Designing Ultra-flat Bands in Twisted Bilayer Materials at Large Twist Angles: Theory and Application to Two-Dimensional Indium Selenide.

Intertwisted bilayers of two-dimensional (2D) materials can host low-energy flat bands, which offer opportunity to investigate many intriguing physics associated with strong electron correlations. In the existing systems, ultra-flat bands only emerge at very small twist angles less than a few degrees, which poses a challenge for experimental studies and practical applications. Here, we propose a new design principle to achieve low-energy ultra-flat bands with increased twist angles. The key condition is to have a 2D semiconducting material with a large energy difference of band edges controlled by stacking. We show that the interlayer interaction leads to defect-like states under twisting, which forms a flat band in the semiconducting band gap with dispersion strongly suppressed by the large energy barriers in the moiré superlattice even for large twist angles. We explicitly demonstrate our idea in bilayer α-In2Se3 and bilayer InSe. For bilayer α-In2Se3, we show that a twist angle of ∼13.2° is sufficient to achieve the band flatness comparable to that of twist bilayer graphene at the magic angle ∼1.1°. In addition, the appearance of ultra-flat bands here is not sensitive to the twist angle as in bilayer graphene, and it can be further controlled by external gate fields. Our finding provides a new route to achieve ultra-flat bands other than reducing the twist angles and paves the way toward engineering such flat bands in a large family of 2D materials.