{"id":"bde9add0-274c-445b-8235-eaf072a9e0c5","arxiv_id":"2511.16393","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Combining disorder with a static electric field lets the boundary accumulation direction of two-dimensional non-Hermitian skin modes be tuned by rotating the field relative to the nonreciprocal hopping.","lead":"This paper proposes a way to steer where non-Hermitian 'skin' modes pile up in two-dimensional lattices by combining random disorder with an electric field. The work could matter for routing light or matter waves in reconfigurable photonic and cold-atom devices.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Disorder-averaged data do not establish deterministic per-sample control of boundary localization, undermining 'arbitrary control'.","rationale":"The reader's weakest_assumption—that ensemble averages may not reflect typical single-disorder-sample behavior—is precisely the most load-bearing concern for the paper's headline claim. The paper asserts 'full control' and 'arbitrary control' of where skin modes accumulate, but every figure supporting this is disorder-averaged. This is not a stylistic issue: in disordered systems, the average position can be smooth and predictable even when individual samples are wildly scattered (e.g., in Anderson localization, the average density is smooth while each sample has a random localization center). Here, the control mechanism is supposed to be deterministic—tuning φ, θ programs the boundary site. If per-realization fluctuations are large, the mechanism only controls the ensemble, not the actual system, which would contradict the abstract and introduction. The proposed concrete test directly measures the per-sample distribution and would settle the matter. I find no fatal mathematical error in the nonreciprocal analytics, and the disorder-averaged results are consistent with the claimed mechanism, but the missing per-realization statistics block the stronger claim. The reader's Eq. (6) Hermiticity concern is also valid and should be fixed, but it affects a secondary reciprocal-lattice section; the per-realization issue hits the central nonreciprocal control claim. Therefore the verdict remains CONDITIONAL, pending the requested data.","tokens_in":19592,"tokens_out":5739,"duration_ms":54598,"concrete_test":"Fix parameters (g/J=1, F/J=1.5, ξ/J=1, θ=π/4, φ=π/3) on a 61×61 lattice. Evolve the same initial Gaussian wave packet under N=1000 independent disorder realizations, recording each realization's final center-of-mass r_f(t_f) and its IPR at t_f=20 T_B. Plot the histogram of r_f and compute the standard deviation of the distance along the boundary. Repeat for φ=0, π/6, π/2. If the per-realization distribution is broad (std comparable to system size) or multimodal, the deterministic-control claim fails; if it is sharply peaked (std ≪ L) at the boundary site predicted by the averaged dynamics, the claim is supported. Additionally, verify that each realization's density is localized at the boundary (finite IPR) rather than diffusing through the bulk.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is 'deterministic and arbitrary control' of the skin-mode localization site by tuning the field orientation φ and nonreciprocity direction θ. All reported evidence for this claim—final center-of-mass positions, trajectories, densities, and IPRs—is averaged over 1000 (or in the SM, 100) disorder realizations (Figs. 2, 3, 4; Figs. S2, S3). The load-bearing premise is that the ensemble average represents a typical single sample: that nearly every disorder realization localizes at the boundary position selected by (φ, θ). However, no per-realization statistics are provided. If individual realizations instead localize at a broad distribution of boundary sites, the averaged trajectory could still lie on the smooth curve of Fig. 3(a) while no single sample ends at the claimed position. The analytic Wannier–Stark expansion (Eqs. 4–5, S41–S43) gives disorder-induced couplings that are symmetric in the (m,n) indices; it does not by itself prove that the drift direction is deterministic or that the final site is unique per sample. Without per-realization data, 'arbitrary control' over the localization site is not established; only the averaged density is shown to be steerable.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes and studies a mechanism for controlling boundary localization in two-dimensional non-Hermitian lattices by combining a static electric field with random on-site disorder. In the nonreciprocal Hatano–Nelson model, the clean system with an electric field exhibits Stark-localized Bloch oscillations rather than the NHSE; the authors show analytically, via an exact solution in the clean limit and a Wannier–Stark expansion, that adding disorder creates effective couplings between localized states. Their numerical simulations, averaged over 1000 disorder realizations, show that the wave-packet center of mass drifts perpendicular to the field and eventually localizes at a boundary position that depends on the field orientation relative to the nonreciprocal hopping direction. They also present analogous results for reciprocal lattices, where geometry controls the localization, and a Lindblad master-equation treatment that maps open-system dynamics onto the same non-Hermitian Hamiltonian. The central claim is that the boundary localization position can be continuously and arbitrarily controlled by tuning the angle between the electric field and the nonreciprocal hopping vector.","tokens_in":19839,"tokens_out":4894,"duration_ms":56500,"significance":"If correct, the proposed mechanism would provide a versatile and experimentally relevant control knob for the non-Hermitian skin effect in two dimensions, going beyond earlier work that only tuned the existence or degree of the skin effect. The manuscript has clear strengths: the clean-limit dynamics are solved exactly (SM Sec. I), the Wannier–Stark expansion leading to the disorder-induced coupling is explicit and not circular, and the numerical checks include IPR and ultra-long-time dynamics. The extension to reciprocal lattices and to a Liouvillian description broadens the applicability. However, the central claim of 'deterministic' and 'arbitrary' control is supported only by disorder-averaged observables; no per-realization distribution is provided. Since the key new assertion is about controlling where a given wave packet localizes, rather than about the ensemble-averaged density, this is a load-bearing gap that must be addressed before the claim can be accepted.","major_comments":[{"comment":"The abstract and introduction claim 'deterministic control' and 'full control' over the skin-mode localization site, but every quantitative result for the disordered case—center-of-mass trajectories, final positions, second moments, and IPRs—is averaged over 1000 disorder realizations (100 in the ultra-long-time SM results). An ensemble-averaged trajectory can lie on a smooth curve such as Fig. 3(a) even if individual realizations localize at a broad distribution of boundary sites. The Wannier–Stark coupling in Eq. (5) and SM Eq. (S43) is linear in the disorder and symmetric in the state indices; it does not by itself imply that the drift direction or the final site is unique per sample. The authors should provide per-realization statistics: for representative parameters, a scatter of the final center-of-mass position over realizations, the standard deviation of that position, and the fr","section":"Figs. 2–4 and SM Secs. III–IV; abstract"},{"comment":"The paper's title and central claim concern 'skin modes', which are eigenstates of an open-boundary non-Hermitian Hamiltonian. For the disordered nonreciprocal case, however, all evidence is dynamical: an initial Gaussian wave packet evolves and becomes boundary-localized. No eigenstate spectrum, eigenstate spatial density, or overlap of the final state with the OBC eigenstates is shown for the disordered Hamiltonian in Eq. (1). The IPR in SM Sec. III demonstrates localization of the time-evolved state, but not that it is a stationary skin mode rather than a transient scattering state pinned at the boundary. The authors should either provide OBC eigenstate calculations for the same parameters or explicitly state and justify a dynamical definition of 'skin-mode localization' that makes the wave-packet dynamics the relevant observable.","section":"Nonreciprocal model and SM Sec. III"},{"comment":"The claim of 'arbitrary' boundary control is demonstrated by sweeping the field orientation φ while keeping the nonreciprocity direction θ fixed at π/4, and the final positions lie along the upper-right quadrant boundary. The full parameter space (θ,φ) is not explored, and no statement is made about whether every point on the complete boundary can be reached by some combination of θ and φ. If the reachable set is limited to a quadrant or an arc, the word 'arbitrary' in the abstract and introduction is an overstatement. Please specify the reachable region of the boundary as a function of the control parameters, or soften the wording accordingly.","section":"Fig. 3(a) and 'arbitrary control'"}],"minor_comments":[{"comment":"Typographical issues: 'remains a significant challenging' should be 'remains a significant challenge'; in the conclusion, 'in clear lattices' should be 'in clean lattices'.","section":"Abstract and conclusion"},{"comment":"The text says the insets show 'the states with the smallest IPR' when verifying boundary localization; since boundary-localized states have large IPR, this likely should be 'largest IPR'. Please check and correct.","section":"SM Sec. III"},{"comment":"The notation g_perp is used informally in the discussion of Figs. 2(d–f) but is not defined. Define it explicitly as the component of g perpendicular to the electric field, e.g., g_perp = g · r_perp, to avoid ambiguity.","section":"General notation"},{"comment":"The reference to the Supplemental Material appears as 'SM in Ref. [83]' with no arXiv identifier or journal link; the manuscript should give full information so the SM is independently retrievable.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The paper is likely to be of interest to the readership of Physical Review B or similar venues. The clean-limit analytics are solid and the overall mechanism is plausible. The key issue is that the headline claim of deterministic arbitrary control is not backed by per-realization statistics; the authors should be asked to provide those data and to either demonstrate eigenstate skin-mode localization or reframe the claim as statistically averaged transport. If the per-realization data show narrow distributions, the paper can be accepted after that revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The genuinely new thing here is the control knob: rotate the electric field relative to the nonreciprocal hopping direction, and you steer where skin modes accumulate in 2D. That is a practical capability people have been hunting for, and the paper gives a plausible mechanism for it. The clean-limit analytics (SM Sec. I) are exact, they match the numerics, and they cleanly show that the field suppresses the NHSE and produces modified Bloch oscillations. Credit where due: that part is solid, and the Wannier–Stark expansion (SM Sec. II) provides a clear physical picture of how disorder breaks Stark localization and lets the transverse component of nonreciprocal hopping drive the wave packet toward a boundary.\n\nThe soft spot is the one the stress-test flagged: every localization figure is an average over 1000 (or 100) disorder realizations, and there is no per-sample distribution. The abstract and introduction promise \"deterministic\" and \"arbitrary\" control of the localization site. If individual realizations land at a broad patch of boundary sites and only the ensemble mean traces the smooth curve in Fig. 3(a), then the claim is false. I don't think this is a fatal flaw — the mechanism looks deterministic in origin, since the perpendicular hopping bias sets a fixed drift direction — but the authors need to show it. Add a histogram of final positions over realizations, maybe for a few representative parameter points. If the spread is small, the claim stands. I suspect it will be, but the data aren't there.\n\nThere is also a concrete error in the reciprocal-lattice section. Eq. (6) as written has the Hermitian conjugate in the hopping terms, so J_x and J_y being complex still leaves the Hamiltonian Hermitian. A Hermitian lattice cannot show the geometry-dependent skin effect claimed in Fig. 4. Either the H.c. is a typo (likely, since the model is meant to be a non-Hermitian reciprocal lattice), or the wrong Hamiltonian is written. That needs to be corrected before the paper is taken seriously on that part. Also, Ref. [52] on disorder-induced boundary localization is conspicuously absent; the authors should explain how their mechanism differs.\n\nThe clean-limit exact solution alone is worth citing, and the control mechanism, if it survives per-sample scrutiny, is a worthwhile result. I'd send it to a serious referee, but I'd tell the authors that the title and abstract's \"deterministic\" language has to be backed by per-realization statistics, and Eq. (6) must be fixed.","headline":"The core idea is fresh and the clean-limit analytics are correct, but the 'deterministic arbitrary control' claim is unsupported without per-realization statistics; Eq. (6) as written is Hermitian and needs fixing.","tokens_in":20384,"tokens_out":4429,"would_cite":true,"duration_ms":48120,"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":"Disorder plus an electric field steers non-Hermitian skin modes to any boundary site","keywords":["non-Hermitian skin effect","disorder","electric field","Wannier-Stark localization","boundary localization","wave-packet dynamics","reciprocal lattice","directed transport"],"falsifier":"Compute the final center-of-mass position for many individual disorder realizations at fixed (g, F, ξ) and plot the per-sample distribution instead of the average; if individual realizations scatter broadly along the boundary or fail to track the field angle φ, the claimed arbitrary control is not a property of typical samples.","tokens_in":1320,"feed_emoji":"⚡","tokens_out":1189,"duration_ms":48566,"temperature":0.7,"pith_summary":"This paper claims that in a two-dimensional non-Hermitian lattice, the place where skin modes accumulate can be chosen continuously by rotating a static electric field relative to the nonreciprocal hopping direction, provided random disorder is present. In a clean system, the field alone suppresses the skin effect and traps wave packets in Bloch oscillations; disorder alone competes with the nonreciprocal hopping. Together, disorder opens transverse transport channels while the component of nonreciprocal hopping perpendicular to the field biases the packet toward a specific boundary point. Varying the field angle sweeps that point along the boundary, and an analogous geometry-dependent control works in reciprocal lattices. If the mechanism holds, it provides a programmable route to directed wave-packet transport in classical and quantum settings.","feed_headline":"Field angle and disorder pin skin modes anywhere on an edge","feed_subtitle":"Rotating the field relative to the nonreciprocal hopping steers wave packets to a chosen boundary site","key_machinery":"The argument is carried by a biorthogonal Wannier-Stark basis expansion of the disordered Hamiltonian. In this basis, the clean part is diagonal with ladder energies E_{m,n} = F_x m + F_y n, and disorder induces couplings between Stark-localized states, given by a product of Bessel functions with arguments γ_α = -2J/F_α. These couplings open transport between Stark-localized states, while the nonreciprocal hopping gauge factor e^{g·r} makes the transport directional. The geometric object that selects the destination is the decomposition of g into components parallel and perpendicular to the field: only the perpendicular component contributes to long-time drift toward the boundary. The clean-","core_discovery":"The paper's central claim is that full, arbitrary control over where skin modes localize in two-dimensional non-Hermitian lattices can be achieved by combining random on-site disorder with a static electric field. In the clean nonreciprocal model, an exact analytical solution shows that the field produces Stark localization and suppresses the skin effect, so the packet stays in the bulk. Adding disorder creates effective couplings between localized Wannier-Stark states, opening new transport channels; the component of the nonreciprocal hopping vector perpendicular to the field then biases the packet to propagate transversely until it accumulates at a boundary site. Rotating the field orienta","pith_inferences":["The reported control is demonstrated through ensemble averages over 1000 disorder realizations; the paper's claim of deterministic, arbitrary control would be strengthened by showing that individual realizations localize at the prescribed site with narrow spread, which is not presented.","The mechanism suggests a testable design rule for classical metamaterials: in a circuit or photonic lattice with engineered asymmetric hopping, rotating the bias direction should steer the output port continuously along the boundary, enabling a reconfigurable router in a single device.","Because only the perpendicular component of the nonreciprocal vector drives transport, the destination should shift approximately linearly with the tangent of the misalignment angle for small deviations; this quantitative angular-dependence prediction could be checked directly in numerical simulations."],"forward_implications":["If the mechanism holds, rotating the field angle φ relative to the nonreciprocal hopping vector g moves the final boundary accumulation continuously along the chosen quadrant, so a single lattice can route wave packets to many destinations.","Because the drift is directed by the perpendicular component of g, control survives moderate variations in field strength, nonreciprocity, and disorder strength, as shown by the parameter sweeps.","In reciprocal lattices, the lattice geometry—square versus slanted-edge triangles—determines whether boundary localization occurs and where along the edge it accumulates, extending the recipe to systems without nonreciprocal hopping.","The open-quantum-system calculation indicates that the same effective dynamics arises from gain and loss channels, so the route is not limited to explicitly non-Hermitian Hamiltonians.","The IPR and ultra-long-time simulations indicate that once the packet reaches the boundary it remains sharply localized rather than spreading diffusively."],"fun_headline_variants":["Disorder and field steer skin modes to any boundary site","Field and disorder give full control of skin mode position","Arbitrary skin-mode placement via field and disorder","Electric field plus disorder directs skin modes to chosen edge","Field and disorder pin skin modes in 2D non-Hermitian lattices"],"cache_read_input_tokens":21632,"weakest_assumption_plain":"The load-bearing premise is that the ensemble average over disorder realizations represents the behavior of a typical single sample—that nearly every disorder configuration localizes at the prescribed boundary site rather than at randomly scattered sites.","fun_headline_variants_meta":{"raw":{"variants":["Disorder and field steer skin modes to any boundary site","Field and disorder give full control of skin mode position","Arbitrary skin-mode placement via field and disorder","Electric field plus disorder directs skin modes to chosen edge","Field and disorder pin skin modes in 2D non-Hermitian lattices"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000834,"raw_usage":{"total_tokens":3474,"prompt_tokens":743,"completion_tokens":2731,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":487,"completion_tokens_details":{"reasoning_tokens":2648}},"tokens_in":487,"tokens_out":2731,"duration_ms":18403,"temperature":1.0,"reasoning_tokens":2648,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T21:09:57.909255+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the final center-of-mass position for many individual disorder realizations at fixed (g, F, ξ) and plot the per-sample distribution instead of the average; if individual realizations scatter broadly along the boundary or fail to track the field angle φ, the claimed arbitrary control is not a property of typical samples.","supporting_citations":[],"review_version":1}