{"id":"25ee2730-bce4-4507-9754-6e617cd3bcd9","arxiv_id":"2412.01394","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Tilted Dirac materials with valley-dependent gaps can produce a sideways Josephson current with asymmetric critical currents, a transverse Josephson diode effect that reaches 100% efficiency at tuned gaps.","lead":"A theory paper predicts a transverse Josephson diode effect in junctions made from tilted Dirac materials, where the sideways supercurrent is stronger in one direction than the other and can reach 100% efficiency. This could enable superconducting devices whose output signal travels perpendicular to the input, fully separating the two paths.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Infinite-strip transverse current is an equilibrium interface quantity; the TJDE device claim requires a finite-width multiterminal calculation that is not provided.","rationale":"The most load-bearing requirement for the central claim is not the algebraic derivation (which is internally consistent and uses standard methods) but the mapping from the computed equilibrium current density to a measurable transverse diode current. The paper explicitly frames the TJDE as a device that can decouple input and output paths; that framing fails if the transverse current is only a local interface current with no terminal attached. The reader's weakest_assumption identifies exactly this premise, and I agree. I would not move to reject: within the stated infinite-strip model, the asymmetry is a legitimate result, and the Furusaki-Tsukada/McMillan formalism is standard. But the device relevance is conditional on a finite-width/multiterminal calculation that is absent. The concrete finite-width tight-binding test would settle whether the concern lands. Secondary concerns (the 100% requiring fine-tuned κ, the heavy-doping approximation, the evaluation at x=0) are subsumed: the finite-width calculation would also test robustness to those choices. Hence the reader's CONDITIONAL verdict remains appropriate.","tokens_in":15161,"tokens_out":14118,"duration_ms":131041,"concrete_test":"Model the same SNS junction on a finite-width strip with transverse normal-metal leads attached to the sides, using a real-space tight-binding implementation (e.g., Kwant) with the 8-Pmmn borophene parameters vx=0.86vF, vy=0.69vF, vt=0.32vF and valley-gap difference κ tuned to the claimed 100% point (≈1.6). Compute the current between the transverse leads as a function of the longitudinal phase difference φ for widths W ≫ ξ0 and W ≈ ξ0. If the transverse two-terminal critical currents become equal or the asymmetric CPR is suppressed, the infinite-strip result is not an accessible transverse diode; if the asymmetric CPR survives with the maximal asymmetry, the device claim is supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim's device-level content — a transverse diode that 'can completely decouple the input signal path from the output' — depends on the transverse current computed in the infinite-strip model being an accessible transport current in a finite multiterminal device. The calculation assumes translational invariance along y (after Eq. 3) and evaluates the current at the NS interface x=0, where it decays exponentially into the S region (TJDE section). No transverse leads, edges, or bias enter the model, and the quality factor Qt in Eq. (7) is defined from the CPR of this local equilibrium quantity. For the claim to hold, a finite-width device must reproduce the asymmetric transverse CPR as the current between transverse leads; contacts would break y-translational invariance, introduce return/edge currents, and back-react on the Andreev amplitudes. Without such a demonstration, the 100% efficiency is an interface property of a boundary-free idealization, not a verified device property.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper proposes a transverse Josephson diode effect (TJDE) in ballistic short SNS junctions based on tilted Dirac materials with valley-dependent gaps. Using a McMillan Green's-function construction and a Furusaki-Tsukada-type formula, the author derives the transverse current density j_y at the NS interface (Eq. (5)) together with the longitudinal Josephson current j_x (Eq. (6)). For parameters representing 8-Pmmn borophene, the transverse current-phase relation is nonsinusoidal and yields unequal positive and negative critical currents, leading to a quality factor Q_t (Eq. (7)) that can reach 100% in magnitude; the longitudinal CPR remains odd with j_x(phi)=-j_x(-phi), so no longitudinal diode effect appears. The ABS analysis attributes the TJDE to tilt-induced asymmetric transverse subgap modes under broken time-reversal symmetry (valley-dependent gaps kappa != 0).","tokens_in":15176,"tokens_out":11585,"duration_ms":99833,"significance":"The strength of the paper is its symmetry bookkeeping and the use of a standard ballistic transport framework. The author explicitly checks the limiting behaviors: j_y vanishes at kappa=0 (time-reversal preserving) and at v_t=0, and the longitudinal current remains reciprocal; these are nontrivial internal consistency checks that are satisfied. The qualitative explanation in terms of asymmetric Andreev subgap modes is physically transparent. The result, if correct, constitutes a new transverse variant of the Josephson diode effect and could be of interest for nonreciprocal superconducting circuits. The paper does not fit parameters to the target effect; the model parameters are taken from the borophene literature and kappa is scanned, so the prediction is not circular. The main caveat is that the calculation is for an infinite strip and computes a local equilibrium current density; the device-level claims go beyond the model.","major_comments":[{"comment":"The abstract states that the TJDE 'can completely decouple the input signal path from the output,' and Fig. 3 presents a 100% quality factor. However, the model is an infinite strip that is translationally invariant along y, and j_y is computed as the equilibrium current density at the NS interface x=0 (Eq. (5) and the discussion after Eq. (3)). No transverse leads, edges, or bias enter the calculation. A transverse current in an infinite strip is not by itself a transport current in a multiterminal device; a finite-width sample would require edge states/return currents and a concrete way to collect the transverse signal. Unless the author provides a finite-width multiterminal calculation or explicitly restricts the claim to the interface current density per unit width, the device-level decoupling claim is unsupported.","section":"Abstract and 'Transverse Josephson diode effect' section (after Eq. (5))"},{"comment":"The quality factor Q_t is defined from j_y(phi) at a single point x=0. The transverse current decays exponentially into the superconducting regions (stated in the TJDE section), so the total transverse current through a finite junction is not computed. To make Q_t an observable, the author should define the measurable quantity (e.g., the transverse current per unit length integrated over the junction region, or the current collected by transverse terminals) and demonstrate that the diode efficiency is unchanged under that definition. As written, Q_t characterizes a local current density rather than a supercurrent in a circuit.","section":"Eq. (7) and Fig. 3"},{"comment":"The central formula (5) is not independently verifiable from the manuscript. The Andreev amplitudes a^ell_1 and a^ell_2 are not given; the SM constructs the Green's function and then jumps to Eq. (S31) after dropping normal-reflection terms, but the matching conditions leading to a^ell_{1,2} are not shown. Because all numerical results and the diode claim follow from these amplitudes, the derivation should be completed (or a computer algebra script should be provided) so that a reader can reproduce Eq. (5) and the CPRs in Figs. 2 and 3.","section":"Eq. (5) and Supplementary Material"}],"minor_comments":[{"comment":"The relation E_ABS(ky,phi) = -E_ABS(ky,phi) is a typo; as written it forces E_ABS = 0. Please state the intended symmetry, e.g., E_ABS(ky,phi) = -E_ABS(-ky,-phi) for the particle-hole symmetry.","section":"ABS analysis, paragraph after Fig. 4(b)"},{"comment":"The notation nu_0 and nu_z is undefined. Please define the Pauli matrices acting in Nambu space.","section":"Eqs. (3) and (S14)"},{"comment":"The 'source current density operator' j_s is not defined. Please provide its explicit form or clarify the decomposition of the total current so that the statement that j_y is contributed only by the electronic term can be checked.","section":"Model and formalism, after the Heisenberg equation"},{"comment":"The caption uses 'mu L / hbar v_F = 4.2'; please specify that L is the junction length and mu is the normal-region chemical potential, and that this product sets the normal-region phase.","section":"Fig. 2 caption"},{"comment":"Typos: 'In order to obtained' should be 'to obtain'; 'Uptonow' and 'somehighlyefficient' in the Introduction are missing spaces in the compiled text.","section":"Introduction and Model and formalism"}],"recommendation":"major_revision","confidential_remarks":"The paper is a single-author theory Letter with a clean symmetry-based prediction, but the abstract oversells a device-level capability that the infinite-strip calculation does not establish. If the author can either implement a finite-width multiterminal geometry or substantially weaken the decoupling claim, the paper could become acceptable. The editor may also wish to consider that the supplementary material is thin; the explicit Andreev amplitudes should be supplied."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a legitimate new calculation, not a new framework. The transverse Josephson diode effect in an infinite-strip tilted Dirac junction is computed cleanly; the symmetry checks pass; the Andreev-level picture explains the mechanism. But the 100% quality factor and the \"complete decoupling\" claim are properties of a boundary-free equilibrium interface current, not of a device with transverse leads. The stress-test concern holds up: Eq. (5) is evaluated at x=0 for a y-translation-invariant strip, and no transverse contacts, edges, or bias appear anywhere. So the advertised application is not derived.\n\nWhat is genuinely good: the symmetry bookkeeping is careful and internally consistent. The transverse current vanishes when time-reversal symmetry is restored (κ=0) and when the tilt is zero; the longitudinal current stays reciprocal, with symmetric critical currents; and jy(φ=0) is odd in κ. The decomposition into skew-tunneling and tilt-induced parts is physically transparent, and the ABS analysis in Fig. 4 gives a clear mechanistic story: broken TRS plus tilt makes the transverse group velocities unequal, which is exactly the condition for a nonreciprocal transverse supercurrent. No parameters are fitted to produce the diode effect; the asymmetry is a computed output.\n\nSoft spots, in order of importance. First, the device-level framing overreaches. A Josephson diode normally means rectified transport between terminals. Here the asymmetry is between the maxima of a local equilibrium current-phase relation along +y and −y in an infinite strip. To call it a diode and claim input-output path decoupling, you need to show this current survives as the current between real transverse leads. That is a missing calculation, not a minor omission, because contacts would break the translational invariance that the whole derivation relies on. Second, the 100% quality factor appears at tuned gap parameters and at the interface position x=0; realistic finite-width and finite-temperature effects could reduce it, though the temperature dependence shown is at least honest. Third, the supplementary algebra is compressed; I could follow the route, but not every step is independently checkable from the text, and the numerical implementation is unspecified.\n\nI do not think any of this makes the central physics wrong. The model is standard, the symmetry constraints are respected, and the qualitative prediction of a tilt-assisted transverse supercurrent under broken TRS is plausible. But the paper should either supply a finite-width multiterminal calculation or explicitly restrict its claims to an interface Hall supercurrent.\n\nMy recommendation: send it to referees. It deserves serious review, and the revision request should center on the device claim, not on the core calculation.","headline":"A clean calculation of a transverse Josephson Hall current in an infinite-strip tilted Dirac junction, with a real but unproven device-level claim: the 100% quality factor is an interface property until someone models transverse leads.","tokens_in":15868,"tokens_out":3037,"would_cite":false,"duration_ms":32661,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["74.50.+r"],"model":"deepseek-v4-flash","headline":"A tilted-Dirac Josephson junction with valley-contrasting gaps develops a phase-driven transverse supercurrent with unequal critical currents, reaching a 100% diode quality factor while the longitudinal current stays reciprocal.","keywords":["transverse Josephson diode effect","Josephson Hall current","tilted Dirac cone","valley-dependent gap","Andreev bound states","current-phase relation","nonreciprocal supercurrent","8-Pmmn borophene"],"falsifier":"Attach transverse normal leads to a finite-width version of the junction and measure the transverse current-phase relation while tuning $\\kappa$: if the positive and negative transverse critical currents are equal once the transverse channel is electrically contacted, or if the contact's back-action on the Andreev amplitudes restores reciprocity, the 100% quality-factor claim fails. A numerical check on a finite-width strip, testing whether the interface current returns through edge channels rather than feeding a transverse reservoir, would likewise settle whether the effect is a device diode or an interface property.","tokens_in":14760,"feed_emoji":"⚡","tokens_out":16275,"duration_ms":122382,"temperature":0.7,"pith_summary":"Most proposals for Josephson diodes rectify supercurrents along the junction axis, so the input and output signals share one path. This paper predicts a transverse version: in a short, ballistic superconductor–normal–superconductor junction built on a tilted Dirac material with valley-contrasting gaps, breaking time-reversal symmetry produces an interface-bound supercurrent that flows perpendicular to the junction, is driven by the superconducting phase difference, and has a nonsinusoidal current-phase relation. Because the positive and negative transverse critical currents are unequal, the junction acts as a transverse Josephson diode, and the paper shows its quality factor can reach $100\\%$ — total one-way character — when the valley-gap asymmetry $\\kappa$ is tuned. The longitudinal Josephson current, by contrast, stays sinusoidal and reciprocal, so the diode behavior is genuinely transverse. If the prediction survives being connected to real leads, this geometry would decouple the output signal path from the input and open a new axis of control for nonreciprocal superconducting devices.","feed_headline":"Supercurrent diode rectifies sideways at 100% efficiency","feed_subtitle":"In a tilted Dirac junction the transverse critical currents become asymmetric, decoupling output from input.","key_machinery":"The load-bearing object is the transverse current formula obtained from McMillan's Green's function in the heavy-doping limit,\n$$j^\\ell_y = e k_B T \\sum_{k_y, \\omega_n>0} \\frac{\\$\\Delta$}{\\sqrt{\\$omega_n^{2}$ + \\$\\Delta$^2}} \\frac{v_y \\tan\\$\\theta$ + \\ell v_t \\sec\\$\\theta$}{v_x} \\operatorname{Re}\\bigl[a^\\ell_1(\\varphi, i\\omega_n) + a^\\ell_2(\\varphi, i\\omega_n)\\bigr] $e^{{2\\Omega_n x/v_x}}$,$$\nwith $a^\\ell_{1,2}$ the Andreev reflection amplitudes and $\\theta = \\arctan(v_y k_y/\\mu_s)$. The prefactor splits into a skew-tunneling piece proportional to $v_y \\tan\\theta$ and a tilt-driven piece proportional to $\\ell v_t \\sec\\theta$; in the heavy-doping regime their ratio is of order $|\\mu/\\mu_s|$, so the transverse Hall current is dominated by the tilt-induced transverse momentum of the Cooper pairs. The diode signature is packaged in the quality factor $Q_t = (j^+_{y,c} - |j^-_{y,c}|)/(j^+_{y,c} + |j^-_{y,c}|)$, and its physical origin is displayed in the Andreev bound states $E_{\\mathrm{ABS}}(k_y, \\varphi)$: the tilt skews the two valleys' spectra in opposite $k_y$ directions, and broken time-reversal symmetry splits the subgap group velocities ($v_+ \\neq v_-$), so that for large $\\kappa$ only one transverse propagation direction per valley survives.","core_discovery":"The paper's central claim is that a ballistic, short Josephson junction built from a tilted Dirac material with valley-dependent gaps carries a transverse supercurrent at its interfaces when time-reversal symmetry is broken by unequal valley masses. Expressed through Andreev reflection amplitudes in a Furusaki-Tsukada-like formula, this current $j_y(\\varphi)$ is $2\\pi$-periodic and nonsinusoidal, is nonzero even at zero phase difference, vanishes at $\\kappa = 0$, and decays into the superconducting banks over the coherence length. The forward and backward transverse critical currents are unequal, so the junction acts as a transverse Josephson diode (TJDE) whose quality factor $Q_t$, evaluated with 8-Pmmn borophene parameters, reaches $\\pm 100\\%$ at tuned valley-gap asymmetry $\\kappa$. The mechanism is the tilt-induced asymmetry of Andreev subgap modes: under broken time-reversal symmetry the two valleys' transverse group velocities satisfy $v_+ \\neq v_-$, and beyond a critical $\\kappa$ each valley has only one allowed transverse propagation direction. The longitudinal current remains a sinusoidal $\\pi$-phase supercurrent with $j_x(\\varphi) = -j_x(-\\varphi)$, so the nonreciprocity is purely transverse.","pith_inferences":["My inference, not the paper's: the paper models an infinite strip, so the 100% quality factor is an equilibrium interface property; whether it survives in a finite multiterminal geometry with transverse contacts, where the contacts back-act on the Andreev amplitudes, is not computed and would decide the device claim.","My inference: because the transverse current grows with the tilt velocity $v_t$ and the mass imbalance, strain-tunable tilted Dirac materials or Floquet-driving schemes that generate the valley-dependent mass could switch the transverse diode on and off optically — a control knob the paper does not propose.","My inference: the short-junction, ballistic treatment leaves the behavior at junction length $L$ comparable to the coherence length, and with disorder, unaddressed; extending the calculation along those axes would test whether the transverse diode is a robust transport feature or a clean-limit phenomenon."],"forward_implications":["The transverse interface current is nonzero only when both the tilt $v_t$ and the valley-gap asymmetry $\\kappa$ are finite; it reverses sign with $\\kappa$ and vanishes at $\\kappa = 0$.","The transverse current-phase relation is $2\\pi$-periodic and nonsinusoidal, with an anomalous contribution at $\\varphi = 0$, and the forward versus backward critical currents differ, defining a transverse diode polarity $Q_t$ that flips sign with $\\kappa$.","The quality factor $Q_t$ reaches $\\pm 100\\%$ at tuned valley-gap asymmetry and is larger at low temperature than near $T_c$.","The longitudinal Josephson current is a sinusoidal $\\pi$-phase supercurrent with reciprocal critical currents, so no diode effect occurs along the junction axis.","The nonreciprocity originates in tilt-induced asymmetric Andreev subgap modes ($v_+ \\neq v_-$) per valley, not in a Doppler shift of quasiparticle energies; at sufficiently large $\\kappa$ each valley retains only a single transverse propagation direction."],"supporting_citations":[{"why":"Supplies the Furusaki-Tsukada formula expressing Josephson current through Andreev reflection amplitudes, which the paper generalizes to the transverse current.","marker":"[34]"},{"why":"Provides the McMillan Green's-function construction for superconductor–normal-metal interfaces used to derive the transverse current.","marker":"[37]"},{"why":"Extends McMillan's method to Josephson effects via scattering basis spinors, the technique used for the retarded Green's function.","marker":"[38]"},{"why":"Establishes the heavy-doping limit and pairing-basis treatment of superconductivity in ballistic graphene junctions that justifies the regime |µs| ≫ {|µ|, Δ}.","marker":"[20]"},{"why":"Demonstrates tilted Dirac fermions generating transverse (tunneling valley Hall) transport in tunnel junctions, the phenomenon this paper ports into Josephson junctions.","marker":"[15]"},{"why":"Supplies the general theory of Josephson diodes and the nonreciprocity/quality-factor framework the transverse effect is measured against.","marker":"[1]"},{"why":"Gives the tunable Josephson diode on a topological-insulator surface whose quality factor shares the sign-reversal symmetry Qt(κ) = −Qt(−κ).","marker":"[6]"},{"why":"Prior field-free graphene device achieving a 100% quality factor, the efficiency benchmark the TJDE claim is compared with.","marker":"[14]"},{"why":"Source of the 8-Pmmn borophene band parameters (vx = 0.86vF, vy = 0.69vF, vt = 0.32vF) used in the numerical evaluation.","marker":"[26]"},{"why":"Supplies the Andreev reflection transfer matrices for ballistic graphene junctions used in the Andreev bound-state analysis.","marker":"[55]"}],"fun_headline_variants":["Transverse supercurrent diode hits 100% efficiency","Sideways supercurrent diode decouples input from output","Tilted Dirac junction yields fully polarized diode","Transverse Josephson diode reaches perfect efficiency","100% efficient transverse supercurrent diode"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The transverse current is computed for an infinitely long strip that is translation-invariant along the transverse direction, with no transverse leads, edges, or bias in the model; the device-level promise that the effect decouples input from output requires this interface-bound equilibrium current to survive as an accessible transverse transport channel in a finite multiterminal device.","fun_headline_variants_meta":{"raw":{"variants":["Transverse supercurrent diode hits 100% efficiency","Sideways supercurrent diode decouples input from output","Tilted Dirac junction yields fully polarized diode","Transverse Josephson diode reaches perfect efficiency","100% efficient transverse supercurrent diode"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00024,"raw_usage":{"total_tokens":1499,"prompt_tokens":909,"completion_tokens":590,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":525,"completion_tokens_details":{"reasoning_tokens":519}},"tokens_in":525,"tokens_out":590,"duration_ms":5170,"temperature":1.0,"reasoning_tokens":519,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T04:27:00.460860+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Attach transverse normal leads to a finite-width version of the junction and measure the transverse current-phase relation while tuning $\\kappa$: if the positive and negative transverse critical currents are equal once the transverse channel is electrically contacted, or if the contact's back-action on the Andreev amplitudes restores reciprocity, the 100% quality-factor claim fails. A numerical check on a finite-width strip, testing whether the interface current returns through edge channels rather than feeding a transverse reservoir, would likewise settle whether the effect is a device diode or an interface property.","supporting_citations":[{"cited_title":"Kapri, B","cited_arxiv_id":null,"evidence_quote":"Supplies the Furusaki-Tsukada formula expressing Josephson current through Andreev reflection amplitudes, which the paper generalizes to the transverse current."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the McMillan Green's-function construction for superconductor–normal-metal interfaces used to derive the transverse current."},{"cited_title":"Chiles, E","cited_arxiv_id":null,"evidence_quote":"Demonstrates tilted Dirac fermions generating transverse (tunneling valley Hall) transport in tunnel junctions, the phenomenon this paper ports into Josephson junctions."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the tunable Josephson diode on a topological-insulator surface whose quality factor shares the sign-reversal symmetry Qt(κ) = −Qt(−κ)."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Prior field-free graphene device achieving a 100% quality factor, the efficiency benchmark the TJDE claim is compared with."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Source of the 8-Pmmn borophene band parameters (vx = 0.86vF, vy = 0.69vF, vt = 0.32vF) used in the numerical evaluation."},{"cited_title":"Scharf, A","cited_arxiv_id":null,"evidence_quote":"Supplies the Andreev reflection transfer matrices for ballistic graphene junctions used in the Andreev bound-state analysis."}],"review_version":1}