Randomly twisted bilayer graphene -- the cascade transitions

TL;DR

This paper models twisted bilayer graphene with disorder as a Dirac equation with a random gauge potential, revealing cascade electronic transitions near the magic angle due to diverging density of states and Coulomb interactions.

Contribution

It introduces a theoretical framework using a Dirac equation with random gauge potential to explain cascade transitions in TBG near the magic angle.

Findings

Density of states diverges at the Dirac point near the magic angle.

All electrons occupy energies very close to zero energy.

Predicted jumps in chemical potential at integer fillings.

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 $\rho(E)\sim E^{(2/z)-1}$ 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 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.