{ "schema_version": "1.0.0", "artifact_id": "qft.artifact.many-body-quantum-matter.doped-mott-pseudogap-momentum-differentiation", "title": "Momentum-selective pseudogap, thresholded arcs, and nodal-antinodal spectra", "classification": "original schematic momentum-space and spectral-function diagram", "reader_question": "How can a closed reference contour display apparent Fermi arcs when antinodal low-energy spectral weight is suppressed, and what is the strongest conclusion licensed by the corresponding nodal and antinodal spectra?", "dominant_point": "Nodal low-energy weight can remain visible while antinodal weight is suppressed on the same closed reference contour, so an intensity threshold can leave apparent arcs without establishing an open Fermi surface, d-wave pairing, or a unique microscopic mechanism.", "status": { "schematic": true, "not_to_scale": true, "contains_experimental_data": false, "contains_simulator_data": false, "contains_solver_data": false, "contains_material_specific_band_structure": false, "contains_quantitative_line_shapes": false }, "conventions": [ "The square-lattice first Brillouin zone uses lattice spacing a = 1, with momentum components bounded by plus or minus pi.", "The nodal sectors lie near the zone diagonals and the antinodal sectors lie near (plus or minus pi, 0) and (0, plus or minus pi). Labels in one quadrant represent fourfold-related sectors.", "The thin rounded-diamond locus is one closed reference contour. It is a geometrical guide, not a calculated Fermi surface, a fitted dispersion, or a second physical surface.", "Solid black and broken gray segments lie on the same reference contour. They encode qualitative above-threshold and suppressed low-energy visibility, respectively; no line width, dash length, segment length, or gray value encodes a number.", "Frequency omega is measured relative to the chemical potential, so omega = 0 is the low-energy point compared in panel B.", "Both schematic spectral curves use the same layout-only axes and remain nonnegative. Their heights, widths, side maxima, and integrated areas are not quantitative and are not normalized by the drawing." ], "panels": [ { "id": "A", "title": "One closed contour, momentum-selective visibility", "purpose": "Show that a single closed square-lattice reference contour can retain above-threshold nodal segments while antinodal low-energy weight is suppressed, leaving apparent arcs after thresholding.", "object_ids": [ "square_brillouin_zone", "zone_diagonals", "closed_reference_contour", "nodal_above_threshold_segments", "antinodal_suppressed_segments", "threshold_topology_statement" ] }, { "id": "B", "title": "Low-energy spectra at a node and an antinode", "purpose": "Compare a schematic nodal spectrum with finite weight at omega = 0 against a schematic antinodal spectrum with a central suppression, then state the evidence ceiling.", "object_ids": [ "nodal_spectrum", "antinodal_spectrum", "evidence_ceiling" ] } ], "objects": [ { "id": "square_brillouin_zone", "panel_id": "A", "kind": "momentum-space frame", "content": "A square first Brillouin zone centered on Gamma with no material-specific dispersion or filling encoded." }, { "id": "zone_diagonals", "panel_id": "A", "kind": "geometric guides", "content": "Two dotted diagonals identify the fourfold-related nodal directions." }, { "id": "closed_reference_contour", "panel_id": "A", "kind": "single closed geometrical locus", "content": "One thin continuous rounded-diamond contour passes through the nodal and antinodal sectors. It remains visible beneath every thick segment so the diagram never introduces a second Fermi surface." }, { "id": "nodal_above_threshold_segments", "panel_id": "A", "kind": "qualitative high-visibility encoding", "content": "Four solid black segments centered near the zone diagonals represent low-energy spectral weight that lies above a declared intensity threshold. These are the apparent arcs in a thresholded map." }, { "id": "antinodal_suppressed_segments", "panel_id": "A", "kind": "qualitative low-visibility encoding", "content": "Four broken gray segments centered on the antinodal directions represent suppressed but not asserted-to-be-zero low-energy spectral weight on the same closed contour." }, { "id": "threshold_topology_statement", "panel_id": "A", "kind": "interpretive boundary", "content": "Applying an intensity threshold changes which parts of the contour are visible; it does not by itself establish that the underlying momentum-space locus is open." }, { "id": "nodal_spectrum", "panel_id": "B", "kind": "schematic nonnegative spectral function", "content": "A solid nonnegative curve has finite central weight at omega = 0 and represents the nodal sector. The curve is explanatory rather than fitted or calculated." }, { "id": "antinodal_spectrum", "panel_id": "B", "kind": "schematic nonnegative spectral function", "content": "A broken gray nonnegative curve has a central depression at omega = 0 and represents antinodal low-energy suppression. Side maxima and widths carry no gap value or line-shape model." }, { "id": "evidence_ceiling", "panel_id": "B", "kind": "strongest licensed inference", "content": "The two panels establish only an operational picture of momentum-selective spectral suppression. Additional discriminants are required for contour topology, pairing symmetry, or microscopic mechanism." } ], "relations": [ { "from": "nodal_above_threshold_segments", "to": "closed_reference_contour", "type": "same_geometrical_locus", "meaning": "The visible nodal segments overlay the single continuous reference contour rather than forming a separate surface." }, { "from": "antinodal_suppressed_segments", "to": "closed_reference_contour", "type": "same_geometrical_locus", "meaning": "The suppressed antinodal segments overlay the same continuous reference contour and are not removed topologically." }, { "from": "antinodal_suppressed_segments", "to": "nodal_above_threshold_segments", "type": "intensity_threshold_selects_visibility", "meaning": "A threshold retains the higher-visibility nodal segments while omitting the lower-visibility antinodal segments, producing apparent arcs." }, { "from": "nodal_above_threshold_segments", "to": "nodal_spectrum", "type": "qualitative_correspondence", "meaning": "Finite nodal weight at omega = 0 is the spectral behavior represented by the above-threshold nodal segments." }, { "from": "antinodal_suppressed_segments", "to": "antinodal_spectrum", "type": "qualitative_correspondence", "meaning": "The antinodal central depression is the spectral behavior represented by the broken gray antinodal segments." }, { "from": "nodal_spectrum", "to": "evidence_ceiling", "type": "supports_bounded_observation", "meaning": "Together with the antinodal spectrum, the nodal curve supports momentum differentiation but not a unique cause." }, { "from": "antinodal_spectrum", "to": "evidence_ceiling", "type": "supports_bounded_observation", "meaning": "A central antinodal suppression supports an operational pseudogap only after baselines, resolution, temperature, and method controls are supplied outside this schematic." } ], "reading_order": [ "panel A title and square Brillouin-zone frame", "dotted zone diagonals and directly labeled nodal and antinodal sectors", "thin continuous closed reference contour", "solid above-threshold nodal segments on that contour", "broken gray suppressed antinodal segments on that contour", "thresholding statement that visibility does not determine topology", "panel B title and common frequency convention", "nodal nonnegative spectrum with finite central weight", "antinodal nonnegative spectrum with central suppression", "final evidence ceiling excluding an open-surface, pairing, or unique-mechanism inference" ], "assumptions": [ "A momentum-resolved low-energy spectral diagnostic has been defined with a declared temperature, resolution, baseline, and intensity threshold outside the figure.", "Nodal and antinodal comparisons refer to the same Hamiltonian, state, temperature, normalization convention, and analysis pipeline.", "The fourfold-related placement is a geometrical square-lattice convention; the figure does not assert that the physical state preserves C4 symmetry or excludes nematicity.", "A central antinodal depression is called a pseudogap only when it is reproducible relative to a declared baseline and survives the relevant method and probe controls." ], "nonclaims": [ "The rounded diamond is not a calculated, measured, or material-specific Fermi surface and does not encode a carrier density, hopping ratio, interaction, temperature, or Luttinger volume.", "The apparent arc endpoints are set only by the illustrative threshold and do not define universal arc lengths, critical angles, hot spots, or a phase boundary.", "The broken antinodal segments mean suppressed visibility, not exactly zero spectral weight or a demonstrated Green-function zero.", "The spectral curves are not data, fits, analytic continuations, self-energies, density-of-states curves, or universal pseudogap line shapes.", "The side maxima of the antinodal curve do not define a gap edge or a numerical pseudogap energy.", "Momentum-selective suppression does not by itself establish an open Fermi surface, a reconstructed pocket, d-wave pairing, precursor superconductivity, fractionalization, stripe order, antiferromagnetic causation, a Widom line, or any other unique mechanism.", "The figure does not identify a zero-temperature phase or assert that every Hubbard-model or cuprate parameter regime has the same pseudogap phenomenology." ], "scientific_checks": [ "The Brillouin-zone frame, closed contour, nodal segments, and antinodal segments are invariant under ninety-degree rotations of the schematic geometry.", "Every thick visibility segment lies on the single thin closed contour; no second closed or open surface is drawn.", "Both plotted spectral curves remain nonnegative over the displayed frequency interval.", "The nodal curve has finite weight at omega = 0, while the antinodal curve has a central local minimum there.", "No numerical ticks, line-shape parameters, gap magnitude, spectral normalization, or arc length are presented to the reader.", "Line style and direct labels distinguish the categories without relying on color.", "The caption, alt text, objects, relations, assumptions, and nonclaims preserve the same observation-versus-mechanism ceiling." ], "intended_alt_text": "Two stacked schematic panels show one closed square-lattice reference contour with solid nodal segments above an intensity threshold and broken gray antinodal segments with suppressed weight, followed by a nodal spectrum with finite weight at zero frequency and an antinodal spectrum with a central depression; thresholding leaves apparent arcs but does not establish an open Fermi surface, d-wave pairing, or a unique mechanism.", "intended_caption": "Momentum-selective pseudogap and the apparent-arc caveat. In the upper schematic, solid nodal and broken gray antinodal segments lie on one closed reference contour; an intensity threshold retains the nodal segments and hides the suppressed antinodal segments without changing contour topology. The lower schematic compares a nodal spectrum with finite weight at omega = 0 to an antinodal spectrum with a central depression. Curves and contour are schematic and not to scale. The observation establishes neither an open Fermi surface, d-wave pairing, nor a unique microscopic mechanism." }