2.3 GPa."],"forward_implications":["If the coexistence is real, 1T'-WS2 becomes a rare tunable superconductor in which an anomalous Hall effect (a broken-time-reversal-symmetry signature) and superconductivity can be switched on and off with pressures of order 1-2 GPa.","The reentrant phase's enhanced anisotropy and high in-plane $\\mu_0 H_{c2}/T_c$ ratio imply a different superconducting condensate from SC1, possibly with triplet pairing, which could be tested by phase-sensitive or spin-sensitive measurements.","The first-principles results place the reentrant phase in a strong topological phase, so surface-sensitive probes could look for topological surface states; the calculated surface cone sits about 50 meV above the Fermi level.","The calculated incommensurate magnetic susceptibility divergence predicts a spin-density-wave-like instability that neutron or muon experiments could detect and link to the anomalous Hall effect.","Because the pressure response is reversible, the same device can be cycled between SC1, the anomalous-Hall metal, and SC2, making 1T'-WS2 a testbed for competing-order physics."],"supporting_citations":[{"why":"supplies the 1T'-WS2 crystals and the structural classification used for all measurements.","marker":"21"},{"why":"prior transport study of 1T'-WS2 establishing the ambient-pressure superconducting and metallic behavior this paper extends.","marker":"22"},{"why":"documents spin-orbit-parity coupled superconductivity in 2M-WS2, the exotic-pairing benchmark against which the reentrant phase is compared.","marker":"25"},{"why":"shows superconductivity in 2M-WS2 weakens monotonically with pressure, providing the contrast for the reentrant behavior reported here.","marker":"33"},{"why":"identifies anomalous Hall effect coexisting with superconductivity in kagome metals AV3Sb5, the context for the coexistence claim.","marker":"35"},{"why":"supports interpreting the anomalous Hall effect as a consequence of an incommensurate spin density wave.","marker":"32"},{"why":"provides the random-phase-approximation method used to compute the susceptibility whose divergence signals magnetic instability.","marker":"48"}],"fun_headline_variants":["Pressure revives superconductivity in 1T'-WS2's Hall state","Reentrant superconductivity appears in 1T'-WS2 under pressure","Pressure tunes superconductivity and Hall effect in 1T'-WS2","Superconductivity resurfaces within 1T'-WS2's anomalous Hall phase","Pressure triggers reentrant pair state in 1T'-WS2's Hall regime"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The identification of the anomalous Hall effect assumes that after subtracting a linear-in-field baseline, the remaining low-field nonlinearity in the Hall resistance is intrinsic rather than a two-band, magnetoresistance, or contact artifact; no magnetic probe or hysteresis is presented in the paper.","fun_headline_variants_meta":{"raw":{"variants":["Pressure revives superconductivity in 1T'-WS2's Hall state","Reentrant superconductivity appears in 1T'-WS2 under pressure","Pressure tunes superconductivity and Hall effect in 1T'-WS2","Superconductivity resurfaces within 1T'-WS2's anomalous Hall phase","Pressure triggers reentrant pair state in 1T'-WS2's Hall regime"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000824,"raw_usage":{"total_tokens":3675,"prompt_tokens":1090,"completion_tokens":2585,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":706,"completion_tokens_details":{"reasoning_tokens":2482}},"tokens_in":706,"tokens_out":2585,"duration_ms":18648,"temperature":1.0,"reasoning_tokens":2482,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T21:05:33.564172+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A muon spin rotation or magnetic torque measurement on 1T'-WS2 near 1.63 GPa and below 30 K could settle the broken-symmetry claim: if no static or slowly fluctuating internal field emerges in that regime, the proposed magnetic order is ruled out and the transport anomaly would require another explanation.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"supplies the 1T'-WS2 crystals and the structural classification used for all measurements."},{"cited_title":"Ultrahigh supercurrent density in a two -dimensional topological material","cited_arxiv_id":null,"evidence_quote":"prior transport study of 1T'-WS2 establishing the ambient-pressure superconducting and metallic behavior this paper extends."},{"cited_title":"M., Fang, Y","cited_arxiv_id":null,"evidence_quote":"documents spin-orbit-parity coupled superconductivity in 2M-WS2, the exotic-pairing benchmark against which the reentrant phase is compared."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"shows superconductivity in 2M-WS2 weakens monotonically with pressure, providing the contrast for the reentrant behavior reported here."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"identifies anomalous Hall effect coexisting with superconductivity in kagome metals AV3Sb5, the context for the coexistence claim."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"supports interpreting the anomalous Hall effect as a consequence of an incommensurate spin density wave."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"provides the random-phase-approximation method used to compute the susceptibility whose divergence signals magnetic instability."}],"review_version":1}