Floquet Engineering of Dirac Cones

The use of periodic drivings to achieve greater control of quantum states is becoming more and more relevant. Indeed, it provides with a level of tunability that is far beyond the limits of the static case. In this thesis, we propose to apply external ac fields to a topological boundary and graphene. Although such scenarios have already been discussed in the literature by using surface effective Hamiltonians and perturbation theory, we show that even with the bulk states the Dirac cones in the quasienergy spectrum remain robust. Moreover, features from the static regime are also observed in this case, with the extra handle of polarization. In particular, a change in the slope of the cones is observed.