{"id":"ea470175-e5f3-4de3-83d5-a584fcea034a","arxiv_id":"2507.00650","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A model calculation predicts that twisting graphene on a TMDC monolayer tunes spin Hall and Edelstein responses and can produce a quantized ±2e^2/h valley Hall conductance.","lead":"This paper computes how twisting graphene on top of a MoSe2, WSe2, MoS2, or WS2 monolayer changes spin-to-charge conversion and valley Hall response. It predicts a twist-tunable valley Hall conductance that can lock to exactly ±2 e^2/h when the Fermi level sits in the band gap.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Valley Hall plateau rests on equating σ_VH with per-valley Berry curvature (Eq. 23), but Eq. 21 defines it using spin-conductivity symbols and Sec. 4 calls the theory provisional; the ±2e²/h may not be a physical valley current.","rationale":"The reader's weakest assumption is precisely the one I find most load-bearing: the valley Hall conductivity is identified with a difference of per-valley Berry-curvature integrals, a quantity the paper itself labels provisional. My independent reading sharpens this with a concrete textual inconsistency: Eq. 21 uses spin-conductivity superscripts s_z while Eq. 22 defines a charge conductivity, and the analytical bridge to Eq. 23 is omitted. This is not merely cosmetic, because the central claim is a quantized transport coefficient. If the computed object is the spin-valley Hall conductivity or a provisional orbital-Hall-like quantity, the headline plateau may not correspond to the valley Hall current one would measure in a transport or Kerr-rotation experiment. The proposed concrete test would settle the issue by comparing the three relevant Kubo responses in the same model. Since the concern is substantive but addressable, the existing CONDITIONAL verdict remains appropriate.","tokens_in":12467,"tokens_out":10224,"duration_ms":135259,"concrete_test":"Within the same four-band model, independently compute three quantities for one twist angle exhibiting the plateau, e.g., θ=30° in WSe2: (i) the per-valley charge Hall conductivity from the full Kubo formula Eq. 22, (ii) the spin-valley Hall conductivity from Eq. 9, and (iii) the intrinsic orbital Hall conductivity using an orbital-angular-momentum current operator following Bhowal and Vignale (2021). Check whether σ^K_xy − σ^K'_xy reproduces the ±2e²/h plateau in Fig. 6 and whether the orbital Hall conductivity agrees with it. If the two disagree at the plateau, the headline quantization is a definition artifact; if they agree, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The headline result is the ±2e²/h plateau in the valley Hall conductivity. That value is obtained by identifying σ_VH with the difference of per-valley Berry-curvature integrals, Eq. 23. Two load-bearing points are insecure. First, the printed definition Eq. 21 writes σ_VH = σ^{s_z K}_{xy} − σ^{s_z K'}_{xy}, where the superscript s_z matches the spin-current operator used in Eq. 9, while the charge-conductivity formula Eq. 22 has no s_z. If Eq. 21 is taken literally, the object computed is a spin-valley Hall conductivity, not a charge valley Hall conductivity. If instead Eq. 22 was intended, the step from it to Eq. 23 is not shown: the paper states only that 'all figures have been ploted based on analytical formulas obtained based on Eq. (22)' and that the formulas are 'long and awkward we decided not to show them'. Second, Sec. 4 concedes that the definition is 'a special case of the valley orbital Hall effect' and that 'the consistent theory of the orbital Hall effects is still under development'. Recent orbital-Hall literature shows that valley Hall and orbital Hall conductivities can differ, and disorder or intervalley processes can renormalize or destroy the distinction. The ±2 plateau is therefore not yet tied to a directly measurable valley current.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper studies low-energy transport in graphene/TMDC heterostructures as a function of the relative twist angle. Using an effective four-band Hamiltonian whose parameters are taken from DFT fits in Ref. 18, the authors derive analytical (or semi-analytical) expressions in the constant-relaxation-time approximation for the spin Hall conductivity, the current-induced spin polarization (Rashba-Edelstein effect), the valley Hall conductivity, and the valley-resolved spin polarization. The headline claim is that the valley Hall conductivity exhibits a quantized plateau of ±2 e^2/h, with the sign and occurrence controlled by the twist angle. The paper also finds that the spin Hall conductivity is independent of the Rashba angle.","tokens_in":12770,"tokens_out":7261,"duration_ms":81189,"significance":"If the valley Hall quantization is correct, the paper offers a concrete twist-tunable platform for valleytronics, based on a simple model with externally fitted parameters rather than a transport fit. Strengths include the use of published DFT parameters, explicit analytical expressions for the spin Hall conductivity, and a frank statement of the clean-limit, no-vertex-correction approximation. The main significance is nevertheless curtailed by the unresolved relationship between the calculated spin-resolved conductivity and the physical charge valley Hall current, and by the withholding of the analytical formulas on which the central plateau claim rests.","major_comments":[{"comment":"Eq. (21) defines σ_VH as σ^{s_z K}_{xy} − σ^{s_z K'}_{xy}, i.e., with a spin-current label, while Eq. (22), the displayed Kubo conductivity, contains no spin operator. If Eq. (21) is literal, the plotted quantity is a spin-valley Hall conductivity, not the charge valley Hall conductivity that would produce a valley-polarized charge current. If Eq. (22) was intended, the step from Eq. (22) to the Berry-curvature expression Eq. (23) is omitted. Since the paper itself notes in Sec. 4 that the definition is a special case of the valley orbital Hall effect and that the consistent theory is still under development, this ambiguity is load-bearing for the central claim. Please clarify which quantity is computed and correct the notation.","section":"Section 4, Eqs. (21)-(23)"},{"comment":"The paper states that 'all figures have been ploted based on analytical formulas obtained based on Eq. (22)' but that the formulas are 'long and awkward we decided not to show them.' This prevents an independent check of the central ±2 e^2/h plateau. The reduction of the Green-function Kubo formula, Eq. (22), to the band-projected Berry-curvature integral, Eq. (23), is not trivial when Rashba coupling is present and spin is not conserved. Please provide the full analytical derivation (or a supplementary file) and state the parameter conditions under which the valley Hall conductivity is exactly quantized to ±2 e^2/h.","section":"Section 4, Eqs. (22)-(23) and Figure 6"},{"comment":"The sentence 'Valley spin conductivity does not depend on the relaxation time, thus it is roboust to the effects of impurities and other disorder' overstates the case. The absence of τ in Eq. (23) refers to the clean-limit intrinsic formula; robustness to disorder requires an evaluation of vertex corrections and intervalley scattering, which are not performed here. The paper's own Section 5 limitation paragraph acknowledges the omission of vertex corrections. Please either remove the robustness claim or qualify it as applying only in the clean limit.","section":"Section 4, last paragraph, and Section 5"}],"minor_comments":[{"comment":"In the text introducing the Hamiltonian, the list of TMDCs reads 'MoSe2, WSe2, MoS2 and WSe2' and should end with 'WS2'.","section":"Section 2"},{"comment":"The caption lists 't-Gr/MoSe2, t-Gr/WSe2, t-Gr/MoS2 and t-Gr/WSe2'; the last entry should be 't-Gr/WS2'.","section":"Figure 3 caption"},{"comment":"The sentence 'In the case of intrinsic valley Hall effect the Eq. (13) leads to the expression connected to the Berry curvature' appears to refer to Eq. (22) or Eq. (23), not to the auxiliary quantity ζ in Eq. (13).","section":"Section 4, after Eq. (23)"},{"comment":"The phrase 'valley Hall effect can appear even in the case of vanishing Berry curvature, providing that it is nonzero locally at distinct valleys' is confusing; since Eq. (23) is a Berry-curvature integral, a nonzero local Berry curvature is required, and what vanishes is the total (valley-summed) anomalous Hall response. Please rephrase for clarity.","section":"Section 4, second paragraph"},{"comment":"There are numerous typos, including 'ploted' in Figure 6, 'roboust' in Section 4, 'eeffect' in the Section 4 heading, 'in-plain' in Figure 4 text, and 't-GrWSe2' in the Introduction. A careful proofreading pass is needed.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"For the editor: the manuscript is within the scope of cond-mat.mes-hall, but the central claim's definitional ambiguity should be resolved before acceptance. The authors should be asked to supply the full analytical derivations and to correct the notation in Eqs. (21)-(23). The paper also has a higher-than-usual number of typographical errors, which suggests a final proofreading pass is needed."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper's real content is a twist-angle map of spin Hall conductivity, Rashba-Edelstein effect, and valley Hall response for graphene on MoSe2, WSe2, MoS2, and WS2, using the DFT-fitted parameters from Ref. 18. That map is useful and, as far as the spin-charge conversion part goes, largely reliable. The analytical expressions for the spin Hall conductivity in the different Fermi-energy regimes are a legitimate contribution, and the authors are upfront about the clean-limit, constant-relaxation-time approximation and the absence of vertex corrections.\n\nThe soft spot is the valley Hall section. The printed definition in Eq. (21) uses spin-resolved conductivities (superscript s_z), while Eq. (22), which the figures are said to be based on, is the charge conductivity. These are different objects. If Eq. (21) is literal, the computed plateau is a spin-valley Hall conductivity, not a charge valley Hall current. If Eq. (22) was intended, the connection to the Berry-curvature formula in Eq. (23) is standard, but then the ±2e²/h plateau is just the valley Chern number, which is textbook physics for gapped graphene. The paper itself concedes that the valley Hall definition is a special case of the orbital Hall effect and that the consistent theory is still under development. That makes this more than a typo: the headline claim may not survive a rigorous definition of a measurable valley current, especially with disorder.\n\nI also agree with the reader that the paper does not benchmark against Refs. 18, 56, 57 or the authors' own Ref. 41, so it is hard to tell what is genuinely new beyond a parameter scan. The Rashba-angle independence of the spin Hall conductivity is an interesting finding but needs to be checked against those works.\n\nThis is a paper for the twistronics/spintronics community that wants quantitative predictions for specific material combinations. It deserves a serious referee because the calculations are nontrivial and the issues are addressable. My recommendation: send it to review with the expectation of major revision. The spin-charge conversion part is probably publishable after a quantitative comparison with prior work; the valley Hall claim should be either redefined properly, with the missing analytical formulas made available, or removed.","headline":"A useful twist-angle parameter scan for spin-charge conversion in graphene/TMDC, but the headline quantized valley Hall result rests on a shaky definition that needs fixing before it can be trusted.","tokens_in":13325,"tokens_out":3865,"would_cite":false,"duration_ms":44172,"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":"Twisting graphene against a TMDC monolayer drives the valley Hall conductivity to a quantized plateau of exactly ±2e²/h, with the sign selected by the twist angle.","keywords":["twistronics","graphene/TMDC heterostructures","spin Hall effect","valley Hall effect","Rashba-Edelstein effect","Berry curvature","proximity spin-orbit coupling","valleytronics"],"falsifier":"Calculate the full orbital Hall conductivity (not just the Berry-curvature difference) for t-Gr/MoS₂ with the same Hamiltonian; if the ±2e²/h plateau is absent or shifts, the claimed quantization is an artifact of the definition. In experiment, a Kerr-rotation measurement of the valley Hall effect that fails to show a sign change when the twist is varied across the predicted angles would falsify the claim.","tokens_in":12237,"feed_emoji":"🔄","tokens_out":5304,"duration_ms":54464,"temperature":0.7,"pith_summary":"This paper asks how rotating graphene relative to a monolayer of MoSe₂, WSe₂, MoS₂, or WS₂ changes the spin- and valley-dependent transport of the proximitized graphene. Using an effective low-energy Hamiltonian whose parameters come from earlier density-functional calculations, the authors derive analytical Kubo–Green function formulas for the spin Hall conductivity, current-induced spin polarization, valley Hall conductivity, and valley spin polarization. Their central result is that the valley Hall conductivity takes the quantized value ±2e²/h inside the energy gap, with the sign toggled by the twist angle, while the spin Hall response is strongly twist-modulated but completely independent of the Rashba angle. If correct, this makes the relative twist a practical dial for switching between opposite valley Hall regimes without changing materials.","feed_headline":"Twist angle sets valley Hall conductivity to ±2e²/h","feed_subtitle":"Analytical transport theory for graphene on MoS₂, WSe₂, WS₂, and MoSe₂ shows the twist—not the Rashba angle—controls spin and valley…","key_machinery":"The Hamiltonian H^ν = H_0^ν + H_Δ + H_I^ν + H_R^ν combines a Dirac kinetic term with velocity v, a staggered sublattice potential Δ, a valley-Zeeman intrinsic spin-orbit coupling $λ_I^{{A,B}}$, and a generalized Rashba coupling with amplitude λ_R and angle φ. The paper feeds twist-dependent parameter tables from density-functional theory into Kubo–Green function formulas: the spin Hall conductivity is the sum over valleys of transverse spin-current responses, the valley Hall conductivity is their difference and reduces to the per-valley Berry-curvature integral, and the nonequilibrium spin polarization is obtained from the retarded–advanced Green function product. The twist enters only through Δ, λ, λ_R, and φ, which is what converts the same Hamiltonian into different responses at different θ.","core_discovery":"On the paper's own terms, the central claim is that the valley Hall conductivity of a graphene/TMDC heterostructure, defined as the difference of per-valley Kubo conductivities and evaluated in the clean limit, is quantized to ±2e²/h when the Fermi level lies in the gap, and which of the two values appears is controlled by the relative twist angle. The same twist angle strongly modulates the spin Hall conductivity and the Rashba–Edelstein spin polarization, but the spin Hall conductivity does not depend on the Rashba angle φ, which only rotates the spin-momentum locking. The quantization follows from the opposite Berry curvatures at K and K′; the total Chern number remains zero, so no anomalous Hall effect appears, and the valley-contrasting response is what remains.","pith_inferences":["Editorial extension: if the quantization survives the still-in-development orbital Hall theory, the ±2e²/h plateau provides a natural electrical switch between two valley-polarized states, possibly readable as a sign change in a nonlocal Hall-bar voltage.","Editorial extension: the paper's clean-limit, constant-τ calculation leaves open whether impurity vertex corrections renormalize the spin Hall conductivity; the authors cite work showing such corrections are order-unity in graphene, so testing the valley Hall plateau in disordered samples would separate intrinsic from vertex-dominated behavior.","Editorial extension: a direct experimental check would be Kerr-rotation microscopy on t-Gr/MoS₂, which should show a sign flip of the valley Hall signal between θ ≈ 1° and θ ≈ 29.3° if the Berry-curvature difference is the right observable."],"forward_implications":["For the four TMDC substrates considered, the same crystal can show σ_VH = +2e²/h at one twist angle and −2e²/h at another, with the gap location in energy shifting accordingly.","The spin Hall conductivity vanishes when the Fermi level sits in the band gap, because there is no topological contribution from the occupied sea; only Fermi-surface states contribute.","The Rashba–Edelstein response acquires a component parallel to the applied electric field whose sign reverses when the Rashba angle is negative, which happens at specific twist angles.","The valley spin polarization (valley Rashba–Edelstein effect) is independent of the relaxation time within the clean-limit approximation, so it is expected to be robust against a constant relaxation-time disorder model.","Because the spin Hall conductivity is independent of the Rashba angle, tuning φ cannot tune the spin Hall response; only the twist angle θ changes it."],"supporting_citations":[{"why":"Supplies the DFT-fitted twist-dependent parameters (λ, λ_R, φ, Δ) for all four heterostructures used in the numerical results.","marker":"[18]"},{"why":"Provides the low-energy Hamiltonian for twisted graphene–TMDC heterobilayers, including the generalized Rashba term.","marker":"[27]"},{"why":"Parameterizes the twist-angle dependence of the proximity spin-orbit coupling that enters the model.","marker":"[28]"},{"why":"Defines the intrinsic spin-orbit coupling and sublattice-resolved proximitized graphene model used in Eq. (4).","marker":"[29]"},{"why":"Defines the valley Hall conductivity as the difference of per-valley Hall responses in graphene-based systems, basis for Eq. (21).","marker":"[40]"},{"why":"Earlier work by the authors giving the intrinsic anomalous, spin, and valley Hall Kubo formulas used here.","marker":"[41]"},{"why":"Supplies the clean-limit Green function treatment of current-induced spin polarization in Rashba graphene without vertex corrections.","marker":"[43]"},{"why":"States that the valley Hall conductivity defined via Berry-curvature difference is a special case of the orbital Hall effect, the source of the paper's caveat.","marker":"[50]"}],"fun_headline_variants":["Twist angle flips valley Hall conductivity to quantized ±2e²/h","Graphene twist tunes valley Hall to ±2e²/h","Twist angle controls quantized valley Hall in graphene/TMDC","Valley Hall conductivity becomes ±2e²/h at twist-tuned gap","Twist angle switches valley Hall to exactly ±2e²/h"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The quantized valley Hall plateau rests on identifying the valley Hall conductivity with the difference of per-valley Berry-curvature integrals, which the paper itself calls a special case of the valley orbital Hall effect whose consistent theory is still under development.","fun_headline_variants_meta":{"raw":{"variants":["Twist angle flips valley Hall conductivity to quantized ±2e²/h","Graphene twist tunes valley Hall to ±2e²/h","Twist angle controls quantized valley Hall in graphene/TMDC","Valley Hall conductivity becomes ±2e²/h at twist-tuned gap","Twist angle switches valley Hall to exactly ±2e²/h"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000628,"raw_usage":{"total_tokens":2861,"prompt_tokens":859,"completion_tokens":2002,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":475,"completion_tokens_details":{"reasoning_tokens":1906}},"tokens_in":475,"tokens_out":2002,"duration_ms":15242,"temperature":1.0,"reasoning_tokens":1906,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T21:11:18.468692+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Calculate the full orbital Hall conductivity (not just the Berry-curvature difference) for t-Gr/MoS₂ with the same Hamiltonian; if the ±2e²/h plateau is absent or shifts, the claimed quantization is an artifact of the definition. In experiment, a Kerr-rotation measurement of the valley Hall effect that fails to show a sign change when the twist is varied across the predicted angles would falsify the claim.","supporting_citations":[{"cited_title":"and Nikoliic, Branislav K","cited_arxiv_id":null,"evidence_quote":"Supplies the DFT-fitted twist-dependent parameters (λ, λ_R, φ, Δ) for all four heterostructures used in the numerical results."},{"cited_title":"& Koshino, M","cited_arxiv_id":null,"evidence_quote":"Parameterizes the twist-angle dependence of the proximity spin-orbit coupling that enters the model."},{"cited_title":"Graphene on transition-metal dichalcogenides: A platform for proximity spin-orbit physics and optospintronics","cited_arxiv_id":null,"evidence_quote":"Defines the intrinsic spin-orbit coupling and sublattice-resolved proximitized graphene model used in Eq. (4)."},{"cited_title":"& Barna´s, J","cited_arxiv_id":null,"evidence_quote":"Defines the valley Hall conductivity as the difference of per-valley Hall responses in graphene-based systems, basis for Eq. (21)."},{"cited_title":"& Dyrdał, A","cited_arxiv_id":null,"evidence_quote":"Earlier work by the authors giving the intrinsic anomalous, spin, and valley Hall Kubo formulas used here."},{"cited_title":"& Barna´s, J","cited_arxiv_id":null,"evidence_quote":"Supplies the clean-limit Green function treatment of current-induced spin polarization in Rashba graphene without vertex corrections."}],"review_version":1}