Periodic to quasi-periodic graphene superlattice transition by Fermi velocity modulation

Graphene superlattices have attracted great research interest in the last years, since it is possible to manipulate the electronic properties of graphene in these structures. They can be periodic, quasi-periodic or disordered, each one presenting different electronic properties. In this work we investigate the possibility of transforming a periodic and quasi-periodic graphene superlattice one into another by a Fermi velocity modulation. We analyzed finite and infinite superlattices. We considered an one-dimensional superlattice and show that the transformation can be perfectly done for charge carriers moving in the direction of the superlattice. However, for oblique moving, some features can not be transformed by the Fermi velocity. The results obtained here are relevant for the development of novel graphene-based electronic devices.