{"id":"73317853-261d-4040-acf6-b4f361ab7881","arxiv_id":"2412.02813","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"STM images of WSe2 show the valence-band electron density shift from tungsten sites near Gamma to hollow sites near K, confirming WSe2 is a topologically obstructed atomic insulator.","lead":"This paper uses scanning tunneling microscopy to show that, in the semiconductor WSe2, electrons at the top of the valence band sit at the hollow sites of the atomic lattice, while electrons deeper in the band sit on the tungsten atoms. This energy-dependent shift in the electron cloud is a direct real-space signature that WSe2 is a topologically obstructed atomic insulator, a material whose electron orbitals cannot be smoothly reshaped into ordinary atomic orbitals.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The key experimental contrast in Fig. 3f is acquired with a simultaneous 0.5 nm tip-height change (SM S3/S6c), so the conclusion that the peak shift reflects K/Γ orbital symmetry—not a height or tunneling-matrix artifact—remains unsupported.","rationale":"The reader's weakest assumption is exactly the one I would stress: the mid-frame bias switch in Fig. 3f is confounded with a tip-height change, and the paper's treatment of z-dependence in SM S2.A does not simulate the actual two-window current-integrated contrast. I agree with the reader that the topological conclusion itself is theoretically well grounded and likely correct; I would not reject the paper. The independent support—defect-based lattice registration, DFT maximally localized Wannier functions, and the s+f toy model in SM S1.B—is real and deserves credit, but it does not remove the confound. The specific new claim of an unambiguous direct real-space imaging of the Wannier-center obstruction requires either a quantitative simulation of the two setpoints or a control measurement at fixed tip height. Therefore the CONDITIONAL verdict is appropriate, and no change from the reader's verdict is needed.","tokens_in":15513,"tokens_out":5241,"duration_ms":63067,"concrete_test":"Perform Tersoff-Hamann simulations of the tunneling current for monolayer WSe2 at the exact experimental parameters used in Fig. 3f: sample bias -1.4 V with tip-sample distance d0 (K window), and bias -1.9 V with distance d0 + 0.5 nm (Γ window), integrating all states within each bias window from DFT wavefunctions. If the simulated lateral positions of the current maxima shift from W-site to hollow-site between the two setpoints when the same k-integrated band character is used at both distances, the artifact concern is confirmed; if the shift disappears when the 0.5 nm height change is removed from the simulation, the experimental diagnostic survives.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central inference is that the bright-feature shift from W sites (Γ window) to hollow sites (K window) in the mid-frame bias-switched images directly images the C3-eigenvalue mismatch of the WSe2 valence band. The load-bearing assumption is that the two images differ only in the dominant momentum window. The procedure does not enforce this: SM S3 and Fig. S6 describe a simultaneous change of bias and tip-sample separation (tip moved 0.5 nm for the K window), so the comparison in Fig. 3f is not constant-height across the switch. Tunneling matrix elements and exponential decay of tip-orbital overlaps are energy-, k-, and orbital-dependent, and can move apparent maxima even for a fixed band character. The paper's own z-dependence check (SM S2.A, Fig. S5) shows that the shape of the simulated partial charge density near Γ changes with height to the point of appearing off-atomic-site at small z, yet it does not simulate the actual two-window current-integrated STM signal at the experimental setpoints. The dominance of the K window at -1.4 V is argued from decay-constant reasoning, not from k-resolved data, and the integrated LDOS in a window (Eq. S2) includes many momenta. Because the topological label of monolayer WSe2 is independently known from symmetry indicators, the theory side is solid; the experimental demonstration of 'real-space imaging of band topology' is what remains conditional.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript reports STM measurements on monolayer WSe2 that are intended to image the real-space valence-band charge density at two high-symmetry momenta. Using substitutional S and Mo dopants to mark the Se and W lattice sites, the authors first establish that bright topographic features at -1.4 V sit at the hollow sites, while at more negative bias near the Γ point the bright features sit at the W sites. They interpret this shift through symmetry-based indicators and maximally localized Wannier functions, concluding that the WSe2 valence band is a topologically obstructed atomic insulator whose Wannier center is pinned to the hollow site. The paper includes supporting DFT/Wannier calculations, two tight-binding model calculations, and a comparison with NbSe2.","tokens_in":15808,"tokens_out":5560,"duration_ms":57876,"significance":"If the experimental spatial shift is substantiated, this would be a novel and valuable real-space diagnostic of band topology: the paper would demonstrate that STM can directly visualize the Wannier-center obstruction in a periodic solid, complementing earlier real-space signatures that require defects or boundaries. The symmetry-based argument is on firm theoretical ground, since the C3 eigenvalue mismatch between Γ and K is a known symmetry-indicator criterion for the obstructed atomic limit, and the DFT/Wannier calculations support the interpretation. The substitutional-doping strategy to identify lattice sites is clever, and the three-band model and the s+f toy model are instructive controls, particularly the s+f model's demonstration that an off-atomic-site orbital shape alone does not imply obstruction. The main weakness is that the central experimental comparison in Fig. 3f is affected by a simultaneous tip-height change, so the experimental evidence for the load-bearing spatial shift is currently conditional rather than conclusive.","major_comments":[{"comment":"The central experimental result, the shift of the current maxima from W sites to hollow sites when the bias is changed from -1.9 V to -1.4 V, is obtained in constant-height current images in which the tip-sample separation is also changed simultaneously with the bias (SM S3, Fig. S6). Because the tunneling current depends exponentially and in an orbital-dependent way on tip height, the apparent peak-position shift could in principle be produced by the height change or by energy-dependent tunneling matrix elements rather than by the K/Γ orbital character. A control measurement at fixed height, or a quantitative simulation of the two-window tunneling current at the actual experimental heights, is required before the topological conclusion can be drawn from Fig. 3f. In addition, the shift is presented through representative images without line cuts or statistics, so the reader cannot assess its robustness.","section":"Fig. 3f and SM S3, Fig. S6"},{"comment":"The simulated images in Fig. 3d and SM Fig. S5 are single-energy partial charge densities, not the bias-integrated local density of states or tunneling current that is actually measured. The measured current is an integral over an energy window (Eq. S2), and the -1.4 V window includes states near Γ as well as K, while the -1.9 V window includes contributions from all higher-lying states. The paper does not demonstrate that the integrated two-window images reproduce the same contrast as the partial charge densities at K and Γ; without such a simulation, the interpretation of the experimental contrast as a direct map of the K and Γ wavefunctions remains an assumption. This point is especially relevant because SM Fig. S5 shows that the spatial shape of the partial charge density near Γ changes with height, and the current simulation does not account for this effect.","section":"SM S2.A, Fig. S5 and Eq. (S2)"},{"comment":"The assignment of the spectroscopic features at -1.24 eV and -1.89 eV to the K and Γ points relies on alignment with the DFT band structure and on tunneling-decay-constant arguments, not on a k-resolved measurement. The claim that the -1.4 V window is dominated by K-point states is therefore not directly verified; a momentum-resolved experiment or a quantitative tunneling simulation establishing the relative weight of K and Γ states in the two windows is needed. At minimum, this dominance should be stated as an assumption rather than an established fact, because the entire experimental inference depends on it.","section":"Fig. 3b and main text"}],"minor_comments":[{"comment":"The word 'unambiguously' in the abstract is too strong given the experimental caveats discussed above; consider softening the claim to reflect that the Wannier-center location is inferred from STM data supported by symmetry analysis and DFT.","section":"Abstract"},{"comment":"The sentence 'following the method of Ref. W and Mo powder of 99.999% ...' appears to have a missing citation number after 'Ref.'; please correct this typographical error.","section":"Methods, TMD Synthesis"},{"comment":"The text states 'Figure 4b shows an STM image of the doped NbSe2', but the caption and panel layout indicate that the STM image is panel (c); please correct the cross-reference.","section":"Fig. 4 and main text"},{"comment":"The notation in Eq. (S2) is nonstandard: the retarded Green's function and the expectation value should be defined explicitly, since the relationship between the Green's function and the LDOS is central to the argument.","section":"SM Eq. (S2)"},{"comment":"The atomic-lattice overlay in Fig. 3e,f is said to be determined from nearby defects, but the caption does not state how the alignment uncertainty is estimated; a brief statement of the method and its accuracy would help the reader trust the peak-position comparison.","section":"Fig. 3e,f caption"}],"recommendation":"major_revision","confidential_remarks":"The theoretical framework and the computational side of this paper are solid, and the doping-based site identification is a strong experimental idea. The main issue is that the key experimental panel, Fig. 3f, changes the tip height simultaneously with the bias, which introduces a confound for the central claim. This is fixable with additional control measurements or a more complete simulation of the two-window tunneling current; if the authors can provide such support, the paper would be a strong contribution. I would not reject at this stage, but the current version does not fully establish the 'real-space imaging' claim."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my take. The paper's real contribution is a new STM protocol: switching bias mid-frame to compare LDOS at different energies at the same location without drift, combined with substitutional dopants to pin down the atomic sites. That is genuinely useful, and the dopant-registration result—that the bright features in WSe2 valence-band images sit at hollow sites, not chalcogen sites—is a nice resolution of an old ambiguity. The Wannier/DFT analysis is sound, and the hBN and s+f toy models are good controls: they show that a trivial band can look off-site at certain energies, so the shift alone is not enough.\n\nThe soft spot is the key experimental figure. Fig. 3f is presented as constant-height current imaging, but the SI makes clear that the tip was moved 0.5 nm closer for the K-point window to keep the current from saturating. So the comparison across the bias switch is not at fixed tip-sample distance. The paper's own z-dependence simulation (SM S2.A) shows that the apparent position of maxima in the Γ window can move off-site at smaller tip heights even for the trivial part of the band. That directly undermines the inference that the hollow-site maximum in the K window is caused by the C3 eigenvalue mismatch rather than by the change in tip height or tunneling matrix element. The dominance of K-point states in the -1.4 V window is argued from decay constants, not measured k-resolved. There are also no line cuts or error bars on the peak shift; the evidence is representative images.\n\nNone of this invalidates the theoretical side. The OAI classification of WSe2 is already established, and the DFT/Wannier results are consistent with it. What is conditional is the claim that these STM images constitute an unambiguous real-space imaging of that topology. I think the authors can fix this with quantitative peak analysis, height-dependent control images, and perhaps a simulation of the integrated current in the two windows at the actual experimental setpoints. As it stands, the experiment is suggestive but not yet conclusive.\n\nThis paper deserves a serious referee. It is a solid, well-written contribution with a genuinely new protocol, and the gap between claim and evidence is repairable. I'd send it to review but ask for major revisions focused on the bias-switch artifact question.","headline":"Clever new STM protocol and solid theory, but the key experimental claim is undercut by the simultaneous tip-height change in the bias-switch images.","tokens_in":16363,"tokens_out":2491,"would_cite":false,"duration_ms":26985,"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 valence band of WSe2 has its Wannier center in the hollow sites between tungsten atoms, and bias-switched STM imaging shows it directly.","keywords":["WSe2","scanning tunneling microscopy","Wannier center","obstructed atomic insulator","transition metal dichalcogenides","band topology","local density of states","C3 symmetry"],"falsifier":"A decisive check would be to image the same WSe2 bias window at several fixed tip-sample separations and compare constant-height current maps: if the hollow-site maximum at the K window is a tunneling-matrix-element or tip-height artifact, it would move or disappear when the tip is retracted, whereas the symmetry-pinned Wannier-center picture predicts the maximum stays at the hollow site as long as the K states dominate the current.","tokens_in":15306,"feed_emoji":"🔬","tokens_out":7569,"duration_ms":78028,"temperature":0.7,"pith_summary":"This paper claims that scanning tunneling microscopy can diagnose band topology from the real-space position of the electronic density within a unit cell. For monolayer WSe2, the authors register the atomic lattice using substitutional dopants and then switch the sample bias mid-frame so the same patch of surface is imaged near the valence-band maximum at K and deeper near Γ. They find the density maximum at K sits in the honeycomb hollow sites between W atoms, while at Γ it sits on the W sites. According to the symmetry-based theory of obstructed atomic insulators, that shift means the valence band's Wannier center is pinned off the atoms and the band cannot be adiabatically connected to a trivial atomic limit. The result matters because it turns a bulk topological invariant into a visible, energy-dependent contrast change in a standard STM image.","feed_headline":"Bias-switched STM pins WSe2's valence band between atoms","feed_subtitle":"A mid-scan bias switch moves the charge maximum from W sites to hollow sites — a direct signature of band topology.","key_machinery":"The load-bearing object is the Wannier function, the real-space orbital obtained by Fourier-transforming the Bloch states of a single band, and its center, the Wannier center, which symmetry can pin to a Wyckoff position in the unit cell. The paper's mechanism is momentum-dependent interference: a Bloch state is a sum of Wannier orbitals with phase factors $e^{i\\mathbf{k}\\cdot\\mathbf{R}}$, and at Γ the phases are equal while at K they differ by 120 degrees, so whether the local density of states peaks on or off the metal sites is decided by the C3 rotation eigenvalue of the band's orbital character. An obstructed atomic insulator is a band whose Wannier center is pinned to bond or hollow positions rather than atomic sites, so it cannot be deformed to a trivial atomic insulator. To make the comparison, the authors use substitutional S and Mo dopants to identify the Se and W sublattices, first-principles maximally localized Wannier functions and a three-band tight-binding model to compute the local density of states, and mid-frame bias-switched constant-current topography and constant-height current images to compare Γ and K contrast on the same lattice patch without lateral drift.","core_discovery":"The central discovery is that the maximum of the valence-band local density of states in monolayer WSe2 moves within the unit cell as the bias energy is swept from the K-point valence-band maximum to the Γ-point region. At K the density is peaked at the honeycomb centers, between the tungsten atoms; at Γ it is peaked at the W atomic sites. Because the C3 eigenvalues at the two high-symmetry points differ, with trivial character at Γ and a chiral $e^{2\\pi i/3}$ character at K, the Bloch states at K interfere destructively on the W sites and constructively at the hollow sites, whereas at Γ they construct on the W sites. This incompatibility with Wannier functions exponentially localized on the atomic sites makes the valence band a topologically obstructed atomic insulator with a quantized Berry phase. The same measurement on NbSe2 shows no such shift because its Γ and K features are nearly degenerate, which the authors present as confirmation that the shift tracks the symmetry-imposed obstruction rather than a generic orbital shape.","pith_inferences":["Beyond the paper: the same mid-frame bias-switch protocol should work for any semiconductor whose high-symmetry valence or conduction states are separated in energy by more than the tunneling-decay contrast, making monolayer MoS2 and other TMDs natural next targets.","Beyond the paper: if the hollow-site maximum is set by the chiral $d\\pm id$ orbital character rather than by WSe2-specific details, the contrast reversal should be reproducible in simulated STM images at fixed tip height, and a null result in such a simulation would point to tunneling-matrix-element artifacts.","Beyond the paper: the result implies that in moiré heterostructures of TMDs, atomic registries inferred from STM topographs at the band edge are offset by half a unit cell from the chalcogen lattice, which could affect the interpretation of moiré reconstructions and twist-angle alignment.","Beyond the paper: the same logic applied to the conduction band would map the Wannier-center flow across the full band structure, offering a real-space proxy for electric polarization and its quantum-geometric corrections."],"forward_implications":["Monolayer WSe2's valence band is confirmed as an obstructed atomic insulator, implying a quantized Berry phase and physical consequences such as corner states and an enhanced dielectric constant.","STM topographs taken near the valence-band maximum of WSe2 show hollow-site contrast, not atomic positions, so previous defect assignments built on the opposite assumption need to be revisited.","Because the symmetry argument is general to 2H transition metal dichalcogenides, the same bias-dependent contrast shift should appear in other semiconducting monolayers whenever the Γ–K energy separation is large enough to isolate the K-point states.","The method offers a real-space diagnostic of band topology that needs no defects, step edges, or sample boundaries, unlike previous STM-based topological probes.","In metals such as NbSe2 the energy-integrated STM signal mixes Γ and K contributions and hides the obstruction, so reading its Berry phase requires bias-dependent interference near symmetry-breaking defects."],"supporting_citations":[{"why":"Supplies the symmetry-based indicator and band-representation theory that classifies WSe2 as an obstructed atomic insulator from its high-symmetry C3 eigenvalues.","marker":"[3]"},{"why":"Establishes the elementary band representations framework used to infer the Wannier-center Wyckoff position from high-symmetry eigenvalues.","marker":"[4]"},{"why":"Provides the minimal three-band tight-binding model of WSe2 whose local density of states reproduces the hollow-site to atomic-site shift.","marker":"[23]"},{"why":"Shows theoretically that chiral orbitals with nontrivial C3 character place charge maxima at triangle centers, which is the mechanism behind the K-point contrast.","marker":"[44]"},{"why":"Provides the prior STM observation of off-atomic-site charge density in indenene that this paper's Wannier-interference picture extends.","marker":"[9]"},{"why":"Documents the large tunneling decay constant for K-point states in TMDs, motivating the closer tip position used in the K bias window.","marker":"[21]"},{"why":"Supplies the constant-current dI/dV spectroscopy method used to identify the K and Γ valence-band energies.","marker":"[22]"},{"why":"Establishes that bright STM contrast in TMD monolayers need not sit at chalcogen sites and provides the oxygen-defect fingerprint used for lattice alignment.","marker":"[20]"},{"why":"Provides the ultrapure flux-grown WSe2 crystals that make substitutional dopants distinguishable from native defects.","marker":"[12]"},{"why":"Provides the method used to construct the maximally localized Wannier functions from first-principles charge densities.","marker":"[52]"}],"fun_headline_variants":["STM reveals WSe2's valence band flips from hollow to atom sites","WSe2 valence band topology imaged: charge hops between atoms","Real-space proof: WSe2 is a topologically obstructed atomic insulator","Bias switch in STM shows WSe2's band charge shifting between sites"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The conclusion rests on treating the bright features in the bias-switched STM current images as direct maps of the valence-band local density of states at the selected momenta, rather than as artifacts of the mid-frame change in bias, tip height, or energy-dependent tunneling matrix elements.","fun_headline_variants_meta":{"raw":{"variants":["STM reveals WSe2's valence band flips from hollow to atom sites","WSe2 valence band topology imaged: charge hops between atoms","Real-space proof: WSe2 is a topologically obstructed atomic insulator","Bias switch in STM shows WSe2's band charge shifting between sites"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000642,"raw_usage":{"total_tokens":2932,"prompt_tokens":901,"completion_tokens":2031,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":517,"completion_tokens_details":{"reasoning_tokens":1949}},"tokens_in":517,"tokens_out":2031,"duration_ms":14307,"temperature":1.0,"reasoning_tokens":1949,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T23:04:53.408084+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A decisive check would be to image the same WSe2 bias window at several fixed tip-sample separations and compare constant-height current maps: if the hollow-site maximum at the K window is a tunneling-matrix-element or tip-height artifact, it would move or disappear when the tip is retracted, whereas the symmetry-pinned Wannier-center picture predicts the maximum stays at the hollow site as long as the K states dominate the current.","supporting_citations":[{"cited_title":"Topological quantum chemistry,","cited_arxiv_id":null,"evidence_quote":"Supplies the symmetry-based indicator and band-representation theory that classifies WSe2 as an obstructed atomic insulator from its high-symmetry C3 eigenvalues."},{"cited_title":"Building blocks of topological quantum chemistry: Elementary band representations,","cited_arxiv_id":null,"evidence_quote":"Establishes the elementary band representations framework used to infer the Wannier-center Wyckoff position from high-symmetry eigenvalues."},{"cited_title":"Three-band tight-binding model for monolayers of group- vib transition metal dichalcogenides,","cited_arxiv_id":null,"evidence_quote":"Provides the minimal three-band tight-binding model of WSe2 whose local density of states reproduces the hollow-site to atomic-site shift."},{"cited_title":"Real-space obstruction in quantum spin hall insulators,","cited_arxiv_id":null,"evidence_quote":"Shows theoretically that chiral orbitals with nontrivial C3 character place charge maxima at triangle centers, which is the mechanism behind the K-point contrast."},{"cited_title":"Design and realization of topological Dirac fermions on a triangular lattice,","cited_arxiv_id":null,"evidence_quote":"Provides the prior STM observation of off-atomic-site charge density in indenene that this paper's Wannier-interference picture extends."},{"cited_title":"Probing critical point energies of transition metal dichalcogenides: Sur- prising indirect gap of single layer WSe 2,","cited_arxiv_id":null,"evidence_quote":"Documents the large tunneling decay constant for K-point states in TMDs, motivating the closer tip position used in the K bias window."},{"cited_title":"Stroscio and W","cited_arxiv_id":null,"evidence_quote":"Supplies the constant-current dI/dV spectroscopy method used to identify the K and Γ valence-band energies."},{"cited_title":"Identifying substitutional oxygen as a pro- lific point defect in monolayer transition metal dichalco- genides,","cited_arxiv_id":null,"evidence_quote":"Establishes that bright STM contrast in TMD monolayers need not sit at chalcogen sites and provides the oxygen-defect fingerprint used for lattice alignment."},{"cited_title":"Two-step flux synthesis of ultrapure transition-metal dichalcogenides,","cited_arxiv_id":null,"evidence_quote":"Provides the ultrapure flux-grown WSe2 crystals that make substitutional dopants distinguishable from native defects."},{"cited_title":"An updated version of wannier90: A tool for obtaining maximally-localised Wannier functions,","cited_arxiv_id":null,"evidence_quote":"Provides the method used to construct the maximally localized Wannier functions from first-principles charge densities."}],"review_version":1}