Electronic properties of graphene multilayers systems and behavior of localized states in twisted double ABC trilayer graphene

Abstract

Interlayer rotation and stacking between the layers in two-dimensional atomic materials generates diverse properties and correlated phenomena. This work shows that by stacking two ABC trilayers with a rotation angle between them, transforms the system into a semiconductor with a gap about 30 meV. Flat bands persist even for large angles and the localization of electrons follows the same pattern as on tri layer ABC. A tight-binding model reveals the charge redistribution in the layers as a function of the angle. Below two degrees of rotation, the charge escapes from the rotated layers and AA zones and goes to the outer layers; this is a general trend for any trilayer ABA with one of the outer layers rotated. We explain this behav ior with a simple toy model. Our findings shed light on some peculiarities of tri layer graphene and contribute to understanding correlated phenomena in graphene multilayers. This study advances knowledge on rotation, stacking, and electronic properties of two dimensional systems, paving the way for future applications.