Behavior of localized states in double twisted ABC trilayer graphene

We show that a double -twisted ABC trilayer graphene, formed by stacking two ABC trilayers with a rotation angle between them, is a semiconductor with a gap of about 30 meV. Importantly, flat bands in the electronic structure are observed even for large angles, and the localization of electrons follows the same pattern as in ABC trilayer graphene. Our first -principles calculations show that this behavior holds at least for rotation angles from 7 to 21 degrees. We further study the charge redistribution as a function of the angle. Below two degrees, the charge escapes from the rotated layers and AA zones, moving to the outer layers. This behavior is general for any ABA trilayer with one of the outer layers twisted (ABT). Our findings shed light on some peculiarities of rotated graphene, explaining the absence of a superconductivity phase on these double-trilayer and ABT systems.