  Inter-twisted 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 challenge for experimental study 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 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 moire
superlattice even for large twist angles. We explicitly demonstrate our idea in
bilayer alpha-In2Se3 and bilayer InSe. For bilayer alpha-In2Se3, we show that a
twist angle -13.2 degree is sufficient to achieve the band flatness comparable
to that of twist bilayer graphene at the magic angle -1.1 degree. 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 towards engineering such flat bands
in a large family of 2D materials.
