{"id":"24b11aed-556a-4885-8355-6b504e472a60","arxiv_id":"2501.02818","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Bulk muon spin relaxation detects spontaneous internal fields below Tc in FeSe0.36Te0.64, indicating time-reversal symmetry breaking superconductivity in a material that also hosts a topological surface state.","lead":"Muon spin relaxation measurements show that the superconductor FeSe0.36Te0.64 develops tiny internal magnetic fields in its interior below its transition temperature, even with no external field applied. This points to a superconducting state that breaks time-reversal symmetry while also hosting a topological surface state, making the material a rare testbed for exotic topological superconductivity.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"For x=0.64, the key unproven premise is that the LF-suppressed ZF relaxation is a homogeneous bulk TRSB field, not a dilute magnetic fraction; a wTF volume-fraction check on raw spectra would settle it.","rationale":"The reader's weakest-assumption analysis and my stress-test converge on the same load-bearing concern: the x=0.64 ZF relaxation enhancement is attributed to a homogeneous bulk TRSB static field, but the published main text does not fully exclude a dilute magnetic component. The paper's own contrast with x=0.75/0.83 is the strongest internal support for this distinction, and the qualitative difference in LF response and the absence of a fast component are real evidence. However, the absence of a fast component is fit-model-dependent, and no wTF muSR volume-fraction data are presented for x=0.64; the wTF test appears only for the AFM x=0.94 sample. Since the central claim is a discovery claim for bulk TRSB superconductivity at x=0.64, the data-release and re-analysis condition attached by the reader is appropriate. I do not see an additional independent objection that would move the verdict away from CONDITIONAL, so the verdict remains UNCHANGED relative to the reader's assessment.","tokens_in":13566,"tokens_out":3167,"duration_ms":35088,"concrete_test":"Re-analyze the raw x=0.64 ZF/LF spectra, and if necessary run a new weak-transverse-field (wTF) measurement on the same crystals, by (i) fitting the ZF data with the same two-component function used for x=0.75/0.83 and testing whether the fast-component amplitude is consistent with zero at 1.9 K, and (ii) comparing the initial asymmetry A0 between normal and superconducting states, as done for x=0.94 in Fig. 3d; in wTF mode, a loss of oscillating amplitude below Tc would directly bound the magnetic volume fraction. If the fast-component amplitude is zero, A0 is constant, and the wTF amplitude shows no loss below Tc, the hidden-magnetic-fraction scenario is excluded; if any of these checks fails, the TRSB assignment would need revision.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central inference is that in x=0.64 the enhanced ZF relaxation below Tc originates from a small static internal field uniformly distributed in the superconducting bulk (TRSB), rather than from a minority magnetic phase. The paper's internal control is the contrast with x=0.75/0.83, where two-component fits reveal a fast, LF-insensitive relaxation assigned to short-range AFM; x=0.64 shows no resolvable fast component and is LF-suppressed at 200 G (Fig. 2b,f). This is suggestive but not conclusive. A magnetic fraction can be missed when only a single stretched exponential is used, especially if its local-field distribution is broad or if it relaxes on timescales shorter than the spectrometer resolution; the reported absence of initial-asymmetry loss is not shown for x=0.64 (it is only demonstrated for the AFM x=0.94 in Fig. 3d). LF suppression at 200 G excludes static fields on the ~1 G scale, but does not by itself exclude a small volume fraction with fields above 200 G or with fluctuating moments. The claim 'without a sign of inclusion of magnetic order' therefore rests on the absence of a fast component and on A0 constancy, neither of which is documented for x=0.64 in the main text. This is the load-bearing point: if even a few percent of the sample develops magnetic correlations below Tc, the TRSB conclusion is not unique.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports zero-field (ZF) and longitudinal-field (LF) muon spin relaxation (μSR) measurements on single crystals of FeSe$_{1-x}$Te$_x$ with $x \\approx 0.35$, $0.64$, $0.75$, $0.83$, and $0.94$. For $x \\approx 0.35$ and $x = 0.64$, the ZF relaxation rate increases below the superconducting transition and is suppressed by a longitudinal field of 100–200 G, which the authors interpret as evidence for static spontaneous fields and thus time-reversal symmetry breaking (TRSB) in the superconducting state. For $x = 0.75$ and $0.83$, a fast, LF-insensitive relaxation component with onset above $T_c$ is attributed to short-range antiferromagnetic correlations, while $x = 0.94$ shows long-range AFM order with a magnetic volume fraction of about 90%. The authors map these findings onto a combined phase diagram and argue that $x = 0.64$ provides a bulk TRSB superconductor with a topological surface state.","tokens_in":13800,"tokens_out":7463,"duration_ms":65514,"significance":"If the interpretation for $x = 0.64$ is correct, the work is significant: it would place FeSe$_{0.36}$Te$_{0.64}$ as a bulk superconductor with broken time-reversal symmetry in the same material that hosts a topological surface state and Majorana zero modes, providing a platform to study the predicted Dirac gap and possible chiral edge modes. The paper is well-contextualized and includes useful internal controls: the two-component relaxation observed for $x = 0.75/0.83$ and the $A_0$ loss for $x = 0.94$ demonstrate that the authors can detect magnetic order when it is present, and the LF decoupling and the agreement of $T_{\\mathrm{TRSB}} \\approx 11.5$ K with Kerr data support the TRSB assignment. Sample characterization (specific heat, magnetization) also supports bulk full superconductivity for $x \\le 0.64$. However, the central claim depends on the absence of a small magnetic fraction in the $x = 0.64$ sample, which is not quantified in the present manuscript; this must be addressed before the conclusion can be accepted.","major_comments":[{"comment":"The central claim for $x = 0.64$ rests on the absence of a magnetic minority phase, but no quantitative bound on the magnetic volume fraction is provided for this composition. The wTF-μSR volume-fraction analysis is shown only for $x = 0.94$ (Fig. 3c–e), and the constancy of the initial asymmetry $A_0$ versus temperature is likewise demonstrated only for $x = 0.94$ (Fig. 3d). For $x = 0.64$, the displayed ZF spectrum (Fig. 2b) is fitted with a single exponential/stretched exponential, and a small volume fraction with a fast-relaxing component could be missed, especially if its relaxation rate exceeds the early-time binning or the local-field distribution is broad. The specific-heat residual-DOS argument (Fig. S2) is not a strong constraint, because a few percent of magnetic clusters would contribute negligibly to the electronic specific heat. Because the sentence “without a sign of inclusion of magnetic order” (p. 7) is the basis for distinguishing TRSB from magnetic order, please perform a wTF-μSR volume-fraction check for $x = 0.64$ (and ideally $x \\approx 0.35$), or fit the base-temperature ZF spectra with a two-component function and report an upper bound on the fast fraction. Without such a constraint, the interpretation is not unique.","section":"Results, Fig. 2b,f and Fig. 3c–e"},{"comment":"The LF decoupling at 200 G is taken as evidence for a static internal field on the ~1 G scale, and this is plausible for the dominant component. However, it does not by itself exclude a minority phase with local fields larger than 200 G or with fast-fluctuating moments, since such a contribution would not be decoupled by 200 G. The early-time asymmetry in Fig. 2b does not resolve a fast component, but a fast component could be hidden in the first ~0.1 μs. Please show the $A_0(T)$ data for $x = 0.64$ (as in Fig. 3d for $x = 0.94$) and report the fit quality or residuals for the single-component fit at base temperature. This is load-bearing because the claim that the spontaneous fields are “distinct from a magnetic order” requires excluding a small magnetic fraction.","section":"Results, Fig. 2f and LF decoupling discussion (p. 6)"}],"minor_comments":[{"comment":"The typo “relaxatio rate” should be “relaxation rate”.","section":"p. 5"},{"comment":"The sentence “the relaxation rate of ZF NSR mode (red circle) and LF (red circles and green squares) correspond to the left axis” is inconsistent; the LF data are plotted as green squares, not red circles. Please correct the caption.","section":"Fig. 2 caption"},{"comment":"The phrase “we discovered the bulk TRSB superconductivity” is stronger than the presented evidence; suggest “we find evidence for bulk TRSB superconductivity.”","section":"p. 7"},{"comment":"For $x \\approx 0.35$, the onset temperature $T_{\\mathrm{TRSB}}$ is not stated numerically; please provide the value and its uncertainty, as given for $x = 0.64$.","section":"Results, Fig. 2e"},{"comment":"The statement that the ZF relaxation-rate temperature dependence is “similar to that in TF measurements (see Fig. S5)” is an important supporting observation; consider displaying this comparison in the main text for $x = 0.64$.","section":"Results, p. 6 and Fig. S5"}],"recommendation":"major_revision","confidential_remarks":"The paper is carefully executed and the internal controls (x = 0.75/0.83 and x = 0.94) strengthen the case. The main gap is the missing wTF volume-fraction constraint for the central composition x = 0.64. If the authors can provide that, the paper would be a strong candidate for publication. I would not reject on the basis of the current evidence, but the claim as written is stronger than the data support."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Roppongi et al. report bulk zero-field muSR evidence for a time-reversal symmetry breaking superconducting state in FeSe1-xTex at x=0.64 and x~0.35. The x=0.64 result is the important one: it's the first bulk muSR detection of spontaneous fields at the composition known to host a topological surface state and Majorana vortex modes. That closes a real gap in the topological superconductivity story, and it's a claim worth taking seriously.\n\nThe experimental case is well built. The relaxation rate grows below Tc, tracks the superfluid density, is suppressed by a longitudinal field, and the onset near 11.5 K matches the earlier Kerr data. The contrast with x=0.75/0.83 is convincing: those samples show a fast component that appears above Tc and does not decouple in LF, so assigning it to short-range magnetism is reasonable. The zero residual specific heat for x<=0.64 is a good thermodynamic cross-check.\n\nThe soft spot is the homogeneity assumption. The x=0.64 spectra are fit with a single stretched exponential, and the interpretation as a uniform TRSB field rather than a dilute magnetic fraction relies on the absence of a fast component and on the LF suppression. A 200 G longitudinal field doesn't exclude a small volume fraction with fields above that or with fluctuating moments. The paper demonstrates initial-asymmetry loss and gives a wTF volume-fraction estimate only for x=0.94, not for x=0.64. The specific heat and the lack of a fast component are supporting evidence, but they are not a direct volume-fraction measurement. I would call this a moderate concern, not a fatal one. The claim is internally consistent and credible, but the wording \"without a sign of inclusion of magnetic order\" is a bit stronger than what the main text proves. I'd want to see the raw spectra and fitting details, and ideally a wTF run at x=0.64.\n\nThe citation pattern and literature placement look fine, and the authors are appropriately cautious about the pairing state. This is a paper for anyone following iron-based superconductors, TRSB, or topological superconductivity. It deserves a serious referee, with special attention to the x=0.64 homogeneity question. I would cite it, with a caveat until the volume-fraction check is done.","headline":"Bulk muSR evidence for TRSB at the topological composition FeSe0.36Te0.64 is new and mostly convincing, but the homogeneity assumption needs a wTF volume-fraction check before I'd call it airtight.","tokens_in":14521,"tokens_out":4897,"would_cite":true,"duration_ms":45701,"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":"Zero-field muon spin relaxation detects spontaneous static internal fields below Tc in bulk FeSe0.36Te0.64, distinct from magnetic order, indicating a time-reversal-symmetry-breaking superconducting state.","keywords":["zero-field muon spin relaxation","time-reversal symmetry breaking","topological superconductivity","iron-chalcogenide superconductors","FeSe1-xTex","spontaneous magnetic field","Majorana zero modes","Dirac surface state"],"falsifier":"A weak-transverse-field muon measurement on the same $x=0.64$ crystals would settle the point: if the oscillating amplitude begins to drop below $T_c$, that loss would reveal a magnetic volume fraction and contradict the homogeneous TRSB interpretation. Equivalently, a high-statistics two-component analysis of the zero-field spectra at 1.9 K that finds a missing fast component or an initial-asymmetry loss would argue for dilute magnetism instead.","tokens_in":13326,"feed_emoji":"🧲","tokens_out":10331,"duration_ms":88093,"temperature":0.7,"pith_summary":"The paper sets out to establish that the iron-chalcogenide superconductor FeSe$_{1-x}$Te$_{x}$ at Te composition $x=0.64$, whose surface is already known to host topological states and vortex Majorana zero modes, breaks time-reversal symmetry in its bulk superconducting state. The evidence comes from zero-field muon spin relaxation: below the superconducting transition at 14.5 K a static internal field appears, with an onset near 11.5 K, and the relaxation is suppressed by a 200 G longitudinal field, which is the signature of a static field rather than magnetic order. The same signature, with a smaller field, appears in the nematic composition near 0.35, while higher-Te samples $x=0.75$ and 0.83 show a fast relaxation component that starts above $T_c$ and is not decoupled by a longitudinal field, which the authors attribute to short-range antiferromagnetism. If correct, this makes FeSe$_{1-x}$Te$_{x}$ a bulk superconductor that combines intrinsic time-reversal symmetry breaking with nontrivial topology, a combination predicted to open a Dirac gap in the surface state and to enable chiral edge physics.","feed_headline":"Muon spin relaxation detects broken time reversal in FeSe0.36Te0.64","feed_subtitle":"Spontaneous fields below the critical temperature reveal a bulk pairing state that coexists with a topological surface band.","key_machinery":"The central probe is zero-field muon spin relaxation, in which spin-polarized muons implanted into the crystal precess and relax according to the local magnetic field distribution. In a time-reversal-symmetry-breaking superconductor, spontaneous currents around defects or domain boundaries generate a small static internal field that raises the muon relaxation rate below $T_c$; applying a longitudinal field of 100-200 G decouples the muons from static fields, which is how the authors distinguish a static spontaneous field from dynamic fluctuations or magnetic order. The argument is carried by a comparative phase-diagram analysis: compositions $x=0.75$ and 0.83 exhibit a fast relaxation component that appears above $T_c$ and survives a longitudinal field, marking short-range antiferromagnetism, while $x=0.64$ and the near-0.35 composition show only the TRSB-type relaxation that decouples under a longitudinal field.","core_discovery":"The core discovery is that the tetragonal superconductor FeSe$_{0.36}$Te$_{0.64}$ hosts a bulk superconducting state with broken time-reversal symmetry, identified by the appearance of spontaneous static magnetic fields below $T_c$ that are distinct from any magnetic order. Zero-field muon spin relaxation spectra show an increased relaxation rate in the superconducting state in both non-spin-rotated and spin-rotated geometries; a longitudinal field of 200 G suppresses this relaxation, proving the source is static. The estimated internal field is about 0.76 G in the non-spin-rotated mode and 1.53 G in the spin-rotated mode at the lowest temperature, and the TRSB onset is about 11.5 K, consistent with the earlier Kerr effect. A parallel measurement at a Te fraction near 0.35 finds the same phenomenon with a smaller field. Crucially, the $x=0.64$ samples show no fast relaxing component, no loss of initial muon asymmetry, and no residual density of states in specific heat, so the authors conclude the entire volume becomes a TRSB superconductor without magnetic inclusions.","pith_inferences":["A testable extension the paper does not perform is a weak-transverse-field muon measurement on $x=0.64$ below $T_c$; a drop in the oscillating amplitude would signal a magnetic volume fraction and contradict the homogeneous TRSB reading.","If the roughly 1 G spontaneous field is intrinsic, one could look for chiral surface currents by scanning SQUID magnetometry on the same crystals, since the predicted two-component order parameter should produce edge currents.","Comparing the internal-field magnitude at the near-0.35 and $x=0.64$ compositions with their transition temperatures might reveal whether the spontaneous field scales with $T_c$ or with spin-orbit coupling, a distinction the current data set is too small to settle.","The same muon protocol applied to FeSe$_{1-x}$S$_{x}$ at compositions with matching $T_c$ could test whether the TRSB field strength is controlled by the chalcogen mass, which would support the spin-orbit-enhancement scenario."],"forward_implications":["At $x=0.64$, the bulk TRSB pairing state coexists with the known topological surface state, so the surface Dirac cone should acquire a gap below the TRSB onset, following the same logic as magnetic topological insulators.","The TRSB onset of about 11.5 K being close to the Kerr-effect onset strengthens the case that earlier surface-sensitive signals reflect a bulk broken-time-reversal state rather than a surface-only effect.","The phase diagram now places bulk TRSB superconductivity in the nematic and tetragonal regions of both FeSe$_{1-x}$S$_{x}$ and FeSe$_{1-x}$Te$_{x}$, implying that broken time reversal is a generic feature of FeSe-based superconductivity rather than a special property of one composition.","For $x=0.75$ and 0.83, any interpretation of topological superconductivity must account for coexisting short-range antiferromagnetic correlations, which appear above $T_c$ and are not suppressed by longitudinal fields."],"supporting_citations":[{"why":"Provides the zero-field muon spin relaxation method and the comparison FeSe1-xSx TRSB results that anchor the phase diagram.","marker":"[22]"},{"why":"Establishes the muon-spin-relaxation signature of spontaneous fields in a TRSB superconductor, the interpretive template used here.","marker":"[40]"},{"why":"Explains how spontaneous currents near surfaces and domain walls generate the local fields that muons detect in a TRSB superconductor.","marker":"[41]"},{"why":"Gives the Kerr-effect TRSB onset at the same composition, used as an independent consistency check for the bulk muon result.","marker":"[36]"},{"why":"Reports the topological surface state on FeSe0.45Te0.55, establishing the topological context the paper builds on.","marker":"[9]"},{"why":"Shows zero-energy vortex bound states in Fe(Se,Te), the Majorana evidence that motivates the topological-superconductor interpretation.","marker":"[11]"},{"why":"Proposes the nearly degenerate pairing channels whose phase difference gives TRSB and a Dirac gap in iron-chalcogenides.","marker":"[48]"},{"why":"Provides the nonunitary multiorbital pairing theory used to account for a large spontaneous field and finite-energy Dirac points.","marker":"[47]"},{"why":"Supplies the FeSe-based phase diagram with the three superconducting domes that place x=0.64 in the topological SC3 region.","marker":"[21]"},{"why":"Provides composition calibration and the Tc values for the FeSe1-xTex series, including the 14.5 K maximum near the nematic quantum critical point.","marker":"[15]"}],"fun_headline_variants":["FeSe0.36Te0.64 shows bulk time-reversal breaking in superconducting state","Topological superconductor FeSe0.36Te0.64 breaks time reversal in bulk","Spontaneous fields reveal time-reversal breaking in FeSe0.36Te0.64 superconductor","Time-reversal symmetry broken in FeSe0.36Te0.64 bulk superconductor"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The claim rests on the assumption that the enhanced zero-field relaxation below $T_c$ in the $x=0.64$ samples comes from a static internal field spread uniformly through the bulk, and not from a small volume fraction of short-range magnetic order that a single-component exponential fit fails to resolve.","fun_headline_variants_meta":{"raw":{"variants":["FeSe0.36Te0.64 shows bulk time-reversal breaking in superconducting state","Topological superconductor FeSe0.36Te0.64 breaks time reversal in bulk","Spontaneous fields reveal time-reversal breaking in FeSe0.36Te0.64 superconductor","Time-reversal symmetry broken in FeSe0.36Te0.64 bulk superconductor"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001421,"raw_usage":{"total_tokens":5780,"prompt_tokens":1031,"completion_tokens":4749,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":647,"completion_tokens_details":{"reasoning_tokens":4649}},"tokens_in":647,"tokens_out":4749,"duration_ms":31820,"temperature":1.0,"reasoning_tokens":4649,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T22:03:42.987289+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A weak-transverse-field muon measurement on the same $x=0.64$ crystals would settle the point: if the oscillating amplitude begins to drop below $T_c$, that loss would reveal a magnetic volume fraction and contradict the homogeneous TRSB interpretation. Equivalently, a high-statistics two-component analysis of the zero-field spectra at 1.9 K that finds a missing fast component or an initial-asymmetry loss would argue for dilute magnetism instead.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the zero-field muon spin relaxation method and the comparison FeSe1-xSx TRSB results that anchor the phase diagram."},{"cited_title":"& Sigrist, M","cited_arxiv_id":null,"evidence_quote":"Explains how spontaneous currents near surfaces and domain walls generate the local fields that muons detect in a TRSB superconductor."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the Kerr-effect TRSB onset at the same composition, used as an independent consistency check for the bulk muon result."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows zero-energy vortex bound states in Fe(Se,Te), the Majorana evidence that motivates the topological-superconductor interpretation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Proposes the nearly degenerate pairing channels whose phase difference gives TRSB and a Dirac gap in iron-chalcogenides."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the nonunitary multiorbital pairing theory used to account for a large spontaneous field and finite-energy Dirac points."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the FeSe-based phase diagram with the three superconducting domes that place x=0.64 in the topological SC3 region."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides composition calibration and the Tc values for the FeSe1-xTex series, including the 14.5 K maximum near the nematic quantum critical point."}],"review_version":1}