{"id":"bd02962c-1ccc-4a4a-af26-69aeb9a1d1af","arxiv_id":"2606.18858","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":7.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Proposes impurity-based tomography to extract electron density matrices and quantum geometric tensor from QPI maps via symmetry disentanglement in honeycomb models.","lead":"The paper introduces a tomography method to reconstruct the density matrix of electron states from quasiparticle interference maps around single impurities in two-orbital honeycomb lattice models. This could enable orbital-resolved band structure characterization in graphene-like materials using standard unpolarized STM tips.","discovery_kind":"unclear","skeptic_critique":{"model":"grok-4.3","headline":"Symmetry disentanglement of orbital QPI contributions may not be bijective for all density-matrix elements","rationale":"The reader's weakest assumption directly identifies the symmetry-disentanglement step as load-bearing; confirming the rank of the symmetry-projected response matrix would settle whether the claimed tomography is possible or requires additional assumptions.","tokens_in":1636,"tokens_out":282,"duration_ms":20932,"concrete_test":"For the explicit two-orbital tight-binding Hamiltonian and on-site impurity T-matrix given in the manuscript, compute the four symmetry-projected QPI Fourier components at the backscattering wave-vector; check whether the resulting 4×4 response matrix to the four density-matrix elements has full rank (condition number < 10).","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim requires that backscattering between time-reversed states maps the full 2×2 density matrix (populations + coherences) into linearly independent orbital channels that transform under distinct irreps of the lattice symmetry group, allowing unique inversion. In the two-orbital honeycomb model this mapping is asserted but its invertibility is not demonstrated; if any two orbital combinations produce QPI patterns that are linearly dependent under the group action (e.g., same irrep content after impurity averaging), the reconstruction of off-diagonal coherences or the quantum geometric tensor becomes under-determined.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper proposes an electron state tomography method that reconstructs the density matrix (populations and coherences) and quantum geometric tensor of scattering states from quasiparticle interference (QPI) maps around single on-site impurities. In two-orbital honeycomb-lattice models, backscattering between time-reversed states is claimed to map the density matrix into distinct orbital contributions in the QPI pattern; these contributions are asserted to transform under different representations of the lattice symmetry group, permitting their disentanglement even with conventional, unpolarized STM tips. The approach is positioned as relevant to graphene heterostructures and direct-gap semiconductors.","tokens_in":1733,"tokens_out":491,"duration_ms":17477,"significance":"If the mapping from density matrix to symmetry-resolved QPI channels is shown to be bijective, the method would provide a practical route to orbital and geometric information from standard STM experiments, extending the utility of impurity-based probes beyond conventional band-structure mapping.","major_comments":[{"comment":"The central claim that orbital contributions in the QPI map transform under distinct irreps and permit unique reconstruction of the full 2×2 density matrix (including off-diagonal coherences) requires an explicit demonstration of invertibility. No linear-algebra check, character-table decomposition, or numerical example confirming that the symmetry-projected channels are linearly independent for all density-matrix elements is provided in the symmetry-analysis section.","section":"Symmetry disentanglement / two-orbital honeycomb model"},{"comment":"The manuscript states that the QPI map directly encodes the density matrix via backscattering between time-reversed states, yet supplies no derivation of the scattering amplitude or the resulting orbital-channel decomposition (e.g., no explicit form of the T-matrix or the Fourier-transformed LDOS expression that isolates the claimed symmetry channels).","section":"QPI map derivation"}],"minor_comments":[{"comment":"The abstract asserts the mapping and disentanglement without referencing the specific equations or symmetry tables that support it; a brief pointer to the relevant section would improve readability.","section":"Abstract"},{"comment":"Notation for the density matrix elements and the quantum geometric tensor should be introduced consistently when first used in the main text.","section":"Introduction / model definition"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the careful reading and constructive comments, which help strengthen the presentation of our tomography method. We address each major comment below and will revise the manuscript to incorporate the requested explicit demonstrations and derivations.","responses":[{"response":"We agree that an explicit demonstration of invertibility is required for rigor. In the revised manuscript we will expand the symmetry-analysis section with a complete character-table decomposition under the C_{3v} point group appropriate to the local impurity environment. We will explicitly verify that the four symmetry-projected channels (A_1, A_2, and the two components of E) are linearly independent and span the four-dimensional space of the 2×2 density matrix, including off-diagonal coherences. A concrete numerical example will also be added, mapping a general density matrix to the symmetry channels and demonstrating the inverse reconstruction.","revision_made":"yes","referee_comment":"[Symmetry disentanglement / two-orbital honeycomb model] The central claim that orbital contributions in the QPI map transform under distinct irreps and permit unique reconstruction of the full 2×2 density matrix (including off-diagonal coherences) requires an explicit demonstration of invertibility. No linear-algebra check, character-table decomposition, or numerical example confirming that the symmetry-projected channels are linearly independent for all density-matrix elements is provided in the symmetry-analysis section."},{"response":"We acknowledge that the detailed derivation was omitted for brevity. In the revision we will add a dedicated subsection (or appendix) that derives the T-matrix for on-site impurities in the two-orbital honeycomb model, starting from the impurity potential and the unperturbed Green function. We will then obtain the explicit Fourier-transformed LDOS expression and show how the backscattering term between time-reversed states isolates the symmetry channels that encode the density-matrix populations and coherences.","revision_made":"yes","referee_comment":"[QPI map derivation] The manuscript states that the QPI map directly encodes the density matrix via backscattering between time-reversed states, yet supplies no derivation of the scattering amplitude or the resulting orbital-channel decomposition (e.g., no explicit form of the T-matrix or the Fourier-transformed LDOS expression that isolates the claimed symmetry channels)."}],"tokens_in":1286,"tokens_out":483,"duration_ms":17081,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The paper proposes extracting the density matrix and quantum geometric tensor of scattering states from standard QPI maps around on-site impurities in two-orbital honeycomb models. The key step is that backscattering between time-reversed partners puts orbital populations and coherences into channels that transform differently under the lattice symmetry group, so they can be separated without polarized tips.\n\nWhat works is the practical framing: it takes existing QPI analysis in graphene-like systems and adds a symmetry-based route to orbital resolution. That matches the needs of people doing STM on heterostructures or direct-gap semiconductors, where conventional tips are the norm.\n\nThe soft spot is invertibility. The claim rests on the orbital contributions being linearly independent under the group action so that the full 2x2 density matrix can be recovered uniquely. If any two combinations produce patterns that are dependent after impurity averaging, the coherences or the geometric tensor become under-determined. The abstract states the mapping but does not show the explicit decomposition or test cases, and the stress-test concern about possible linear dependence is not obviously resolved by the description given. If the full text has the derivation and checks, that would fix it; otherwise the reconstruction is not guaranteed to be bijective.\n\nThis is for condensed-matter experimentalists and theorists who already work with QPI and want orbital or geometric information from routine STM data. A reader looking for new characterization protocols would find the protocol worth testing.\n\nIt deserves peer review because the idea is concrete and the symmetry argument is worth checking in detail, even if the current evidence for uniqueness is thin.","headline":"Symmetry disentanglement of QPI orbital channels is the new element, but the paper needs to show the mapping is actually invertible for the full density matrix.","tokens_in":2202,"tokens_out":392,"would_cite":false,"duration_ms":18740,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Quasiparticle interference around on-site impurities reconstructs the full density matrix and quantum geometric tensor of electron states in two-orbital honeycomb models.","keywords":["quasiparticle interference","density matrix tomography","quantum geometric tensor","honeycomb lattice","on-site impurities","backscattering","scanning tunneling microscopy","time-reversed states"],"falsifier":"Measure whether the symmetry-filtered components extracted from experimental QPI maps around an on-site impurity in a honeycomb material quantitatively match the independently known density-matrix elements of the scattering states.","tokens_in":2548,"feed_emoji":"🔬","tokens_out":683,"duration_ms":19581,"temperature":0.7,"pith_summary":"The paper shows that backscattering between time-reversed states at on-site impurities encodes the populations and coherences of the electron density matrix as distinct orbital contributions in the QPI pattern. Because these orbital signals transform differently under the lattice symmetry group, they can be separated even with an unpolarized tip to recover the complete density matrix and the quantum geometric tensor. The method applies to two-orbital honeycomb lattices relevant to graphene heterostructures and direct-gap semiconductors. A sympathetic reader would see this as turning ordinary local STM measurements into a tomographic tool for wave-function details that momentum-space probes usually supply. The central claim is that symmetry provides the missing orbital resolution without hardware changes.","feed_headline":"QPI maps around impurities recover electron density matrix","feed_subtitle":"Symmetry separation of orbital signals from time-reversed backscattering yields populations, coherences and quantum geometry in honeycomb mo","key_machinery":"The symmetry-distinct orbital decomposition of QPI intensity arising from time-reversed backscattering at on-site impurities, which isolates density-matrix elements and the quantum geometric tensor.","core_discovery":"For on-site impurities, backscattering between time-reversed states directly maps the density matrix populations and coherences into distinct orbital contributions in the interference map. These contributions transform under distinct symmetry group representations and can thus be disentangled to reveal the density matrix and quantum geometric tensor of the scattering states. This establishes impurities as tomographic probes for band structures in scanning tunneling microscopy using conventional, unpolarized tips.","pith_inferences":["The same symmetry-separation logic might be tested in other multi-orbital lattices where point-group representations remain non-overlapping.","Local impurity tomography could complement ARPES by supplying real-space geometric information that momentum-resolved methods average over.","If the disentanglement remains robust under weak disorder, the method could be applied to disordered samples without requiring perfect crystals."],"forward_implications":["The full density matrix of scattering states becomes accessible from a single local QPI measurement in two-orbital honeycomb systems.","The quantum geometric tensor is recovered as a direct byproduct of the same disentanglement procedure.","Conventional unpolarized STM tips suffice to obtain orbital information that normally requires spin- or orbital-polarized probes.","The technique applies to graphene heterostructures and direct-gap semiconductors modeled by two-orbital honeycomb lattices."],"fun_headline_variants":["Impurity QPI recovers density matrix","Tomography from impurity QPI maps","QPI disentangles density matrix via symmetry","Electron density matrix from impurity QPI"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The orbital contributions to the QPI map transform under distinct symmetry group representations that permit clean separation without mixing.","fun_headline_variants_meta":{"raw":{"variants":["Impurity QPI recovers density matrix","Tomography from impurity QPI maps","QPI disentangles density matrix via symmetry","Electron density matrix from impurity QPI"]},"model":"grok-4.3","cost_usd":0.006947,"raw_usage":{"total_tokens":3173,"prompt_tokens":573,"num_sources_used":0,"completion_tokens":50,"cost_in_usd_ticks":69474500,"prompt_tokens_details":{"text_tokens":573,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2550,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":573,"tokens_out":50,"duration_ms":14940,"temperature":1.0,"reasoning_tokens":2550,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-26T20:06:07.914623+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Measure whether the symmetry-filtered components extracted from experimental QPI maps around an on-site impurity in a honeycomb material quantitatively match the independently known density-matrix elements of the scattering states.","supporting_citations":[],"review_version":1}