Twisted double-layer graphene

Crystalline multilayer graphene systems have received much attention over the past few years due to their versatile electronic band structures and due to their potential use in applications. In marked contrast, non-crystalline systems have so far defied a thorough theoretical understanding. Misalignments between adjacent layers are abundant in graphene grown epitaxially on SiC and often appear in exfoliated samples. Understanding the electronic structure of these twisted systems is therefore not only a conceptual challenge but also of prime importance for applications.

In this talk I will formulate a simple framework for describing the electronic structure of twisted multilayer graphene, focusing on the double-layer system. The notion of energy bands will be extended to these non-crystalline structures.
I will explain why for some twist angles the layers are strongly coupled while for other angles the layers are electronically isolated despite the fact that they are but a fraction of a nanometer apart.
The Dirac  velocity is found to oscillate as the twist angle is reduced. For a discrete set of magic angles the velocity vanishes, the lowest energy band flattens, and the Dirac-point density-of-states and the counterflow conductivity are strongly enhanced.