{"id":"28e83a7e-b038-484e-919f-823cb2912e93","arxiv_id":"1909.02491","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"The Hall coefficient of stripe-ordered La-214 cuprates is zero across the field-revealed normal state below about 2 to 6 times the superconducting transition temperature.","lead":"In two stripe-ordered cuprates, a strong magnetic field that suppresses superconductivity also makes the Hall effect disappear over a wide range of temperatures and fields. The result hints at a hidden particle-hole symmetry in the normal state, a property not observed in other cuprate families.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The result hinges on Hpeak identifying Hc2, a boundary imported from companion preprints; if superconducting correlations persist above Hpeak, zero RH may be pair-related rather than a normal-state particle-hole symmetry.","rationale":"Agree with the reader that the paper reports a careful, reproducible measurement: antisymmetrized Hall data, multiple magnets, consistency across runs, and an internally consistent phase diagram. The vortex-liquid interpretation of negative RH is supported by the ρxx^2/ρxy∝H scaling in Fig. S4, which is independent evidence beyond the companion preprints. The conditional verdict is appropriate. The single most load-bearing unresolved point is whether each sample is truly in the normal state for H>Hpeak; this is the foundation for excluding pair-based explanations. The companion preprints are plausible but not independent, and the Hall data alone cannot rule out a residual pair contribution that exactly cancels RH. A Nernst experiment is a clean, decisive check. If Nernst is zero above Hpeak, then the experimental core is solid and the remaining debate is whether 'dynamically generated particle-hole symmetry' is the unique or best theoretical interpretation; that interpretive step should be presented as a hypothesis, not as a logical necessity. I do not recommend changing the verdict.","tokens_in":19500,"tokens_out":7470,"duration_ms":89094,"concrete_test":"Measure the Nernst coefficient on the same two crystals across Hpeak at T near 0.1 T0 (down to ~0.05 K in the dilution refrigerator) in fields up to 31 T. Vortices and superconducting phase fluctuations produce a large Nernst signal; if a Nernst signal persists for H>Hpeak, then Hpeak is not the boundary of all superconducting correlations and the RH=0 plateau cannot be assigned to the normal state. A null Nernst response across the entire RH=0 region would independently confirm the normal-state identification and remove the main obstacle to the particle-hole symmetry interpretation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is the assertion that the field-revealed normal state begins at Hpeak(T)≈Hc2(T), so that the RH=0 plateau at H>Hpeak is free of superconducting correlations. The Hall data in this paper only show that the negative-vortex contribution and non-Ohmic transport end near Tpeak/Hpeak; the identification of Hpeak with Hc2, and the claim that no Cooper pairs or PDW survive above it, are imported from the authors' companion preprints (refs 12,13) via interlayer anisotropy and I-V measurements on the same samples, not independently established here. If vortex-liquid remnants, fluctuating Cooper pairs, or an intra-stripe PDW persist above Hpeak, then pair contributions can cancel the Hall response (as argued for La1.875Ba0.125CuO4 in ref 33) and no particle-hole symmetry of the normal state follows. Since the paper's 'has to imply dynamically generated charge conjugation symmetry' depends on excluding exactly this class of explanations, the normal-state boundary is the most load-bearing assumption. A secondary concern is that even with the boundary granted, equal electron/hole pockets produced by stripe-induced Fermi surface reconstruction could give RH=0 without the additional step of 'dynamically generated' symmetry, so the theoretical inference is stronger than the transport data alone require.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper reports Hall-effect measurements on two stripe-ordered cuprate families, La1.7Eu0.2Sr0.1CuO4 and La1.48Nd0.4Sr0.12CuO4, over an extended range of temperature (down to 0.019 K) and perpendicular magnetic field (up to 31 T). The authors find that the Hall coefficient RH is positive and nearly field-independent at high temperature, drops to zero at a weakly field-dependent temperature T0(H) ~ (2–6)Tc0, and remains zero for all T < T0(H) in the high-field regime H > Hpeak, which they identify with the upper critical field Hc2. At lower fields, RH becomes negative in a regime attributed to vortex motion, and the data are used to construct a T–H phase diagram. The central claim is that RH = 0 is a robust property of the field-revealed normal state of stripe-ordered cuprates and that it implies a dynamically generated charge-conjugation (particle-hole) symmetry, in contrast to other cuprates such as YBa2Cu3O6+x.","tokens_in":19756,"tokens_out":5691,"duration_ms":63113,"significance":"If the experimental observation is correct, it is a striking and potentially important result: it identifies a new property of the normal state of stripe-ordered cuprates, distinguishes these materials from other cuprate families, and provides a strong constraint on theories of intertwined orders. The measurements appear careful: the authors use multiple magnets and cryostats, check consistency between runs, ensure linear response by comparing excitation currents, and extract RH from antisymmetrized Hall voltages. The paper also gives a useful phase diagram for two closely related compounds. The strongest part is the direct observation of RH consistent with zero over a wide T–H region; the weakest part is the inference from that observation to a dynamically generated particle-hole symmetry, which is not uniquely required by the data.","major_comments":[{"comment":"The conclusion that RH = 0 in the field-revealed normal state is uncontaminated by superconducting correlations depends on identifying Hpeak(T) with Hc2(T) and on the assertion that no vortices, Cooper pairs, or pair-density wave survive for H > Hpeak. This boundary is imported from the authors' companion preprints (refs 12 and 13) via non-Ohmic transport and interlayer-anisotropy measurements on the same samples; it is not independently established in the present manuscript. The Hall data alone cannot exclude pair contributions above Hpeak; indeed, RH = 0 is also observed in the viscous vortex-liquid regime H < Hpeak (Fig. S1B), so the interpretation hinges entirely on the imported boundary. If superconducting remnants persist above Hpeak, the zero Hall response could be explained by the same pair-related mechanism invoked for La1.875Ba0.125CuO4 (ref. 33), and no normal-state particle-hole symmetry follows. The authors should either reproduce the relevant control measurements or state explicitly that the normal-state designation is inherited from refs 12 and 13 and discuss how the central claim would be affected if that identification fails.","section":"Main text, 'The remaining, most intriguing question…' (p. 8–9) and Fig. 1"},{"comment":"The claim that RH = 0 'has to imply that charge conjugation symmetry is dynamically generated' overreaches what the transport data can establish. A compensated two-band Fermi surface with equal electron and hole densities, which is a natural consequence of stripe-induced Fermi-surface reconstruction, gives RH = 0 identically without any dynamical symmetry. The paper itself acknowledges that electron pockets would imply n_e = n_h. To sustain the stronger conclusion, the authors would need to rule out this conventional two-band compensation and other kinematic mechanisms, or reframe the conclusion as an interpretive possibility rather than a logical necessity. As written, the phrase 'In standard models, RH can only vanish accidentally' is an assertion that conflicts with the paper's own two-band discussion.","section":"Abstract and p. 10, concluding paragraph"},{"comment":"At the lowest temperatures, the error bars on RH are large, as the Fig. 2 caption attributes to the extremely small excitation currents needed to remain in the linear-response regime. The data are consistent with RH = 0 but also with a small nonzero value. The paper would be strengthened by a quantitative upper bound on |RH| (or, equivalently, on the apparent carrier density) in the normal-state region H > Hpeak for T < T0, with statistical and systematic uncertainties. Without such a bound, 'remains zero' should be softened to 'is zero within experimental resolution'.","section":"Fig. 2, Fig. S2, and Fig. 3"}],"minor_comments":[{"comment":"The title uses 'zero Hall response' while the abstract says 'vanishing Hall response'; please use one formulation consistently.","section":"Title and abstract"},{"comment":"'unprecendented' should be 'unprecedented'.","section":"p. 3, first paragraph"},{"comment":"Refs 12 and 13 are cited as preprints; if published versions are now available, they should be cited instead.","section":"References 12 and 13"},{"comment":"Fig. 1 is dense; the numerous boundary curves and shaded regions are hard to distinguish, especially in grayscale; consider distinct line styles and a legend. Also, 'h/4e2' should be defined at first use as h/(2e)^2.","section":"Fig. 1 and main text, 'h/4e2' notation"},{"comment":"The sentence 'In standard models, RH can only vanish accidentally' needs a supporting reference or a derivation; as written it is an unsupported assertion.","section":"p. 10, 'In standard models…'"}],"recommendation":"major_revision","confidential_remarks":"The manuscript relies heavily on two companion preprints (refs 12 and 13) by the same group for the Hpeak = Hc2 identification and for the absence of superconductivity above Hpeak. This is not a problem per se, but the present paper's central interpretation stands or falls with those results. The editor may wish to verify that the companion papers are published or peer-reviewed and that the quoted findings are not in dispute. There is also a scope issue: the paper reports a striking experimental observation, but the theoretical conclusion (dynamically generated particle-hole symmetry) is not derived here; a revised version that separates the robust experimental result from the more speculative interpretation would be more suitable for the journal."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nYou should know about arXiv:1909.02491 for the measurement, not for the interpretation. Shi et al. report a striking experimental result: in the field-revealed normal state of two stripe-ordered La-214 cuprates, the Hall coefficient vanishes over a wide range of T and H, down to T/Tc ~ 0.003 and fields well above the vortex-liquid regime. That is new, and it is the kind of observation that constrains theories of intertwined order.\n\nThe measurements look careful. They used multiple magnets, antisymmetrized Hall traces, tiny excitation currents to stay in the linear regime, and they cross-checked the negative Hall response in the vortex liquid against a vortex scaling law. The fact that the zero Hall state appears in two compounds with different doping and different stripe strengths makes the phenomenology more credible. They also put real effort into distinguishing their situation from the ultraquantum metal in La1.875Ba0.125CuO4, where Cooper pairs inside stripes explain the zero Hall effect.\n\nThe soft spot is exactly where the stress-test note puts its finger: the identification of Hpeak with Hc2, i.e. the claim that the zero Hall region is free of all superconducting correlations. That boundary is imported from the authors' own companion preprints, refs 12 and 13. The present paper does not itself show the non-Ohmic transport or interlayer anisotropy data that would pin down the absence of pairs and PDW. If some form of superconducting remnant survives above Hpeak, the zero Hall coefficient could be pair-related and not a property of the true normal state. This is not a minor concern, because the paper's central inference—dynamically generated particle-hole symmetry—depends on excluding that class of explanations.\n\nI also think the authors overstate the theoretical conclusion. They write that RH=0 'has to imply' dynamically generated charge-conjugation symmetry. That is too strong. A striped Fermi surface with equal electron and hole pockets could give a robust zero Hall response without any new dynamical symmetry; the authors acknowledge this possibility in the penultimate paragraph but then set it aside as 'accidental'. Over a wide field range, an accidental fine-tuning is unlikely, but stripe order could naturally fix the carrier balance. So the data are consistent with emergent particle-hole symmetry, but they do not force it.\n\nThe low-T Hall data carry large error bars, as expected given the tiny currents, but the zero trend is consistent across many traces and both compounds.\n\nBottom line: this is a solid experimental paper with an important observation and an overinterpreted conclusion. It deserves serious peer review. I would send it to referees—ideally one who knows the companion transport papers—and ask them to hold the authors to a more careful statement of what the data do, and do not, imply. The measurement should stand; the symmetry claim should be softened.\n\nBring it to reading group; you'll get a good debate.","headline":"Robust zero Hall effect in the stripe-ordered normal state is a real experimental advance, but the particle-hole symmetry conclusion is overreach.","tokens_in":20342,"tokens_out":6359,"would_cite":true,"duration_ms":58846,"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":"In the field-revealed normal state of stripe-ordered La-214 cuprates, the Hall coefficient is zero for all T below T0(H) ≈ (2–6) Tc0, and the paper argues this zero implies a dynamically generated particle–hole symmetry.","keywords":["cuprate superconductors","Hall coefficient","particle-hole symmetry","stripe order","charge order","spin stripes","pair-density wave","high magnetic fields"],"falsifier":"Measure the Nernst coefficient, or the out-of-plane versus in-plane conductivity anisotropy, in the same samples at fields above $H_{\\rm peak}$ and temperatures below $T_0$: a finite Nernst signal or a field-dependent anisotropy would reveal surviving superconducting-phase fluctuations, breaking the link between $R_H = 0$ and particle-hole symmetry. Conversely, resolving two compensated Fermi-surface pockets by quantum oscillations above $H_{\\rm peak}$ would confirm the equal-electron/hole-pocket picture.","tokens_in":19301,"feed_emoji":"🧲","tokens_out":13350,"duration_ms":129871,"temperature":0.7,"pith_summary":"High magnetic fields can suppress superconductivity and expose the underlying normal state of copper-oxide superconductors, but what that state is has remained unresolved. This paper reports that in two stripe-ordered cuprates, La1.7Eu0.2Sr0.1CuO4 and La1.48Nd0.4Sr0.12CuO4, the Hall coefficient $R_H$ becomes zero as the temperature is lowered below $T_0(H) \\sim (2$–$6)T_c^0$ and stays zero down to 0.019 K, throughout the field-revealed normal state above $H_{\\rm peak}$. Because an accidental zero of the Hall coefficient over such a wide range of temperature and field is implausible in standard transport models, the authors conclude that this normal state has a dynamically generated particle–hole (charge-conjugation) symmetry. The result matters because it identifies a robust qualitative property of the normal state of cuprates with intertwined charge and spin stripes, and it sharply distinguishes these materials from other cuprates such as YBa2Cu3O6+x.","feed_headline":"Zero Hall effect in striped cuprates implies particle-hole symmetry","feed_subtitle":"The zero persists from a few times Tc down to 0.019 K and is absent in non-striped cuprates.","key_machinery":"The load-bearing probe is the Hall coefficient $R_H = \\rho_{xy}/H$, obtained from the magnetic-field-antisymmetric part of the transverse voltage, used as a measure of the balance between electron-like and hole-like carriers: $R_H = 0$ means the Hall conductivity $\\sigma_{xy}$ vanishes. The argument is carried by combining $R_H$ with the longitudinal resistivity $\\rho_{xx}(T,H)$ and with previously established phase-diagram boundaries: $T_0(H)$ marks where the positive $R_H$ collapses to zero and coincides with the onset of phase fluctuations, where the normal-state sheet resistance per layer crosses the quantum resistance $R_Q = h/(2e)^2$; $H_{\\rm peak}(T)$ marks the crossover from positive to negative magnetoresistance and is identified with the upper critical field; and the negative $R_H$ region at lower fields is identified as vortex motion through the scaling $\\rho_{xx}^2/\\rho_{xy} \\propto H$. This combination lets the authors separate ordinary vortex-Hall physics from the normal-state zero and attribute $R_H = 0$ above $H_{\\rm peak}$ to charge-conjugation symmetry.","core_discovery":"The central discovery is that $R_H = 0$ is a property of the entire normal-state phase, not a fine-tuned crossing point. In both materials, the positive, roughly field-independent Hall coefficient at high temperature drops to zero at $T_0(H)$; the drop does not depend on $H$, and $T_0(H)$ is almost flat, staying near $(2$–$3)T_c^0$ in the La-Eu compound and near $6T_c^0$ in the La-Nd compound. Below $T_0$, for fields above $H_{\\rm peak}(T)$ — the boundary identified with the upper critical field by the companion transport studies and by the field-independence of the interlayer anisotropy — $R_H$ remains zero down to the lowest measured temperature, 0.019 K. At lower fields, inside the vortex-liquid regime, $R_H$ becomes negative and later returns to zero as vortex motion freezes; the vortex contribution is independently confirmed by the scaling $\\rho_{xx}^2/\\rho_{xy} \\propto H$. Since the normal state shows no superconducting remnants, the zero Hall coefficient cannot be explained by Cooper pairs; the paper concludes that it must come from an approximate particle-hole symmetry that is dynamically generated, with equal electron and hole response, a property unique to stripe-ordered cuprates and not present in, for example, YBa2Cu3O6+x.","pith_inferences":["A natural extension, not developed in the paper: if $R_H = 0$ arises from equal electron and hole populations, the Seebeck and Nernst coefficients should show systematic sign and cancellation behavior in the same $T$–$H$ region, offering a transport-level check.","The weakly field-dependent $T_0(H)$ suggests that $R_H = 0$ is a property of the zero-field ground state, so one could search for quantum oscillations from two compensated Fermi-surface pockets at fields well above $H_{\\rm peak}$; detecting a single hole pocket would speak against the equal-population picture.","Whether static stripe order is the essential ingredient could be tested by measuring the same Hall protocol in La-214 compounds where stripe correlations are weakened by pressure or by moving doping away from $x = 1/8$; the zero-$R_H$ plateau should weaken or disappear if stripes are causal.","The combination of $\\ln(1/T)$ resistivity and zero Hall response suggests that a useful next step is a theory in which charge-conjugation symmetry is emergent yet the longitudinal conductivity remains anomalous, a direction the paper points to only briefly."],"forward_implications":["A correct theory of the cuprate normal state must reproduce a phase in which $\\sigma_{xy} = 0$ over a wide range of $T$ and $H$ while $\\sigma_{xx}$ remains nonzero and weakly insulating-like.","The zero-$R_H$ state is a phase property: it persists from onset temperatures a few times $T_c^0$ down to 0.019 K in two compounds, ruling out fine-tuned band-structure cancellations.","Superconducting pairs are ruled out as the cause of the zero in the normal state, because no vortex, Cooper-pair, or pair-density-wave signal survives above $H_{\\rm peak}$; particle-hole symmetry is the remaining explanation.","The pair-density-wave model, which attributes a zero Hall effect to pairs surviving inside charge stripes, applies to compounds such as La1.875Ba0.125CuO4 but not to the materials studied here, where no pairs survive.","The difference from YBa2Cu3O6+x and YBa2Cu4O8 shows that the emergent particle-hole symmetry is tied to static spin and charge stripes rather than to cuprate superconductivity generally."],"supporting_citations":[{"why":"This companion paper establishes the vortex phase diagram and the identification of $H_{\\rm peak}$ with the upper critical field, so the normal state above $H_{\\rm peak}$ is defined by its evidence.","marker":"[12]"},{"why":"This companion paper reports pair-density-wave signatures and shows through the field independence of the out-of-plane transport anisotropy that no superconducting correlations remain above $H_{\\rm peak}$.","marker":"[13]"},{"why":"This earlier measurement of zero Hall response in La1.875Ba0.125CuO4 attributes the zero to surviving Cooper pairs; the present paper must exclude that explanation to claim particle-hole symmetry.","marker":"[33]"},{"why":"A model of a pair-density-wave superconductor predicts a metallic high-field normal state and a zero Hall response from equal electron- and hole-like Fermi-surface pockets.","marker":"[34]"},{"why":"This study reports electron pockets in the Fermi surface of underdoped cuprates inferred from Hall measurements, providing the Fermi-surface-reconstruction context into which the new zero is placed.","marker":"[16]"},{"why":"This earlier Hall study of stripe-ordered La2-xBaxCuO4 showed a strongly suppressed Hall coefficient at low temperature and 9 T, a precursor of the zero plateau reported here.","marker":"[28]"},{"why":"This study documents sign reversals of the Hall and Seebeck coefficients in stripe-ordered Nd-doped cuprates, the comparison set for the sign-change behavior in the vortex regime.","marker":"[29]"}],"fun_headline_variants":["Zero Hall response in stripe-ordered cuprates implies particle-hole symmetry","Vanishing Hall coefficient in striped cuprates hints at particle-hole symmetry","Stripe-ordered cuprates: Hall effect vanishes in normal state","Zero Hall effect in cuprates with stripes hints at particle-hole symmetry","Particle-hole symmetry emerges as Hall response vanishes in striped cuprates"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the field $H_{\\rm peak}(T)$ is indeed the upper critical field — the highest field at which superconductivity can survive — so that above it no superconducting correlations remain; if remnants persisted, the zero Hall coefficient could be produced by Cooper pairs rather than by particle-hole symmetry.","fun_headline_variants_meta":{"raw":{"variants":["Zero Hall response in stripe-ordered cuprates implies particle-hole symmetry","Vanishing Hall coefficient in striped cuprates hints at particle-hole symmetry","Stripe-ordered cuprates: Hall effect vanishes in normal state","Zero Hall effect in cuprates with stripes hints at particle-hole symmetry","Particle-hole symmetry emerges as Hall response vanishes in striped cuprates"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001263,"raw_usage":{"total_tokens":5242,"prompt_tokens":1083,"completion_tokens":4159,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":699,"completion_tokens_details":{"reasoning_tokens":4063}},"tokens_in":699,"tokens_out":4159,"duration_ms":27279,"temperature":1.0,"reasoning_tokens":4063,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T04:48:33.332814+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the Nernst coefficient, or the out-of-plane versus in-plane conductivity anisotropy, in the same samples at fields above $H_{\\rm peak}$ and temperatures below $T_0$: a finite Nernst signal or a field-dependent anisotropy would reveal surviving superconducting-phase fluctuations, breaking the link between $R_H = 0$ and particle-hole symmetry. Conversely, resolving two compensated Fermi-surface pockets by quantum oscillations above $H_{\\rm peak}$ would confirm the equal-electron/hole-pocket picture.","supporting_citations":[{"cited_title":"Vortex phase diagram and the normal state of cuprates with charge and spin orders","cited_arxiv_id":"1907.11706","evidence_quote":"This companion paper establishes the vortex phase diagram and the identification of $H_{\\rm peak}$ with the upper critical field, so the normal state above $H_{\\rm peak}$ is defined by its evidence."},{"cited_title":"Signatures of a pair density wave at high magnetic fields in cuprates with charge and spin orders","cited_arxiv_id":"1907.11708","evidence_quote":"This companion paper reports pair-density-wave signatures and shows through the field independence of the out-of-plane transport anisotropy that no superconducting correlations remain above $H_{\\rm peak}$."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"This earlier measurement of zero Hall response in La1.875Ba0.125CuO4 attributes the zero to surviving Cooper pairs; the present paper must exclude that explanation to claim particle-hole symmetry."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"A model of a pair-density-wave superconductor predicts a metallic high-field normal state and a zero Hall response from equal electron- and hole-like Fermi-surface pockets."},{"cited_title":"LeBoeuf, N","cited_arxiv_id":null,"evidence_quote":"This study reports electron pockets in the Fermi surface of underdoped cuprates inferred from Hall measurements, providing the Fermi-surface-reconstruction context into which the new zero is placed."},{"cited_title":"Adachi, N","cited_arxiv_id":null,"evidence_quote":"This earlier Hall study of stripe-ordered La2-xBaxCuO4 showed a strongly suppressed Hall coefficient at low temperature and 9 T, a precursor of the zero plateau reported here."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"This study documents sign reversals of the Hall and Seebeck coefficients in stripe-ordered Nd-doped cuprates, the comparison set for the sign-change behavior in the vortex regime."}],"review_version":1}