{"id":"c1249ccb-0b6b-4e80-a42b-960063b39dfe","arxiv_id":"2506.14106","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Transport and tunnel-diode measurements on (PbSe)1.14(NbSe2)3 reveal a second superconducting phase at high in-plane fields, attributed to a layer-selective FFLO state.","lead":"This paper reports on the misfit layered superconductor (PbSe)1.14(NbSe2)3, where transport and tunnel-diode measurements reveal a kink in the in-plane critical field and an internal phase boundary at low temperature and high field. The authors interpret the new high-field phase as a layer-selective FFLO state, based on a theoretical calculation from a companion paper by co-authors.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The high-field phase assignment rests on a submitted companion theory with no quantitative B2(T) comparison, and the TDO peak could be a vortex effect rather than a phase transition.","rationale":"The reader's weakest assumption identified the same core gap: the measured B2 is tied to a predicted phase boundary that is not quantitatively tested. My analysis sharpens this: the TDO data also contain a vortex-related B1, so B2 itself is not unambiguously a thermodynamic transition, and the theory comparison is admitted to lack a calculated temperature dependence. These points do not refute the paper; they justify the conditional verdict. The concrete NMR/torque test would settle whether B2 is an electronic phase boundary. If it passes, the claim is substantially strengthened; if it fails, the phase diagram reduces to vortex-lattice effects.","tokens_in":11702,"tokens_out":12293,"duration_ms":137298,"concrete_test":"Measure 77Se NMR (or torque magnetometry) on bulk (PbSe)1.14(NbSe2)3 at T ≈ 0.7 K while sweeping in-plane field from 25 T to 40 T, and look for a linewidth or Knight-shift anomaly at B2 ≈ 27 T. A layer-selective FFLO boundary should change the local-field distribution at B2; if no spectral or torque anomaly appears there, the TDO feature is more plausibly a vortex-lattice effect and the FFLO identification is not supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that the high-field phase is layer-selective FFLO rests on two premises: (i) the d^2F/dB^2 peak B2 in Fig. 3e,f is a genuine phase boundary inside the zero-resistance state, and (ii) this boundary is the Ising/layer-selective FFLO boundary predicted by companion theory (ref 31). Premise (ii) is not quantitatively supported in the text. The Discussion says 'the calculation of temperature dependence of the phase boundary still remains a challenge,' so the black dashed line in Fig. 5 cannot be compared with the measured B2(T) in Fig. 4; the only link is that the boundary starts at the kink and that B2 ~ 27 T is 'consistent with' B_c2^ab = 29.1 T, with no uncertainty or criterion. Premise (i) is also insecure: B2 is only a peak in the second derivative of the TDO frequency, and the same data contain B1, a vortex feature assigned to Josephson-vortex melting. A vortex-lattice order-disorder transition, depinning, or Josephson-vortex dimensional crossover could mimic B2. The Conclusion defers verification to 'layer-selective bulk measurement probes, such as nuclear magnetic resonance,' acknowledging that the microscopic identification is not yet made. The load-bearing gap is therefore that no decisive test shows B2 is an electronic phase boundary corresponding to the predicted layer-selective FFLO line.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports single-crystal synthesis, structural characterization, and transport/TDO measurements on the misfit layered superconductor (PbSe)1.14(NbSe2)3. The authors show bulk 2D Ising superconductivity with Tc ~ 5.1 K, an in-plane upper critical field that exceeds the Pauli limit, a kink in Bc2(T) near 3 K, and a two-regime angle dependence of Bc2 at 0.7 K. TDO measurements reveal two field-induced anomalies inside the zero-resistance state, B1 and B2; the paper assigns B2 to a phase boundary between q = 0 Ising superconductivity and a layer-selective FFLO state predicted by an unpublished co-authored theory (ref 31). The paper presents this as evidence for a previously unobserved superconducting phase in a bulk 2D system.","tokens_in":12114,"tokens_out":5570,"duration_ms":53074,"significance":"If the assignment is correct, this would be the first report of a layer-selective FFLO phase in a bulk 2D superconductor, and the misfit-layer platform would be a promising route to interlayer-engineered superconductivity. The experimental work is substantial: it combines clean single-crystal growth, resistive phase diagrams, angle-dependent critical-field measurements, and TDO-based bulk detection of an anomaly inside the zero-resistance state. The manuscript is also honest about several limitations. Its main weakness is that the phase identification is not quantitatively tested: the theoretical boundary in Fig. 5 cannot be compared with the measured B2(T) because the temperature dependence of that boundary is not calculated, and the conclusion defers microscopic verification to future NMR experiments.","major_comments":[{"comment":"The identification of the high-field phase as layer-selective FFLO is load-bearing for the abstract, but it is imported from ref 31, a submitted co-authored paper, and the present text explicitly states that 'the calculation of temperature dependence of the phase boundary still remains a challenge.' Consequently, the black dashed line in Fig. 5 cannot be quantitatively compared with the measured B2(T) in Fig. 4. The only quantitative link offered is that B2 ~ 27 T is 'consistent with' Bc2^ab = 29.1 T from a 0.7 K fit, with no uncertainty or matching criterion. Please either include the full theory and a quantitative fit to B2(T), or soften the abstract and Discussion to 'consistent with a possible layer-selective FFLO state.'","section":"Discussion, Fig. 5; abstract"},{"comment":"The premise that B2 is an electronic phase boundary is not secured. B2 is identified as a peak in the second derivative of the TDO frequency, while the same dataset contains B1, attributed to Josephson-vortex melting. A vortex-lattice order-disorder transition, depinning, or a dimensional crossover of Josephson vortices can also produce such a peak in the second derivative. The manuscript does not provide a discriminating test, such as the angle dependence of B2, a heat-capacity or thermal-conductivity signature, or a theoretical prediction for the TDO response at the predicted phase boundary.","section":"TDO measurement, Figs. 3e, 3f"},{"comment":"The angle-dependent Bc2 analysis at 0.7 K uses two Tinkham fits with different Bc2^c values (1.00 T for the near-90° region and 1.55 T for the rest), but no fit residuals or error bars are shown, and Bc2 is defined as the transport midpoint. Because the two-regime behavior is central evidence for a new phase, please quantify the quality of the fits and demonstrate that the deviation from a single Tinkham formula is not an artifact of the midpoint definition applied to broad transitions.","section":"Resistivity Bc2, Fig. 2f"}],"minor_comments":[{"comment":"The caption contains 'd2B/dF2' where the text and data require 'd2F/dB2'; please correct this typo.","section":"Fig. 3 caption"},{"comment":"The main text and Fig. 2f give two different Bc2^c values for the 0.7 K fits (1.00 T for the light blue region and 1.55 T for the black dashed curve). Please check these values and make the caption, the main text, and the figure consistent.","section":"Fig. 2f and main text"},{"comment":"The sentence 'the coil was a part of the self-resonance circuit made of the tunnel diode' and the phrase 'a double counter would pick-up coil' appear to contain typos; the latter should likely read 'a double counter-wound pick-up coil.'","section":"Methods"},{"comment":"The acknowledgment names 'M.H.' but the author list includes 'H.M.'; please correct the initials.","section":"Acknowledgments"},{"comment":"The title says 'possible layer-selective FFLO state' and the Conclusion speaks of 'the theoretical consideration implies,' while the abstract states that the phase 'is identified.' Please harmonize the strength of the claim across the title, abstract, results, and conclusion.","section":"Title and abstract"},{"comment":"The Bc2 points are reported without error bars or a statement of the transition width used to define the midpoint. Adding uncertainties, or at least reporting the 10-90% width, would make the kink and the comparison with B2 more quantitative.","section":"Phase diagram, Fig. 4"}],"recommendation":"major_revision","confidential_remarks":"The paper's central phase identification rests on an unpublished companion manuscript by two of the authors (ref 31). I recommend that the journal require either inclusion of the full theory and a quantitative comparison of the predicted phase boundary with B2(T), or a preprint of ref 31, before final acceptance. This is not a question of misconduct but of independent verifiability: as written, the key theoretical input cannot be checked by the reader. The experimental anomalies are interesting and worth publishing once the claim's strength is matched to the available evidence."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Worth a serious look. The experiment is new: a misfit layered superconductor with clean tri-layer NbSe2 units, showing a kink in in-plane Bc2, an angle dependence that refuses a single Tinkham fit, and a TDO anomaly inside the zero-resistance state. Those are real, reproducible-looking observations, and the material is a credible platform for bulk 2D superconductivity. The paper is honest about its own limits—title says possible, and the conclusion explicitly defers microscopic verification to future NMR-style probes. That matters. This is not a case of overclaiming; it is a case of a suggestive but incomplete case. The soft spots are exactly where the reader and stress-test put them. The identification of the high-field phase as layer-selective FFLO rests on ref 31, a submitted paper by two co-authors, and the main text does not give enough of the theory to check the phase boundary. The measured B2(T) is not compared against a calculated line—the theory itself does not yet provide that. Bc2 points come from transport midpoints without error bars. And the TDO feature B2, while clearly distinct from the vortex-melting line B1, could in principle be another vortex effect (melting, depinning, or a dimensional crossover). The paper does not present a decisive test that B2 is an electronic phase boundary rather than a vortex-lattice transition. Still, I would not call this a central flaw. The experimental anomalies are new and interesting regardless of the interpretation. The kink and the two-Tinkham-fit angle dependence are unusual and deserve scrutiny. The FFLO assignment is a hypothesis, not a conclusion dressed up as one. The missing theory is a legitimate reason to demand the companion paper be part of the review package, or to ask the authors to soften the identification further. But the paper should not be desk-rejected. Any serious editor should send it to referees, with at least one referee asked to check whether the B2 assignment could be explained by vortex physics and whether the unpublished theory is sufficient. For the reading group: yes, this would generate a good discussion about what counts as evidence for FFLO in layered systems. I would cite it if I worked on TMD superconductors or misfit compounds, because the phase diagram and the material synthesis are useful. The authors are clearly thinking carefully, and the paper is on its own terms an honest report. Give it to referees.","headline":"A solid experimental paper with a real discovery—an anomalous high-field phase in a bulk 2D superconductor—but the phase identification as layer-selective FFLO leans on an unpublished companion theory and a qualitative TDO feature.","tokens_in":788,"tokens_out":1165,"would_cite":true,"duration_ms":24941,"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":"Inside the zero-resistance state of (PbSe)1.14(NbSe2)3, a second phase appears at high in-plane field, identified as a layer-selective FFLO state.","keywords":["misfit layered compound","Ising superconductivity","FFLO state","layer-selective FFLO","tunnel diode oscillator","upper critical field","niobium diselenide","bulk two-dimensional superconductor"],"falsifier":"Grow the monolayer- and bilayer-NbSe2 members of the same misfit family and repeat the TDO and angle-resolved critical-field measurements: if a $B_2$ anomaly still appears without a tri-layer block, the layer-selective interpretation fails. Alternatively, use layer-resolved NMR in the high-field phase: if all three NbSe2 layers show uniform order, or if no separate phase boundary appears between $B_2$ and $B_{c2}$, the proposed layer-selective FFLO state is ruled out.","tokens_in":11533,"feed_emoji":"🧲","tokens_out":10137,"duration_ms":95577,"temperature":0.7,"pith_summary":"The paper reports a bulk crystalline superconductor, (PbSe)1.14(NbSe2)3, built from alternating tri-layers of NbSe2 and non-superconducting PbSe layers, and argues that this misfit structure keeps two-dimensional Ising superconductivity while making the tri-layers clean enough to support a nonuniform superconducting phase. Resistivity and tunnel diode oscillator (TDO) measurements under in-plane magnetic fields reveal a kink in the upper critical field near 3 K and a separate phase boundary inside the zero-resistance state at about 27 T. Combined with a companion mean-field calculation for tri-layer NbSe2, the authors identify the high-field phase as a layer-selective Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, in which the outer NbSe2 layers carry a finite-momentum order parameter while the middle layer retains a uniform component. If correct, this would be the first observation of such a layer-selective FFLO state in a bulk two-dimensional superconductor, and it would show that misfit compounds make spatially modulated superconducting phases accessible to bulk thermodynamic probes.","feed_headline":"Bulk crystal shows a layer-selective FFLO phase at high field","feed_subtitle":"Resistance and TDO data put the boundary between uniform Ising and finite-momentum order near 27 tesla.","key_machinery":"The load-bearing object is the misfit structure itself: incommensurate PbSe block layers alternate with 2Ha-stacked NbSe2 tri-layers, electrically isolating each tri-layer so that Ising spin-orbit pairing and a long mean free path survive in a bulk crystal. On the measurement side, the tunnel diode oscillator is the decisive probe: its second derivative with respect to field shows two peaks, the higher one marking the upper critical field and the lower one marking $B_2$, the boundary where the system leaves the uniform Ising phase. On the theory side, a companion mean-field calculation for tri-layer NbSe2 with Zeeman-type Ising spin-orbit coupling predicts a layer-selective FFLO phase, defined as a state in which $q=0$ and finite-$q$ order parameters mix across layers: FF-like finite-momentum pairing on the outer layers, an induced LO-like component in the middle layer, and a proximately induced uniform component shared by all three layers.","core_discovery":"The central claim is that (PbSe)1.14(NbSe2)3 has not one but two superconducting phases under an in-plane magnetic field. At low fields the state is the usual $q=0$ Ising superconducting phase, made robust by inversion-symmetry breaking and Ising spin-orbit coupling in each NbSe2 layer. Above a well-defined field $B_2$, which the TDO data place near 27 T at low temperature, a second zero-resistance phase appears; the authors identify it as a layer-selective FFLO phase. In that phase the top and bottom NbSe2 monolayers develop FF-like finite-momentum order, the middle monolayer develops an induced LO-like component, and a uniform component is proximately induced in all layers, so uniform and modulated pairing coexist. The evidence is a kink in $B_{c2}(T)$ near 3 K, an angle dependence of $B_{c2}$ that deviates from the standard two-dimensional critical-field curve only within about two degrees of the in-plane direction, and a clear TDO second-derivative signature whose field position matches the value where the angle-resolved fit changes. The kink and the TDO anomaly are absent in exfoliated tri-layer and bulk NbSe2, which the authors attribute to the isolation of the tri-layers by the PbSe block layers.","pith_inferences":["If the tri-layer is the essential ingredient, the $B_2$ anomaly should vanish or shift when the superconducting block is changed to a monolayer or a bilayer of NbSe2; this is a testable extension not stated in the paper.","Layer-resolved NMR inside the high-field phase should detect different local susceptibilities on the outer and middle NbSe2 layers, giving direct microscopic evidence of the mixed FF-like and LO-like order.","The same TDO and angle-resolved protocol applied to other members of the misfit family could map how the layer-selective FFLO phase depends on the number of NbSe2 layers per block, turning this compound into a tunable test bed for finite-momentum superconductivity."],"forward_implications":["At low temperatures the zero-resistance state of (PbSe)1.14(NbSe2)3 is split at about 27 T into a low-field $q=0$ Ising phase and a high-field layer-selective FFLO phase.","The in-plane upper critical field reaches roughly 40 T, about four times the Pauli limit, showing how strongly Ising pairing raises the depairing field in this bulk compound.","Below the kink temperature, the angle dependence of $B_{c2}$ cannot follow a single two-dimensional critical-field curve, so the high-field phase has a different order parameter.","Because the kink is missing in exfoliated tri-layer and bulk NbSe2, physically separating the tri-layers with PbSe block layers is necessary for the layer-selective FFLO phase.","Misfit bulk compounds allow transitions inside the zero-resistance state to be seen with thermodynamic probes such as TDO, beyond what resistivity alone can show in small exfoliated flakes."],"supporting_citations":[{"why":"Provides the mean-field prediction of the layer-selective FFLO phase and the B-T phase boundary in tri-layer NbSe2, which the experiment is matched against.","marker":"31"},{"why":"Shows Ising pairing in few-layer NbSe2 and supplies the exfoliated tri-layer comparison in which the Bc2 kink is absent.","marker":"3"},{"why":"Reports the orbital FFLO state in multilayer NbSe2 flakes, the prior phase the paper distinguishes from the layer-selective FFLO scenario.","marker":"14"},{"why":"Establishes bulk Ising superconductivity in misfit layered transition-metal dichalcogenides, the platform idea that motivates the compound.","marker":"26"},{"why":"First synthesis and Tc determination of powder (PbSe)1.14(NbSe2)3, the baseline for the new single crystals.","marker":"28"},{"why":"Gives the two-dimensional angle dependence of the critical field used to detect the low-temperature deviation near the in-plane orientation.","marker":"34"},{"why":"Provides the tunnel diode oscillator technique that detects the B2 phase boundary inside the zero-resistance state.","marker":"45"},{"why":"Supplies the band-structure and Ising spin-orbit-coupling model used in the companion mean-field calculation.","marker":"49"}],"fun_headline_variants":["Two superconducting phases in one misfit crystal","Layer-selective FFLO phase emerges in bulk superconductor","Misfit superconductor hides a high-field quantum phase","Bulk crystal pairs uniform and modulated superconductivity"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the companion mean-field calculation correctly describes clean tri-layer NbSe2 with Ising spin-orbit coupling, and that the measured kink in the upper critical field and the TDO anomaly $B_2$ are the same predicted phase boundary rather than unrelated background effects.","fun_headline_variants_meta":{"raw":{"variants":["Two superconducting phases in one misfit crystal","Layer-selective FFLO phase emerges in bulk superconductor","Misfit superconductor hides a high-field quantum phase","Bulk crystal pairs uniform and modulated superconductivity"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000162,"raw_usage":{"total_tokens":1291,"prompt_tokens":1050,"completion_tokens":241,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":666,"completion_tokens_details":{"reasoning_tokens":177}},"tokens_in":666,"tokens_out":241,"duration_ms":2858,"temperature":1.0,"reasoning_tokens":177,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T19:54:10.121298+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Grow the monolayer- and bilayer-NbSe2 members of the same misfit family and repeat the TDO and angle-resolved critical-field measurements: if a $B_2$ anomaly still appears without a tri-layer block, the layer-selective interpretation fails. Alternatively, use layer-resolved NMR in the high-field phase: if all three NbSe2 layers show uniform order, or if no separate phase boundary appears between $B_2$ and $B_{c2}$, the proposed layer-selective FFLO state is ruled out.","supporting_citations":[{"cited_title":"and Yanase,Y","cited_arxiv_id":null,"evidence_quote":"Provides the mean-field prediction of the layer-selective FFLO phase and the B-T phase boundary in tri-layer NbSe2, which the experiment is matched against."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows Ising pairing in few-layer NbSe2 and supplies the exfoliated tri-layer comparison in which the Bc2 kink is absent."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reports the orbital FFLO state in multilayer NbSe2 flakes, the prior phase the paper distinguishes from the layer-selective FFLO scenario."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes bulk Ising superconductivity in misfit layered transition-metal dichalcogenides, the platform idea that motivates the compound."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"First synthesis and Tc determination of powder (PbSe)1.14(NbSe2)3, the baseline for the new single crystals."},{"cited_title":"Effect of fluxoid on transitions of superconducting films","cited_arxiv_id":null,"evidence_quote":"Gives the two-dimensional angle dependence of the critical field used to detect the low-temperature deviation near the in-plane orientation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the tunnel diode oscillator technique that detects the B2 phase boundary inside the zero-resistance state."},{"cited_title":"& Morari, C","cited_arxiv_id":null,"evidence_quote":"Supplies the band-structure and Ising spin-orbit-coupling model used in the companion mean-field calculation."}],"review_version":1}