Twisted graphene bilayer around the first magic angle engineered by heterostrain

Abstract

Very recently, twisted graphene bilayers (TGBs) around the first magic angle $\ensuremath{\theta}\ensuremath{\approx}1.{1}^{\ensuremath{\circ}}$ have attracted much attention for the realization of exotic quantum states, such as correlated insulator behavior and unconventional superconductivity. Here we elaborately study a series of TGBs around the first magic angle engineered by heterostrain, where each layer is strained independently. Our experiment indicates that a moderate heterostrain enables the structural evolution from the small-angle TGB (\ensuremath{\theta} \ensuremath{\sim} 1.5\ifmmode^\circ\else\textdegree\fi{}) to the strained magic-angle TGB (\ensuremath{\theta} \ensuremath{\sim} 1.1\ifmmode^\circ\else\textdegree\fi{}), exhibiting the characteristic low-energy flat bands. The heterostrain can even drive the system into highly strained tiny-angle TGBs (\ensuremath{\theta}$\ensuremath{\ll}1.1$\ifmmode^\circ\else\textdegree\fi{}) with large deformed tetragonal superlattices, where a unique network of topological helical edge states emerges. Furthermore, the predicted domain wall modes, which are strongly localized and result in a hexagon-triangle-mixed frustrated lattice derived from the Kagome lattice, are observed in the strained tiny-angle TGBs.