Emergence and Tuning of Multiple Flat Bands in Twisted Bilayer γ-Graphyne.

Using twisted bilayer γ-graphyne (TBGY) as an example, we show that it is possible to create multiple flat bands in carbon allotropes without the requirement of a specified magic angle. The origin of the flat bands can be understood by a simple two-level coupling model. The narrow bandwidth and strong localization of the flat band states might lead to strong correlation effects, which make TBGY a good platform for studying correlation physics. On the basis of the two-level coupling model, we further propose that the width and extent of localization of flat bands can be tuned by an energy mismatch ΔE between the two layers of TBGY, which can be realized by either applying a perpendicular electric field or introducing a heterostrain. This allows continuous modulation of TBGY from the strong-correlation regime to the medium- or weak-correlation regime, which could be utilized to study the quantum phase transition.