Reshaping of Dirac cones by Floquet engineering

Dirac cones seem to be ubiquitous to nontrivial materials, such as topological insulators and graphene. Manipulating the aforementioned Dirac cones is expected to have consequences on the quantum transport properties of these materials. In this work, we propose to Floquet-engineer Dirac cones at the surface of a three-dimensional topological insulator, as well as in graphene. We show that a large tunability of the Fermi velocity can be achieved, as a function of the polarization, direction and amplitude of the driving field. Using this external control, the Dirac cones in the quasienergy spectrum may become elliptic or massive, in accordance to experiments done in these materials. These results help us to understand the interplay of surface states and external ac driving fields in topological insulators.