{"id":"38a1c48c-3140-49eb-a880-33c51fc1f292","arxiv_id":"2411.12572","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"In grounded superconducting multiterminal devices, thermal background charge noise can encode heat-conductance information, and thermal shot noise contains Andreev-specific interference terms.","lead":"This theoretical paper computes current noise in multiterminal normal-superconductor devices under temperature biases, using the Landauer-Buttiker scattering approach to split noise into background and excess parts. It finds that background self-correlation noise contains heat-conductance terms and that thermal shot noise reveals interference signatures of Andreev processes.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The headline heat-conductance interpretation of background noise requires s(E)=s; for energy-dependent scattering, Eq. (12) and Eq. (10) have different energy kernels, so the claim as stated in the abstract is not established.","rationale":"Read in good faith, the paper's central algebraic result is Eq. (15), which I verified by substituting Eq. (5) and Eq. (6); the signs and factors are consistent, and the normal-system limit correctly reduces to the Johnson-Nyquist and shot-noise formulas. The reader's weakest_assumption identifies the same limiting condition as I would: the equality between the background-noise kernel and the heat-conductance kernel is special to energy-independent s(E). I checked whether any other assumption is more load-bearing (superconductor temperature, charge conservation, sign conventions) and found no internal inconsistency that would overturn Eq. (15) within the stated model. The issue is that the claim's public presentation, in the abstract and conclusions, does not carry the energy-independence qualification, even though Sec. II C 1 does. Since the applications also use energy-independent scattering, the science can be repaired by a caveat; the current framing is conditional, not wrong. Therefore the Reader's CONDITIONAL verdict stands unchanged.","tokens_in":24130,"tokens_out":29623,"duration_ms":316891,"concrete_test":"Compute Eq. (12) for a one-channel NSN model with an energy-dependent \\ell^-_{ik}(E), e.g. \\ell^-_{12}(E)=-\\Gamma^2/[(E-E_0)^2+\\Gamma^2] and \\ell^-_{11}(E)=-\\ell^-_{12}(E) to satisfy Eq. (6), at T_1=T+\\delta, T_2=T, V=0. Compare \\partial\\bar S_{11}/\\partial\\delta at \\delta=0 with L^{HH}_{12} from Eq. (10) under the same parameters. If the ratio depends on \\Gamma/E_0, the heat-conductance interpretation requires energy independence; the abstract should then be qualified.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Equations (12) and (10) are the key pair. In the general (energy-dependent) case the background self-correlator contains \\int dE F_k(E)\\ell^-_{ik}(E), with F_k=2f_k(1-f_k), while the linear-response heat conductance is L^{HH}_{ik} \\propto \\int dE E^2(-\\partial f/\\partial E)\\ell^-_{ik}(E). These kernels coincide only if \\ell^-_{ik}(E) is constant, i.e. s(E)=s. The derivation in Sec. II C 1 is honest about this limit, and Eq. (15) is algebraically correct within it, but the abstract and the conclusions present the heat-conductance dependence as a general property of multiterminal hybrid systems. That is the load-bearing point, because the claimed heat-transport inference would quantitatively fail when \\ell^-_{ik}(E) has structure on the scale of k_BT. This is an overgeneralization, not an internal contradiction.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper develops a Landauer-Büttiker scattering theory for zero-frequency charge-current noise in multiterminal normal-superconducting systems under both voltage and temperature biases. After recalling the current and Onsager formulas, the authors split the noise into a background part (Eq. 12) and an excess (partition) part (Eq. 13). Their central claim is that, in the presence of temperature differences with grounded superconducting terminals, the background self-correlator contains a contribution involving the heat-conductance-related functions ℓ^-, in contrast to the equilibrium Johnson-Nyquist form; this is made explicit in Eqs. (14)-(15) for an energy-independent scattering matrix. The excess noise is then analyzed in the electrical and thermal shot-noise limits, and the formalism is applied to a three-terminal NSN junction and to a chiral integer quantum Hall device with a superconducting finger, where the authors identify signatures of spin-mixing versus Andreev processes and an interference term in the thermal shot-noise cross-correlator.","tokens_in":24382,"tokens_out":14996,"duration_ms":130767,"significance":"The analytic framework is clean, and the central algebraic step leading to Eq. (15) follows correctly from Eq. (12) and unitarity with no fitted parameters. If the heat-conductance interpretation of background charge noise is valid, the paper offers a concrete, experimentally relevant route to access heat-transport information from charge-noise measurements. The NSN and chiral-device examples produce specific, falsifiable predictions (partition forms x(1−x), an AR/SM interference term, and sign changes controlled by the relative strengths of Andreev and spin-mixing processes). The paper is also careful to state its key limit in the derivation section. The main reservation, detailed in the major comments, is that the abstract and conclusions present the heat-conductance dependence without the energy-independence qualification that the derivation actually requires.","major_comments":[{"comment":"The abstract and conclusions present the dependence of the background self-correlator noise on heat conductance as a general property of multiterminal hybrid systems, but the derivation of Eq. (15) in Sec. II.C.1 explicitly assumes an energy-independent scattering matrix, s(E)=s. For energy-dependent scattering, the background self-correlator in Eq. (12) contains an integral of F_k(E) ℓ^-_{ik}(E), whereas the linear-response heat conductance in Eq. (10) involves E^2(−∂f/∂E) ℓ^-_{ik}(E); these two kernels coincide only when ℓ^-_{ik}(E) is constant on the scale of k_B T. The paper should either add the energy-independence qualification to the abstract and conclusions, or quantify the error for weakly energy-dependent ℓ^-_{ik}(E).","section":"Abstract; Sec. II.C.1, Eqs. (10), (12), (14), (15)"},{"comment":"Equations (35) and (36) as printed contain stray symbols 'r' and 'z' and appear to be intended as square roots, namely √{−ℓ^-_{i1}(1+ℓ^-_{i1})} and √{−ℓ^+_{31}ℓ^+_{41}}. If that is the intended reading, the normal limit is problematic: for a single normal channel of transmission τ, ℓ^-_{31}=−τ, so Eq. (35) would give s̃S_{33}/(2G_0 η k_B T_1)=√{τ(1−τ)}, whereas the known thermal shot noise for a normal channel is τ(1−τ) (see Ref. [37]). The authors should correct the typography and verify the physical content of these expressions.","section":"Sec. III.B.1, Eqs. (35)-(36)"},{"comment":"The 4×4 matrix t(E) in Eq. (30) has duplicated entries in its third and fourth columns: seh_{31}, seh_{41}, shh_{31}, and shh_{41} appear twice, while the corresponding elements for contact 2 (seh_{32}, seh_{42}, shh_{32}, shh_{42}) are missing. Since this matrix is used to construct the ℓ^± matrix in Eq. (31) and the subsequent noise expressions, the authors should correct the typo and verify any consequences for Eqs. (31)-(36).","section":"Sec. III.B, Eq. (30)"}],"minor_comments":[{"comment":"The device scheme appears twice in the text with the same caption; one copy should be removed.","section":"Sec. III.A, Fig. 2"},{"comment":"The notation '6kBT' and '18kBT' should use explicit k_B (e.g., 6 k_B T) for clarity and consistency with the rest of the text.","section":"Eq. (17)"},{"comment":"The phrase 'Andreev's processes' should be 'Andreev processes'.","section":"Sec. IV"},{"comment":"The sign function sgn(α) is defined in Sec. II.A, but it would be helpful to restate its definition at its first use in Eq. (16), since the notation appears again in several later equations.","section":"Eq. (16)"}],"recommendation":"major_revision","confidential_remarks":"The paper's central algebraic content is sound within the stated energy-independent limit, but the abstract overstates the generality of the heat-conductance result. The chiral-device section also contains apparent typographical issues in Eqs. (30) and (35)-(36). If the authors qualify the energy-independence condition and correct the chiral formulas, the paper would be suitable for publication. The novelty relative to Refs. [63-66] is incremental but adequate for a mesoscopic physics journal."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThis paper gives scattering-theory expressions for zero-frequency charge noise in multiterminal normal-superconductor systems under thermal biases. The genuinely new piece is the observation that, when the scattering matrix is energy-independent, the background (thermal) noise in the self-correlators contains the same l^-_ik functions that enter heat conductances, not just the electrical l^+ functions. Eq. (15) is a clean consequence of unitarity and the algebra checks out. The excess-noise section also contains something I read as new: explicit thermal shot-noise expressions for NSN and chiral quantum-Hall devices, including an interference term in the NSN cross-correlator that requires both normal and Andreev reflections.\n\nThe paper does honest work in Section II C 1, where the energy-independent assumption is stated and used. The normal limits reduce correctly, and the physical discussion of why self-correlators but not cross-correlators pick up l^- is sensible.\n\nThe soft spots are real. The abstract and conclusions present the heat-conductance dependence as a general property of multiterminal hybrid systems, but Eq. (12) and Eq. (10) only share the same energy kernel when l^-_ik(E) is constant, i.e. s(E)=s. For energy-dependent scattering the identification between background noise and heat conductance fails in general. That qualification is in the derivation but not in the headline. That is an overgeneralization, not a contradiction: within the stated limit Eq. (15) is correct. Also the excess-noise results are quoted without intermediate algebra, Eq. (30) has clear typos, and the manuscript contains duplicated text and figures. None of this transmits a fatal flaw—the load-bearing pieces are the energy-independent formulas—but it needs revision.\n\nWho gets value: people working on thermoelectric noise in hybrid structures, and experimenters who want a formula sheet for extracting heat conductance from charge noise. It deserves a serious referee; I would send it out with encouragement to fix the abstract and clean up the examples. My own verdict would be conditional acceptance after those revisions.","headline":"Solid scattering-theory results for delta-T noise in multiterminal N/S systems, with the heat-conductance identification valid only for energy-independent scattering but presented as general.","tokens_in":24881,"tokens_out":1536,"would_cite":true,"duration_ms":15828,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["72.70.+m","74.45.+c","73.23.-b"],"model":"deepseek-v4-flash","headline":"In multiterminal hybrid superconductor-normal devices, temperature-bias noise at a terminal encodes the heat conductances to all other terminals, not just the electrical conductance.","keywords":["Delta-T noise","hybrid normal-superconducting systems","Landauer-Büttiker scattering theory","background noise","excess noise","heat conductance","Andreev reflection","thermal shot noise"],"falsifier":"Calculate the difference between the background self-noise integrand of Eq. (12) and the heat-conductance combination of Eq. (10) for a scatterer whose transmission functions vary with energy on the scale of $k_B T$ (e.g., a resonant level or an Andreev bound state near the Fermi energy); a nonvanishing difference at finite temperature bias would show that the heat-conductance interpretation fails outside the energy-independent limit. Experimentally, one could heat one terminal $k$ of a multiterminal NSN device and compare the rise in the self-noise of a distant terminal $i$ with the independently measured heat conductance $L^{HH}_{ik}$; agreement would confirm the claim only within the energy-independent regime.","tokens_in":2054,"feed_emoji":"🌡️","tokens_out":5916,"duration_ms":126042,"temperature":0.7,"pith_summary":"This paper studies charge-current noise in multiterminal normal-superconductor hybrid devices when the contacts are held at different temperatures, a regime known as $\\Delta T$-noise. Using the Landauer–Büttiker scattering approach, the authors split the noise into a background part and an excess (partition) part. Their central claim is that in the presence of temperature biases, with superconducting terminals grounded, the background noise in the self-correlation of a terminal's current contains terms strictly related to the heat conductances to all other terminals, not only the electrical conductance that enters the equilibrium Johnson-Nyquist formula. This would make a charge-noise measurement a potential probe of heat transport. The paper also shows that thermally induced excess noise acquires Andreev-specific interference terms, and it illustrates both effects in a three-terminal NSN junction and in a spin-resolved quantum Hall device.","feed_headline":"Thermal noise can now reveal heat flow in superconductor devices","feed_subtitle":"A charge-noise measurement alone may map heat conductances in multiterminal hybrid nanodevices.","key_machinery":"The central object is the scattering matrix $s(E)$ of a Bogoliubov–de Gennes description, from which the paper defines transmission functions $\\ell^\\pm_{ik}(E) = N_i \\delta_{ik} - \\mathrm{Tr}[s^{ee\\dagger}_{ik}s^{ee}_{ik}] \\pm \\mathrm{Tr}[s^{he\\dagger}_{ik}s^{he}_{ik}]$, where $\\ell^+$ governs charge transport and $\\ell^-$ enters the heat conductance. The argument separates the zero-frequency noise into background noise (Eq. (12), built from Fermi-function factors $F_i^e = 2 f_i^e(1-f_i^e)$) and excess noise (Eq. (13), built from squared Fermi-difference integrals $D^{k\\gamma l\\delta} = [f^\\gamma_k - f^\\delta_l]^2$). The load-bearing step is the energy-independent reduction of the background self-correlator to Eq. (15), which uses the unitarity identity $\\sum_k \\ell^-_{ik} = 0$ to expose the $\\ell^-$ (heat-conductance) terms. For the excess noise, the asymptotic slope $\\eta = 2\\ln 2 - 1$ of the squared-difference integrals defines the thermal shot-noise regime, and the NSN example expresses all results in terms of the normal and Andreev probabilities $R, T, R_A, T_A$.","core_discovery":"The paper's central discovery is the exact structure of the background noise for multiterminal hybrid systems. At thermal equilibrium the background noise of terminal $i$ reduces to the Johnson-Nyquist term governed by $\\ell^+$ (electrical conductance); but when terminals are held at different temperatures, the self-correlator $\\bar{S}_{ii}$ gains a sum over other terminals $k$ of terms proportional to $(T_k - T_i)$ times the transmission functions $\\ell^-_{ik}$ that also enter the heat conductance $L^{HH}_{ik}$. In the energy-independent limit the background noise takes the closed form $\\bar{S}_{ii}/(2 k_B G_0) = 2 T_i \\ell^+_{ii} + \\sum_k (T_k - T_i)[\\mathrm{Tr}(s^{ee\\dagger}_{ik}s^{ee}_{ik}) + \\mathrm{Tr}(s^{he\\dagger}_{ik}s^{he}_{ik})]$, so the thermal part measures excitation transport irrespective of quasiparticle charge. The paper further shows that the excess noise under temperature bias differs from the voltage-bias case: self-correlators obey partition-type forms built from $\\ell^-$ only, and cross-correlators contain an interference term proportional to $\\sqrt{R R_A T T_A}$ that is nonzero only when normal and Andreev processes coexist. These features are demonstrated for an NSN junction and for a four-terminal integer quantum Hall bar with a superconducting finger.","pith_inferences":["If the background-noise/heat-conductance link survives contact with experiment, it provides a route to heat metrology in nanoscale hybrid devices where direct heat-current measurement is impractical; the paper identifies this possibility but does not develop a measurement protocol.","The energy-independent restriction suggests a testable extension: the mismatch between the noise and heat-conductance kernels at finite energy dependence could itself be used to spectroscopically probe the energy structure of the scattering matrix.","The interference term in the thermal shot noise of cross-correlators points toward phase-sensitive detection of Andreev processes, e.g., an experiment that varies the relative phase between normal and Andreev scattering amplitudes (here encoded in φ−ψ) and tracks the resulting noise modulation."],"forward_implications":["In a grounded-superconductor multiterminal device, the background charge noise of a terminal becomes a combined probe of electrical and heat conductances, so a measurement at a single terminal can give access to heat-transport information that normally requires separate heat-current measurements.","The thermal shot-noise self-correlators take the partition form $x(1-x)$ with $x$ the sum of normal and Andreev transmission (or reflection) probabilities, so their noise is set by the total quasiparticle flux regardless of charge sign.","The cross-correlator thermal shot noise contains an interference term $\\propto \\sqrt{R R_A T T_A}$ that exists only when normal and Andreev processes coexist, making the ratio of electrical to thermal shot noise a marker of superconducting proximity.","In the chiral quantum Hall device, the sign of the voltage floor in the excess noise reveals which process, spin mixing or Andreev conversion, dominates current partitioning between the edge states."],"supporting_citations":[{"why":"Provides the scattering-theory formalism for current noise in mesoscopic conductors, including the definition of symmetrized correlators and the background/excess decomposition the paper builds on.","marker":"[10]"},{"why":"Supplies the scattering-matrix treatment of current fluctuations with Andreev scattering, the foundation of the $\\ell^\\pm$ transmission-function structure used throughout.","marker":"[61]"},{"why":"Gives the average-current formulas and the Onsager-matrix form for charge and heat currents from which the paper defines the $\\ell^\\pm$-based conductances.","marker":"[70]"},{"why":"Defines the thermoelectric Onsager coefficients of mesoscopic superconductors, i.e., the heat-conductance combination the background noise is claimed to reproduce.","marker":"[73]"},{"why":"Shows experimentally that shot noise in NSN structures can probe thermal conductance, the precedent the paper extends to the $\\Delta T$ background term.","marker":"[64–66]"},{"why":"Introduced $\\Delta T$-noise in atomic-scale junctions, the phenomenon this paper generalizes to multiterminal hybrid superconducting systems.","marker":"[35]"},{"why":"Analyzed noise in NSN junctions under a temperature gradient, providing the direct comparison point for the paper's NSN application.","marker":"[53]"}],"fun_headline_variants":["Thermal noise maps heat conductance in hybrid nanodevices","ΔT-noise exposes heat flow in superconductor junctions","Temperature bias noise reveals heat transport in hybrids","Noise under temperature bias measures heat conductance","Hybrid noise: thermal bias unveils heat flow channels"],"cache_read_input_tokens":27136,"weakest_assumption_plain":"The load-bearing premise is that the scattering matrix is energy independent, $s(E) = s$; only then do the background-noise integral and the heat-conductance integral share the same energy kernel, making the claim 'background noise measures heat conductance' exact rather than approximate.","fun_headline_variants_meta":{"raw":{"variants":["Thermal noise maps heat conductance in hybrid nanodevices","ΔT-noise exposes heat flow in superconductor junctions","Temperature bias noise reveals heat transport in hybrids","Noise under temperature bias measures heat conductance","Hybrid noise: thermal bias unveils heat flow channels"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000227,"raw_usage":{"total_tokens":1572,"prompt_tokens":1145,"completion_tokens":427,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":761,"completion_tokens_details":{"reasoning_tokens":351}},"tokens_in":761,"tokens_out":427,"duration_ms":4052,"temperature":1.0,"reasoning_tokens":351,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T17:23:32.798260+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Calculate the difference between the background self-noise integrand of Eq. (12) and the heat-conductance combination of Eq. (10) for a scatterer whose transmission functions vary with energy on the scale of $k_B T$ (e.g., a resonant level or an Andreev bound state near the Fermi energy); a nonvanishing difference at finite temperature bias would show that the heat-conductance interpretation fails outside the energy-independent limit. Experimentally, one could heat one terminal $k$ of a multiterminal NSN device and compare the rise in the self-noise of a distant terminal $i$ with the independently measured heat conductance $L^{HH}_{ik}$; agreement would confirm the claim only within the energy-independent regime.","supporting_citations":[{"cited_title":"Local thermometry of NbSe$_2$ flake with delta-$T$ noise measurements","cited_arxiv_id":"2407.09075","evidence_quote":"Supplies the scattering-matrix treatment of current fluctuations with Andreev scattering, the foundation of the $\\ell^\\pm$ transmission-function structure used throughout."},{"cited_title":"Mohapatra and C","cited_arxiv_id":null,"evidence_quote":"Gives the average-current formulas and the Onsager-matrix form for charge and heat currents from which the paper defines the $\\ell^\\pm$-based conductances."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduced $\\Delta T$-noise in atomic-scale junctions, the phenomenon this paper generalizes to multiterminal hybrid superconducting systems."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Analyzed noise in NSN junctions under a temperature gradient, providing the direct comparison point for the paper's NSN application."}],"review_version":1}