{"id":"9952e00f-8b88-4cbb-a999-38322bd172df","arxiv_id":"2507.01941","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Disorder enhances the orbital Hall response in 2D mesoscopic devices through skew scattering, and width-dependent decay of the orbital current yields long orbital relaxation lengths.","lead":"Numerical simulations show that adding disorder to a 2D lattice can strengthen and even reverse the orbital Hall current, a sideways flow of orbital angular momentum. The same simulations use wide, rectangular devices to measure how far orbital information travels before it fades, giving an orbital relaxation length.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The skew-scattering attribution rests on an unverified regime classification: 1–4 eV is called 'diffusive' with a citation to Fig. S2, which shows size scaling of the OHC, not charge transport versus U; the 1/(U+U0) scaling alone does not identify the mechanism.","rationale":"The reader's weakest assumption correctly identifies the unverified diffusive-regime classification. I agree that this is the most load-bearing issue, because the paper's signature result—'dominance of skew-scattering mechanism in the diffusive regime'—is inferred from the functional form 1/(U+U0) and from the linear Hall angle, and both inferences presuppose that the system is in the diffusive transport regime. Without a transport-regime diagnostic, the same curves could be produced by other disorder-induced mechanisms (e.g., resonant scattering or localization precursors), so the central attribution is not uniquely determined. This is an internal-support problem rather than a disagreement with the community's skew-scattering calculations; the numerical simulations themselves are standard KWANT calculations and the averaging is adequate. The concern is also addressable: a conductance scaling study over L would settle the regime. Therefore I retain the reader's CONDITIONAL verdict: the paper should not be accepted as definitive until the diffusive-window claim is demonstrated, but the findings are plausible and the fix is concrete. Secondary issues (lack of uncertainty estimates for λ_L, the repeated Fig. S2 citation for the localized regime) are worth correcting but do not change the verdict.","tokens_in":12900,"tokens_out":9009,"duration_ms":108884,"concrete_test":"Recompute the disorder-averaged conductance G(L) for the square device at U=1, 2, 3, and 4 eV (E_F=-0.7 eV, t_sp=0.5 eV, λ_SOC=0) for L=30a, 60a, 120a, and 240a, with at least 300 disorder realizations, and examine the scaling of the typical conductance g_typ = exp⟨ln G⟩. If g_typ is approximately scale-invariant or follows the 2D weak-localization correction (g ≈ g0 - a ln L), the 1–4 eV window is genuinely diffusive; if g_typ decays exponentially with L, transport is localized. In the localized case, the skew-scattering interpretation of Fig. 3 would have no basis. This directly tests the sentence that currently cites the wrong figure.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that disorder enhances the OHC through skew scattering depends entirely on the sentence in the Fig. 3 discussion: 'For intermediate disorder (1 eV≲U≲4 eV), where charge transport is diffusive (see Fig. S2 in SM)'. The cited supplement does not support this. Fig. S2 plots J_Lz and Θ_OHE versus device size L at U=0.1, 0.5 and 1.0 eV; it contains no charge-transport observable and does not cover the claimed 1–4 eV interval. Fig. S3 is the only place with ⟨I⟩(U), but it merely shows a monotonic decrease, which is compatible with diffusive, quasiballistic, or localized transport. No mean free path, no localization length, and no conductance scaling versus L are presented for the 1–4 eV window. If that window is not actually diffusive, the fitted 1/(U+U0) dependence and the linear-in-U Hall angle do not uniquely identify skew scattering, and the paper's main physical conclusion is unsupported. The same miscitation is repeated for the localization regime ('see Fig. S2 in SM'), underscoring that the transport-regime classification is asserted rather than demonstrated.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript presents a numerical tight-binding study, implemented with Kwant, of the orbital Hall effect (OHE) in disordered mesoscopic square and rectangular devices. In square geometries, it reports that the orbital Hall current follows a 1/(U+U0) scaling for intermediate disorder, which the authors attribute to skew scattering, and that the orbital Hall angle becomes linear in disorder. In rectangular geometries, it reports an exponential decay of the orbital current with device width and extracts orbital relaxation lengths λ_L for several disorder strengths and Fermi energies. The manuscript also discusses the suppression of orbital-flip scattering by the two-dimensional character of the model.","tokens_in":13153,"tokens_out":6799,"duration_ms":69979,"significance":"The central claim is significant: if confirmed, it identifies a concrete disorder-based enhancement mechanism for the orbital Hall response and proposes a mesoscopic route to measuring orbital relaxation lengths, connecting to recent experimental efforts in orbitronics. The manuscript benefits from a transparent model, standard numerical methods (Kwant), and substantial disorder averaging. However, the key physical interpretation — dominance of skew scattering in the diffusive regime — depends critically on identifying the intermediate disorder range as diffusive, and this identification is currently unsupported by the data and supplementary figures. The quantitative extraction of relaxation lengths also lacks uncertainty estimates. These issues make the central conclusions not yet fully supported, although they are likely addressable within the manuscript's scope.","major_comments":[{"comment":"The sentence 'For intermediate disorder (1 eV≲U≲4 eV), where charge transport is diffusive (see Fig. S2 in SM)' is not supported by the cited supplementary figure. Fig. S2 plots the orbital Hall current density and Hall angle versus device size L, not any charge-transport observable as a function of U. Fig. S3 shows only that ⟨I⟩ decreases monotonically with U, which is equally compatible with diffusive, quasiballistic, or localized transport. Unless direct evidence of diffusive transport in this window is provided (e.g., conductance scaling with L, or a mean free path estimate), the attribution of the 1/(U+U0) dependence to skew scattering following Ref. [40] is not established. The same miscitation for the localized regime ('see Fig. S2 in SM') further indicates that the transport-regime classification is asserted rather than demonstrated. This issue is load-bearing for the paper's central claim.","section":"Main text, Fig. 3 discussion"},{"comment":"The exponential fits yield relaxation lengths λ_L = 224a, 130a, and 76a, but no uncertainty estimates or goodness-of-fit measures are reported, and the data points are shown without error bars. Since the text itself acknowledges that for U=0.5 and 1.0 eV the decay can be described by either a power law or an exponential, the quantitative extraction of λ_L for U=2.0 and 3.0 eV requires confidence intervals (or at least bootstrap estimates) to support the claim that the decay is exponential and to justify the reported dependence of λ_L on disorder and Fermi energy.","section":"Main text, Fig. 4(c)"},{"comment":"The fit ⟨J_Lz⟩ ∝ 1/(U+U0) with U0≈0.78 is presented for a single curve (tsp=0.7 eV), while the text implies that this scaling is a general feature of the diffusive regime. No uncertainty on U0 is given, and it is not demonstrated that the functional form holds for the other tsp values or device sizes. Since U0 is a fitted parameter, the authors should clarify the fitting procedure (e.g., the U range used, the number of points, and a goodness-of-fit metric) so that the claimed scaling can be evaluated independently.","section":"Main text, Fig. 3(a)"}],"minor_comments":[{"comment":"The notation P Lη η and P Sη η uses a doubled subscript that is confusing; it should be corrected to, for example, P^L_η and P^S_η.","section":"Equation (2) and surrounding text"},{"comment":"The dashed lines for panels (c,f) are stated to overlap with the left vertical axes and are not visible; the authors should adjust the plotting range or use a different linestyle so that the reference parameter (λ_SOC = 0.1 eV) can be identified.","section":"Figure 2"},{"comment":"The disorder-averaged currents are presented without error bars; adding them (or explicitly stating that they are smaller than the symbol size) would strengthen the reliability of the reported trends.","section":"Figures 3 and 4"},{"comment":"The main text refers to 'Fig. S2 in SM' for both the diffusive and localized regimes, but the relevant supplementary figure appears to be Fig. S3 (charge current versus U). Please update the cross-references accordingly.","section":"Main text, references to Supplementary Material"},{"comment":"The manuscript does not define a quantitative criterion for 'diffusive' transport; a precise definition (e.g., sample size L much larger than the elastic mean free path, or a scaling law of conductance with L) would make the regime classification testable and strengthen the interpretation.","section":"Main text, transport regime definitions"},{"comment":"The statement that the orbital current 'decays exponentially with increasing device width' is supported only for U=2.0 and 3.0 eV; for U=0.5 and 1.0 eV the text allows a power-law decay. Please rephrase to avoid overgeneralization.","section":"Main text, discussion of Fig. 4(a)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within the journal's scope. Apart from the mis-cited supplementary figure, the numerical work appears carefully executed. The main concern is that the central physics claim rests on a regime identification that is not currently documented; this seems addressable with additional computation (e.g., conductance scaling versus L in the 1–4 eV window) rather than a fundamental flaw. I also recommend that the authors add uncertainty estimates for the fitted parameters, as the quantitative claims about λ_L and U0 are otherwise difficult to assess."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"I largely agree with the reader's conditional verdict, but I want to be a bit more pointed about the soft spot. The genuinely new results are in the geometry: square device for generation, rectangular device for relaxation, with the exponential decay giving lambda_L values. That part is solid and useful. The disorder enhancement and sign reversal are also plausible in this model; the numerics are standard and the averaging is decent. The stress-test note is correct, and it hits a load-bearing sentence. The Fig. 3 discussion claims diffusive transport for 1-4 eV and cites Fig. S2; Fig. S2 is a size-scaling plot at U=0.1, 0.5, 1.0 and contains no charge-transport observable. The same citation backs the localization claim at U>4 eV. So the regime classification is asserted. The 1/(U+U0) scaling and linear theta are only evidence of skew scattering if the window is diffusive; if not, the central attribution is unsupported. This is fixable, but it's more than cosmetic. Also, lambda_L fits lack error bars, and the weak-U power-law vs exponential is by eye. The side-jump saturation story is plausible but unproven. The skew-scattering concept itself is not new—it follows Ref [40] by two co-authors—but the mesoscopic separation of generation and relaxation is new, and that's the contribution. Bottom line: this paper should be sent to referees, not desk-rejected. The authors need to show actual transport data for the 1-4 eV window, add error bars to the fits, and tone down the skew-scattering claim until the diffusive label is earned. For an orbitronics audience, it's a useful numerical addition.","headline":"Solid mesoscopic orbitronics numerics with a real, fixable flaw: the diffusive-regime claim is backed by a mis-cited supplementary figure.","tokens_in":13723,"tokens_out":3666,"would_cite":true,"duration_ms":38497,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper shows that scalar disorder can enhance the orbital Hall response in mesoscopic square devices, with a $\\langle J_{L_z}\\rangle \\propto 1/(U+U_0)$ scaling indicating skew scattering in the diffusive regime, and that in rectangular…","keywords":["orbital Hall effect","orbitronics","Anderson disorder","skew scattering","orbital relaxation length","mesoscopic transport","tight-binding model","orbital angular momentum"],"falsifier":"Compute the disorder-averaged conductance or elastic mean free path as a function of $U$ in the same square device: genuine diffusive transport at $U \\approx 1$--$4$ eV requires metallic scaling with system size and a mean free path well below $L$, whereas exponential size dependence would signal localization. If localization or ballistic effects are present, the $\\langle J_{L_z}\\rangle \\propto 1/(U+U_0)$ fit would not uniquely establish skew scattering. Alternatively, a direct Boltzmann calculation of the skew-scattering contribution for the same Hamiltonian could be compared quantitatively with the fitted $U_0 \\approx 0.78$ eV.","tokens_in":12658,"feed_emoji":"🌀","tokens_out":12401,"duration_ms":133104,"temperature":0.7,"pith_summary":"This paper asks how random disorder, rather than pristine crystal structure, controls orbital angular momentum currents in small devices. Using a real-space tight-binding model with $s$ and $p$ orbitals on a square lattice, it shows that moderate disorder can enhance the orbital Hall current and even reverse its sign, and that in an intermediate disorder range the current density follows $\\langle J_{L_z}\\rangle \\propto 1/(U+U_0)$ with $U_0 \\approx 0.78$ eV while the orbital Hall angle grows linearly with $U$ --- the signature of skew scattering. In longer rectangular devices the orbital current falls exponentially with width, giving a directly measured orbital relaxation length $\\lambda_L$ that depends on disorder and Fermi energy. The broader point is that disorder is not just a nuisance for orbitronics: it is a controllable source of orbital Hall response, and mesoscopic multi-terminal geometries can measure the relaxation length that determines how far orbital information travels.","feed_headline":"Disorder boosts orbital Hall currents and reveals decay length","feed_subtitle":"Atomic-level disorder can boost orbital Hall currents; their decay with width reveals the orbital relaxation length.","key_machinery":"The load-bearing object is a nearest-neighbor tight-binding Hamiltonian with one $s$ and three $p$ orbitals per site, scalar Anderson disorder $U$, and an $sp$-hopping $t_{sp}$ whose $k$-dependent hybridization creates the momentum-space orbital texture needed for the intrinsic orbital Hall effect. Transport is computed from the Landauer-Büttiker scattering matrix, with orbital-resolved transmissions obtained by inserting projectors $P^{L_z} = l_z \\otimes \\sigma_0$ into the transmission trace. The same model produces the extrinsic effect: scalar disorder scatters the orbitally textured Bloch states and, in the diffusive regime, yields the $1/(U+U_0)$ current scaling that identifies skew scattering; the $p_z$ decoupling is what protects long orbital relaxation lengths.","core_discovery":"The central claim is that in a centrosymmetric two-dimensional square lattice with $s$, $p_x$, $p_y$, $p_z$ orbitals, scalar Anderson disorder generates an extrinsic orbital Hall response that dominates in the diffusive regime. The disorder-averaged orbital Hall current density follows $\\langle J_{L_z}\\rangle \\propto 1/(U+U_0)$ with $U_0 \\approx 0.78$ eV for $U$ between about 1 and 4 eV, and the orbital Hall angle is linear in $U$; both behaviors match the skew-scattering prediction. At larger $U$ the response saturates, which the authors read as a crossover toward side-jump or intrinsic-dominated transport. In rectangular devices, the orbital current decays as $\\exp(-L/\\lambda_L)$ with device width, and the extracted relaxation lengths are long because the $p_z$ orbital remains dynamically decoupled in the strictly two-dimensional model, suppressing the $L_\\pm$-mediated orbital-flip channels that would relax $L_z$.","pith_inferences":["If the scaling survives in other geometries, the orbital Hall angle could serve as a quantitative impurity-strength probe in orbitronic devices, analogous to skew-scattering resistivity in spintronics.","A direct test of the $p_z$-decoupling explanation: add a small interlayer hopping or an off-diagonal disorder term that couples $p_x/p_y$ to $p_z$, and check whether $\\lambda_L$ drops by orders of magnitude.","The sign reversal between clean and disordered limits implies opposing intrinsic and extrinsic contributions; a two-sample experiment (clean vs doped, same band structure) could separate them.","Because the rectangular setup separates generation and detection regions, the same exponential-decay measurement could be adapted to nonlocal transport in light-metal films where orbital currents propagate over microns."],"forward_implications":["Moderate disorder can be used as a tuning knob: it enhances the orbital Hall response and can reverse its sign, so impurity engineering becomes a design tool for orbitronic devices.","The observed $1/(U+U_0)$ scaling and linear orbital Hall angle single out skew scattering as the dominant extrinsic mechanism in the diffusive regime, with a side-jump or intrinsic crossover at higher $U$.","The exponential decay of orbital current with device width provides a direct, geometry-based route to measuring orbital relaxation lengths $\\lambda_L$ in mesoscopic samples.","Long relaxation lengths are tied to the two-dimensional decoupling of $p_z$; systems with out-of-plane hopping or orbital-off-diagonal disorder should show much shorter $\\lambda_L$.","Near band degeneracy the orbital Hall angle becomes width-dependent, meaning orbital and charge currents can decay at different rates; relaxation is not a single universal rate."],"supporting_citations":[{"why":"Supplies the clean-limit orbital-texture mechanism that the model's t_sp term activates and whose disorder dependence this paper tests.","marker":"[27]"},{"why":"Gives the non-perturbative prediction that skew scattering yields ⟨J_Lz⟩ ∝ 1/(U+U0) and a side-jump/intrinsic crossover, the exact scaling used to interpret Figures 3(a,c).","marker":"[40]"},{"why":"Establishes the multi-terminal mesoscopic geometry and the orbital-projected Landauer-Büttiker formulas used to extract pure orbital currents.","marker":"[36]"},{"why":"Provides the four-orbital s/p tight-binding Hamiltonian and the on-site and hopping parameter values adopted in the simulations.","marker":"[44]"},{"why":"Earlier real-space numerical study reporting disorder-dependent orbital Hall responses in topological materials, the background this work extends to a simpler orbital-active lattice.","marker":"[39]"},{"why":"Proposes Dyakonov-Perel-like orbital relaxation, one of the competing relaxation mechanisms the rectangular-device results are compared with.","marker":"[41]"},{"why":"Computes orbital relaxation lengths from first-principles scattering calculations, providing a reference point for the extracted λ_L values.","marker":"[42]"}],"fun_headline_variants":["Disorder enhances orbital Hall effect in mesoscopic devices","Skew scattering drives orbital Hall enhancement","Orbital relaxation length from width-dependent decay","Extrinsic orbital Hall effect in disordered mesoscopics","Orbital Hall current scales with disorder via skew scattering"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the range $1 \\text{ eV} \\lesssim U \\lesssim 4 \\text{ eV}$ is genuinely diffusive transport; the paper cites supplementary Fig. S2 for this, but that figure plots orbital current and angle versus device size rather than a charge-diffusion or localization diagnostic, so the skew-scattering interpretation of the $1/(U+U_0)$ scaling rests on that regime being diffusive rather than already localized or ballistic.","fun_headline_variants_meta":{"raw":{"variants":["Disorder enhances orbital Hall effect in mesoscopic devices","Skew scattering drives orbital Hall enhancement","Orbital relaxation length from width-dependent decay","Extrinsic orbital Hall effect in disordered mesoscopics","Orbital Hall current scales with disorder via skew scattering"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000608,"raw_usage":{"total_tokens":2823,"prompt_tokens":930,"completion_tokens":1893,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":546,"completion_tokens_details":{"reasoning_tokens":1819}},"tokens_in":546,"tokens_out":1893,"duration_ms":15555,"temperature":1.0,"reasoning_tokens":1819,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T20:39:52.107314+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the disorder-averaged conductance or elastic mean free path as a function of $U$ in the same square device: genuine diffusive transport at $U \\approx 1$--$4$ eV requires metallic scaling with system size and a mean free path well below $L$, whereas exponential size dependence would signal localization. If localization or ballistic effects are present, the $\\langle J_{L_z}\\rangle \\propto 1/(U+U_0)$ fit would not uniquely establish skew scattering. Alternatively, a direct Boltzmann calculation of the skew-scattering contribution for the same Hamiltonian could be compared quantitatively with the fitted $U_0 \\approx 0.78$ eV.","supporting_citations":[{"cited_title":"Kontani, T","cited_arxiv_id":null,"evidence_quote":"Supplies the clean-limit orbital-texture mechanism that the model's t_sp term activates and whose disorder dependence this paper tests."},{"cited_title":"Veneri, T","cited_arxiv_id":null,"evidence_quote":"Proposes Dyakonov-Perel-like orbital relaxation, one of the competing relaxation mechanisms the rectangular-device results are compared with."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Computes orbital relaxation lengths from first-principles scattering calculations, providing a reference point for the extracted λ_L values."}],"review_version":1}