Year: 2026
Type: article
Abstract: 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 $ρ(E)\sim E^{(2/z)-1}$ 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 interaction energy. The various bands in TBG are related by either ${\bf A}({\bf r})\rightarrow {\bf A}({-\bf r})$ or ${\bf A}({\bf r})\rightarrow -{\bf A}({\bf r})$ which affects the interband interaction energy. We find, within Hartree-Fock, jumps in the chemical potential at each integer filling, accounting for the cascade transitions.
DOI: 10.1103/c6rt-6qg1
Authors: Baruch Horovitz, Pierre Le Doussal
Language: English
Subfield: Materials Chemistry
Field: Materials Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416181025