Magic-angle helical trilayer graphene

Abstract

We propose helical trilayer graphene (HTG), a helical structure featuring identical rotation angles $\hat{I}¸\approx 1.5^{\circ }$ between three consecutive layers of graphene, as a unique and experimentally accessible platform for realizing exotic correlated topological states of matter. While nominally forming a supermoiré (or moiré-of-moiré) structure, we show that HTG locally relaxes into large regions of a periodic single-moiré structure in which $C_{2z}$ is broken, giving rise to flat topological bands carrying valley-Chern numbers $C=\pm (1,-2)$. These bands feature near-ideal quantum geometry and are isolated from remote bands by a large gap $E_{\mathrm{gap}}\sim 100$ meV, making HTG a promising platform for experimental realization of correlated topological states such as integer and fractional quantum anomalous Hall states in $C=1$ and $2$ bands.