{"paper":{"title":"Randomly twisted bilayer graphene -- the cascade transitions","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cond-mat.dis-nn"],"primary_cat":"cond-mat.mes-hall","authors_text":"Baruch Horovitz, Pierre Le Doussal","submitted_at":"2025-08-09T15:42:27Z","abstract_excerpt":"Twisted bilayer graphene (TBG) is known to have disorder in its twist angle. We show that in terms of a Dirac equation with a random gauge potential ${\\bf A}({\\bf r})$ this disorder becomes huge when the average twist angle is near the magic angle where the Dirac velocity vanishes. The density of states (DOS) then diverges at the Dirac point as $\\rho(E)\\sim E^{(2/z)-1}$ with $z\\gg 1$ and we deduce that all electrons occupy energies very near $E=0$. We prove a sum rule on the disorder averaged eigenfunctions from which we deduce that each added electron contributes equal intraband Coulomb inter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.07024","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.07024/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"}