{"paper":{"title":"Mobility-edge-embedded Hofstadter butterfly from a tilt-induced quasiperiodic potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Aligning a periodic potential at an angle to a square lattice produces a Hofstadter butterfly whose fractal spectrum contains mobility edges separating extended and localized states.","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"Kyoung-Min Kim, Sanghoon Lee","submitted_at":"2026-04-14T08:58:16Z","abstract_excerpt":"The Hofstadter butterfly (HB) and mobility edges (MEs) are hallmark phenomena of quasiperiodic systems, yet their interplay remains elusive. Here, we demonstrate their coexistence within a tilt-induced quasiperiodic potential on a square lattice, giving rise to a ``mobility-edge-embedded Hofstadter butterfly'' (MEE-HB). This potential is generated by aligning a periodic potential at an angle relative to the lattice axes -- a configuration readily accessible in optical lattice experiments. Using a tight-binding model, we show that the MEE-HB manifests as a fractal energy splitting pattern hosti"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we demonstrate their convergence within a tilt-induced quasiperiodic potential on a square lattice, giving rise to a ``mobility-edge-embedded Hofstadter butterfly'' (MEE-HB). This potential is generated by aligning a periodic potential at an angle relative to the lattice axes--a configuration readily accessible in optical lattice experiments. Using a tight-binding model, we show that the MEE-HB manifests as a fractal energy splitting pattern hosting MEs that separate extended and localized states.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The tight-binding model and derived Harper-like equation accurately capture the physics without higher-order effects or lattice imperfections dominating, and that the effective long-range hopping is the sole origin of the mobility edges.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Tilt-induced quasiperiodic potentials on square lattices generate a mobility-edge-embedded Hofstadter butterfly with fractal dimension 0.8-1.0, combining fractal spectra from 1D-like behavior with mobility edges from effective long-range hopping.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Aligning a periodic potential at an angle to a square lattice produces a Hofstadter butterfly whose fractal spectrum contains mobility edges separating extended and localized states.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"7208cf6545ed81c9ed8042eaf9fa5de3ca443ec37b0deac424030012a83deb31"},"source":{"id":"2604.12472","kind":"arxiv","version":2},"verdict":{"id":"083e77df-1d60-4c17-8ae9-7237a9fea9b8","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T14:02:31.745718Z","strongest_claim":"we demonstrate their convergence within a tilt-induced quasiperiodic potential on a square lattice, giving rise to a ``mobility-edge-embedded Hofstadter butterfly'' (MEE-HB). This potential is generated by aligning a periodic potential at an angle relative to the lattice axes--a configuration readily accessible in optical lattice experiments. Using a tight-binding model, we show that the MEE-HB manifests as a fractal energy splitting pattern hosting MEs that separate extended and localized states.","one_line_summary":"Tilt-induced quasiperiodic potentials on square lattices generate a mobility-edge-embedded Hofstadter butterfly with fractal dimension 0.8-1.0, combining fractal spectra from 1D-like behavior with mobility edges from effective long-range hopping.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The tight-binding model and derived Harper-like equation accurately capture the physics without higher-order effects or lattice imperfections dominating, and that the effective long-range hopping is the sole origin of the mobility edges.","pith_extraction_headline":"Aligning a periodic potential at an angle to a square lattice produces a Hofstadter butterfly whose fractal spectrum contains mobility edges separating extended and localized states."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.12472/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}