{"id":"54be7cf7-1470-4a3d-a7c1-9febfa8e680c","arxiv_id":"2506.13399","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Hydrogen at the apical oxygen vacancy in NdNiO2 strengthens the interstitial-orbital superconducting dome and leaves the nickel d-wave dome nearly unchanged, in a two-band Hubbard model solved by variational Monte Carlo.","lead":"This paper uses computer simulations to test whether hydrogen atoms left over from making the superconductor NdNiO2 change the material's superconductivity. It finds that hydrogen mostly affects one of the two electronic bands, slightly boosting the superconductivity from the interstitial orbital while leaving the nickel d-orbital part almost unchanged.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The IS-dome enhancement is evaluated only under an imposed extended-s-wave pairing ansatz; if the IS channel prefers a different symmetry, the hydrogenation effect is an artifact.","rationale":"The paper does a credible job on the DFT side: the two-band description is tested through Wannier downfolding, the Fermi-surface changes are documented, and the H-induced modification of the IS hopping parameters is concrete and internally consistent. The VMC part, however, is where the headline claim lives. The reader's weakest assumption already flagged the pairing symmetries as part of the model, but I would sharpen the concern to the single most load-bearing point: the IS dome is computed under an imposed s-wave ansatz, with no calculation testing whether that symmetry is the leading one in the hydrogenated compound. This is more specific than the broader two-orbital concern, because the paper presents direct evidence that two orbitals suffice for the band structure; the unvalidated step is the pairing channel. This does not overturn the paper, because the s-wave IS choice is motivated by prior nickelate literature and the comparative trend may survive a symmetry-unbiased test. It does, however, make the central claim conditional on a check that is currently absent, which is exactly the CONDITIONAL status the reader assigned. I therefore keep the verdict unchanged while noting that if the proposed symmetry test revealed a different leading IS channel, the conclusion would need to be rejected or substantially revised.","tokens_in":15141,"tokens_out":7219,"duration_ms":87852,"concrete_test":"Repeat the VMC optimization for both compounds with a trial state that includes, per orbital, several competing pairing symmetries (extended s, d_x2-y2, d_xy, and p) with independent gap parameters, plus inter-orbital pairing terms; compare optimized variational energies and the long-range pair-pair correlations in each channel. If an alternative symmetry has lower variational energy than the imposed s-wave IS state in the hydrogenated case, or if the IS s-wave correlation no longer survives optimization, then the central claim of selective enhancement is not supported. A cheaper complementary check is to compute the RPA pairing vertex of the downfolded two-band model and identify the leading eigenvector in the IS channel before and after hydrogenation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central conclusion that hydrogenation strengthens IS-derived superconductivity rests on the VMC result for the IS order parameter, but that result is obtained with the pairing symmetry fixed by input rather than by calculation. Equation (4) restricts pairing to intra-orbital nearest-neighbor terms only: an extended s-wave form for the IS orbital (the same amplitude on x, y, and z bonds) and a d-wave form for the d_x2-y2 orbital. The VMC wavefunction of Eq. (2) therefore cannot discover whether the IS channel is actually s-wave in either compound; it can only optimize the magnitude of the imposed s-wave gap. The hydrogenated system has a strongly modified IS Wannier function, an increased out-of-plane IS-IS hopping, and a nearly disappearing IS pocket at k_z = pi; these changes could plausibly alter the momentum structure of the pairing interaction and favor a different symmetry, such as a nodal s-wave, d-wave, or a mixed-symmetry state. If the leading IS instability in the hydrogenated compound is not extended s-wave, the computed enhancement of Phi_s in Fig. 6(a) is not a statement about superconductivity in that channel. The paper acknowledges the assumption as 'motivated' by prior work, but provides no variational comparison with alternative symmetries and no inter-orbital pairing terms, so the orbital-selective conclusion is not yet tested against the most dangerous alternative.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript combines DFT, Wannier downfolding, and variational Monte Carlo (VMC) to address whether topotactic hydrogen affects superconductivity in infinite-layer nickelate NdNiO2. DFT in a 2x2x2 supercell with H at apical oxygen vacancy sites shows that hydrogen strongly modifies the interstitial (IS) Wannier function for the Ni bonded to H, suppresses the IS electron pocket at kz=pi, and leaves the two-band low-energy picture intact. The authors then solve a two-orbital Hubbard model (d_x2-y2 and IS) with interaction parameters U_d=3 eV, U_s/U_d=0.5, U_sd/U_d=0.2, and with pairing restricted to intra-orbital nearest-neighbor terms: extended s-wave for IS and d-wave for d_x2-y2. VMC yields two overlapping superconducting domes as a function of electron filling; hydrogenation increases the IS s-wave order parameter and slightly decreases the d_x2-y2 order parameter. The paper concludes that hydrogen, if present, selectively strengthens IS-derived superconductivity and is not a prerequisite for superconductivity.","tokens_in":15461,"tokens_out":4764,"duration_ms":53245,"significance":"If the central result holds, it offers a concrete microscopic mechanism for the conflicting experimental reports on hydrogen in nickelates: hydrogen can strengthen the interstitial-channel pairing while leaving the Ni-d_x2-y2 channel essentially unchanged. The DFT part is careful, and the Wannier-function analysis (Figs. 3-5) gives clear, quantitative evidence of the hydrogen-induced renormalization of the IS orbital. The VMC calculation is large-scale, and the two-dome structure in the order parameter is an interesting zero-temperature prediction. The main significance is conditional: the orbital-selective conclusion is not yet tested against alternative pairing symmetries in the IS channel, and the Hubbard parameters are chosen inputs rather than computed values. Nonetheless, the paper is a useful and falsifiable step: it predicts that hydrogen selectively enhances the IS-derived dome while leaving the d_x2-y2-derived dome nearly unchanged.","major_comments":[{"comment":"The central claim that hydrogenation strengthens IS-derived superconductivity is obtained with the IS pairing symmetry imposed by input: Eq. (4) fixes extended s-wave pairing for the IS orbital (equal amplitude on x, y, and z bonds) and d-wave for the d_x2-y2 orbital. The VMC wavefunction of Eq. (2) can therefore only optimize the magnitudes of the imposed gaps; it cannot determine whether the leading IS pairing symmetry in the hydrogenated compound is still extended s-wave. Because hydrogenation strongly changes the IS Wannier function and the out-of-plane IS-IS hopping (Figs. 3 and 5), the momentum structure of the pairing interaction could plausibly change, and the enhanced Phi_s in Fig. 6(a) could be an artifact of the fixed ansatz. I request a variational comparison with alternative pairing symmetries for the IS channel (e.g., d-wave, nodal s-wave, s+/-), or an independent calculation of the pairing vertex, before the orbital-selective enhancement can be accepted.","section":"Sec. V, Eq. (4) and Fig. 6(a)"},{"comment":"The Hubbard parameters U_d=3 eV, U_s/U_d=0.5, and U_sd/U_d=0.2 are chosen rather than derived from the DFT calculation, and all quantitative results in Fig. 6(a) are presented for this single parameter set. The text states that variations of U_d over 1-2 eV and of the ratios by 0.2-0.3 leave the qualitative trend unchanged, but no such data are shown. Since the relative enhancement of Phi_s versus Phi_d is the paper's main quantitative conclusion, the robustness statement needs to be substantiated, for example with a supplementary figure showing the order parameters for several parameter sets.","section":"Sec. V, Eq. (1)"},{"comment":"The two-band Hubbard model omits spin-exchange and pair-hopping terms, and the paper notes this is done 'for numerical ease.' In a multi-orbital Hubbard model these terms are generically not small; for nickelates, Hund's-coupling-related physics is emphasized in the literature (e.g., Refs. 66-68). Their omission could alter the relative stability of s-wave versus d-wave pairing and hence the orbital-selective response to hydrogenation. At minimum, the authors should estimate the size of the omitted terms in their Wannier basis and discuss the possible impact on the order parameters; ideally, a calculation including these terms for at least one representative doping should be provided.","section":"Sec. V, Eq. (1)"},{"comment":"The comparison between the computed two-dome structure and the experimental T_c dome (Refs. 44-47) is qualitative: Phi_alpha is a zero-temperature VMC superconducting order parameter, not a critical temperature, and the theory finds superconductivity over a much broader doping range than experiment. The paper acknowledges this discrepancy in the Summary, but the text around Fig. 6(a) should be careful to state explicitly that the 'dome' comparison is suggestive rather than a quantitative match, and that finite-temperature or superfluid-stiffness calculations would be needed to connect Phi to T_c.","section":"Sec. V, Fig. 6(a)"}],"minor_comments":[{"comment":"The sentence 'show a two-hump superconductivity arising the two overlapping domes' is missing 'from' and should read 'arising from the two overlapping domes.'","section":"Abstract"},{"comment":"The caption says 'square planner O coordination'; this should be 'square planar O coordination.'","section":"Fig. 1 caption"},{"comment":"The word 'topotatic' should be 'topotactic' in the first sentence of the Summary and Discussion.","section":"Sec. VI"},{"comment":"The dashed line is described as marking 'the fall of total electron density,' but the meaning is unclear; please state explicitly what the dashed line represents and why it is included.","section":"Fig. 6(b)"},{"comment":"The definition of Phi_alpha via the long-distance limit of the pair-pair correlation function is standard, but the notation F_alpha(r_i-r_j) is introduced without explicitly stating that the bond directions delta and delta' are fixed by the pairing symmetries in Eq. (4); clarifying this would help the reader.","section":"Sec. V, Eq. (5)"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of the journal and the DFT/Wannier analysis is solid. The main risk is that the paper's central claim depends on an imposed s-wave pairing symmetry for the IS channel, so the enhancement of Phi_s in Fig. 6(a) is not yet a tested prediction about the leading superconducting instability. This is fixable within the scope of the manuscript by adding variational comparisons with alternative pairing symmetries or by providing an independent pairing-vertex calculation, so I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is the first variational Monte Carlo study of superconductivity in nickelates and the first low-energy two-band model for hydrogenated NdNiO2. That alone earns it a careful read. The DFT part is convincing: the Wannier analysis clearly shows that hydrogen at the apical vacancy strongly reshapes the interstitial orbital, suppresses the kz=pi electron pocket, and leaves the d_x2-y2 Wannier function nearly untouched. The authors are also honest about their model's limitations—they mention neglecting spin-exchange and pair-hopping terms, the choice of Hubbard parameters, and possible substrate and capping effects. The two-dome structure emerging from the VMC calculation is an interesting output, not a fit to experiment, and the qualitative robustness to variations in U is a plus.\n\nThe soft spot is exactly what the stress-test flags. The pairing symmetry in Eq. (4) is imposed: extended s-wave for the IS orbital and d-wave for d_x2-y2. The VMC wavefunction optimizes the magnitude of those gaps but cannot discover whether the IS channel actually prefers a different symmetry. Since the hydrogenated system has a strongly modified IS Wannier function and an almost vanished IS pocket at kz=pi, the momentum structure of the pairing interaction could plausibly favor a nodal s-wave, d-wave, or mixed-symmetry state. If so, the reported enhancement of the IS order parameter under hydrogenation could be an artifact of the ansatz. The authors call the symmetry choice 'motivated' by prior work and STM data, but that is not a substitute for a variational test of alternative pairing channels. This is a load-bearing assumption, and the paper would be much stronger if it acknowledged and addressed it directly.\n\nIs the central claim wrong? Not necessarily. The mechanism they propose—enhanced out-of-plane IS-IS hopping strengthening J_s—is physically reasonable, and the marginal effect on the d-wave dome is consistent with the unchanged d_x2-y2 Wannier functions. But the conclusion as stated outruns the evidence. A referee should ask for either a test of alternative pairing symmetries or a more cautious interpretation.\n\nWho gets value from this? Researchers working on nickelate superconductors and on multi-orbital Hubbard models more broadly. It is a solid step forward, not a paradigm shift, and it deserves serious peer review even though the final version should probably soften the orbital-selective claim until the symmetry question is settled.","headline":"A solid DFT+VMC study of hydrogen in NdNiO2 whose central claim—that H selectively strengthens the interstitial-orbital dome—is physically plausible but rests on an imposed pairing symmetry that the paper never tests.","tokens_in":15951,"tokens_out":1641,"would_cite":true,"duration_ms":19483,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["74.20.-z","74.70.-b","71.15.Mb","71.10.Fd"],"model":"deepseek-v4-flash","headline":"Hydrogen in NdNiO2 acts as a selective enhancer of the interstitial-orbital superconducting dome, not as a prerequisite for superconductivity.","keywords":["infinite-layer nickelates","NdNiO2","topotactic hydrogen","two-band Hubbard model","interstitial orbital","variational Monte Carlo","orbital-selective superconductivity","superconducting dome"],"falsifier":"If a high-resolution measurement of the kz=pi Fermi surface showed the IS-derived electron pocket still present in hydrogenated NdNiO2, the paper's electronic-structure mechanism would fail; alternatively, a VMC calculation allowing d-wave pairing on the IS orbital that reproduces the same low-doping enhancement would show the conclusion depends on the fixed pairing ansatz rather than on hydrogen itself.","tokens_in":14933,"feed_emoji":"⚛️","tokens_out":5851,"duration_ms":52916,"temperature":0.7,"pith_summary":"The paper tries to settle whether topotactic hydrogen, unintentionally inserted during the synthesis of infinite-layer nickelate superconductors, is a necessary ingredient for superconductivity or just an accidental dopant. Using density functional theory, Wannier downfolding, and variational Monte Carlo on a two-band Hubbard model, it argues that hydrogen at the apical oxygen vacancy mainly reshapes the interstitial (IS) orbital at the Ni site it binds to, leaving the Ni d_x2-y2 orbital essentially intact. The resulting Fermi-surface change is confined to the kz=pi plane, where the IS electron pocket nearly disappears. In the superconducting order parameters, the paper finds two overlapping domes, one s-wave IS-derived at lower hole doping and one d-wave d_x2-y2-derived at higher doping; hydrogenation strengthens the IS dome while barely changing the d_x2-y2 dome. That supports the view that hydrogen is not essential for superconductivity, but it does select which orbital pairing channel benefits from it.","feed_headline":"Hydrogen boosts one of NdNiO2's two superconducting domes","feed_subtitle":"First-principles and Monte Carlo work says topotactic H enhances IS-pairing, leaving the d_x2-y2 dome nearly unchanged.","key_machinery":"The central object is the two-band Hubbard model in a Wannier basis of Ni d_x2-y2 and an effective interstitial (IS) orbital per Ni site, with the IS orbital itself renormalized by hydrogen for the Ni site bound to hydrogen. The mechanism that carries the argument is the set of DFT-derived hopping parameters: hydrogenation substantially increases the first-neighbor IS-IS hopping at that Ni site while suppressing d_x2-y2-IS hopping, which in the variational Monte Carlo state translates into a stronger s-wave pairing scale J_s ~ $t_s^{2}$/U_s for the IS dome and a slightly weaker d-wave J_d. A second key ingredient is the pairing ansatz fixing s-wave symmetry on the IS orbital and d-wave symmetry on d_x2-y2, motivated by prior two-gap nickelate studies and by scanning tunneling microscopy and Hall data.","core_discovery":"The central claim is that hydrogen sits at the apical oxygen vacancy in a negative charge state, forms a Ni-H-Ni chain, and acts as a selective enhancer of the interstitial-orbital superconductivity rather than as a prerequisite for superconductivity. Concretely, hydrogen changes only the local IS Wannier function at the Ni site bound to hydrogen, making it more localized in-plane and strongly bonded out-of-plane to H, while the d_x2-y2 Wannier function is essentially unchanged. This depletes the IS electron pocket at kz=pi but leaves the kz=0 Fermi surface intact, so the minimal two-band description survives hydrogenation. In the variational Monte Carlo solution of the DFT-derived two-band Hubbard model, superconductivity appears as two overlapping domes as a function of hole doping: an extended-s-wave dome from the IS orbital at lower hole doping and a d-wave dome from d_x2-y2 at higher doping. Hydrogenation raises the IS dome appreciably and suppresses the d_x2-y2 dome only marginally, a consequence the paper attributes to a hydrogen-induced increase in the nearest-neighbor IS-IS hopping (hence superexchange J_s) and a slight reduction in d_x2-y2 hopping.","pith_inferences":["Because the enhancement traces to a single hopping integral (nearest-neighbor IS-IS), a testable extension would be to tune the hydrogen concentration and check whether the IS-dome height scales monotonically with that hopping, or to find other interstitial dopants that mimic hydrogen's Wannier reshaping.","The double-dome structure persists in both compounds, suggesting the two-dome phenomenology is intrinsic to the two-orbital physics rather than to hydrogen; if so, strain or capping layers that alter only the IS orbital could selectively control the low-doping dome.","The VMC result is obtained with a fixed pairing ansatz; if the IS pairing symmetry is allowed to vary and the hydrogen-induced enhancement disappears, the 'selective enhancer' conclusion would need to be reattributed to the ansatz rather than to the material physics."],"forward_implications":["If correct, hydrogenated samples in the 0.22-0.28 hydrogen window should show a raised low-doping (IS, s-wave) superconducting dome compared with hydrogen-free samples, with little change at higher doping.","The two-band model remains a valid minimal description even with hydrogen present, so future many-body studies of hydrogenated nickelates can keep the same d_x2-y2/IS basis.","The near-disappearance of the kz=pi IS electron pocket gives a specific electronic-structure signature of hydrogenation that angle-resolved photoemission or quantum-oscillation experiments could look for.","The results side with experimental reports that hydrogen incorporation is not necessary for superconductivity, while identifying a specific orbital channel through which hydrogen can nevertheless strengthen pairing."],"supporting_citations":[{"why":"The secondary-ion mass spectroscopy evidence that hydrogen is present in (Nd,Sr)NiO2, including the 0.22-0.28 concentration window that the 25% hydrogen supercell is chosen to match.","marker":"[35]"},{"why":"Prior DFT result that hydrogen occupies apical oxygen vacancies and forms Ni-H-Ni chains, the structural model adopted here.","marker":"[42]"},{"why":"Establishes the two-band (Ni d_x2-y2 plus interstitial) low-energy electronic structure of NdNiO2 that the model is built on.","marker":"[25]"},{"why":"Supports the two-band scenario and the cuprate-nickelate comparison that motivates treating d_x2-y2 and IS as the active orbitals.","marker":"[27]"},{"why":"Introduces the orbital-selective two-band superconductivity framework in nickelates that the VMC pairing ansatz (s-wave IS, d-wave d_x2-y2) extends.","marker":"[30]"},{"why":"Reports the experimental double-dome superconducting phase diagram of Nd1-xSrxNiO2 that the computed two-hump order parameter is compared against.","marker":"[44]"},{"why":"Provides an additional experimental superconducting dome measurement used to benchmark the double-hump feature.","marker":"[46]"},{"why":"The recent report that extensive hydrogen incorporation is not necessary for superconductivity, which the paper's conclusion explicitly supports.","marker":"[36]"}],"fun_headline_variants":["Hydrogen tips NdNiO2's pairing toward the interstitial dome","Hydrogen selectively enhances NdNiO2's IS superconducting dome","Topotactic H boosts one dome, spares the other in NdNiO2","Hydrogen gives NdNiO2's interstitial dome a boost"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The computed selective enhancement of the IS superconducting dome rests on the assumption that the hydrogenated low-energy physics is faithfully captured by a two-orbital (d_x2-y2 and IS) Hubbard model with pairing symmetries fixed to s-wave on IS and d-wave on d_x2-y2; if additional orbitals or alternative pairing channels matter, the hydrogen-induced IS-dome enhancement could be an artifact of that truncation.","fun_headline_variants_meta":{"raw":{"variants":["Hydrogen tips NdNiO2's pairing toward the interstitial dome","Hydrogen selectively enhances NdNiO2's IS superconducting dome","Topotactic H boosts one dome, spares the other in NdNiO2","Hydrogen gives NdNiO2's interstitial dome a boost"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000976,"raw_usage":{"total_tokens":4173,"prompt_tokens":998,"completion_tokens":3175,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":614,"completion_tokens_details":{"reasoning_tokens":3098}},"tokens_in":614,"tokens_out":3175,"duration_ms":23126,"temperature":1.0,"reasoning_tokens":3098,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T20:02:30.406263+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"If a high-resolution measurement of the kz=pi Fermi surface showed the IS-derived electron pocket still present in hydrogenated NdNiO2, the paper's electronic-structure mechanism would fail; alternatively, a VMC calculation allowing d-wave pairing on the IS orbital that reproduces the same low-doping enhancement would show the conclusion depends on the fixed pairing ansatz rather than on hydrogen itself.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The secondary-ion mass spectroscopy evidence that hydrogen is present in (Nd,Sr)NiO2, including the 0.22-0.28 concentration window that the 25% hydrogen supercell is chosen to match."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Prior DFT result that hydrogen occupies apical oxygen vacancies and forms Ni-H-Ni chains, the structural model adopted here."},{"cited_title":"Nomura, M","cited_arxiv_id":null,"evidence_quote":"Establishes the two-band (Ni d_x2-y2 plus interstitial) low-energy electronic structure of NdNiO2 that the model is built on."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supports the two-band scenario and the cuprate-nickelate comparison that motivates treating d_x2-y2 and IS as the active orbitals."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reports the experimental double-dome superconducting phase diagram of Nd1-xSrxNiO2 that the computed two-hump order parameter is compared against."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides an additional experimental superconducting dome measurement used to benchmark the double-hump feature."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The recent report that extensive hydrogen incorporation is not necessary for superconductivity, which the paper's conclusion explicitly supports."}],"review_version":2}