Floquet engineering the band structure of materials with optimal control theory
We demonstrate that the electronic structure of a material can be deformed into Floquet pseudo-bands with arbitrarily tailored shapes. We achieve this goal with a novel combination of quantum optimal control theory and Floquet engineering. The power and versatility of this framework is demonstrated here by utilizing the independent-electron tight-binding description of the $\pi$ electronic system of graphene. We show several prototype examples focusing on the region around the K (Dirac) point of the Brillouin zone: creation of a gap with opposing flat valence and conduction bands, creation of a gap with opposing concave symmetric valence and conduction bands -- which would correspond to a m…
Floquet engineering with quantum optimal control theory
Abstract Floquet engineering consists in the modification of physical systems by the application of periodic time-dependent perturbations. The search for the shape of the periodic perturbation that best modifies the properties of a system in order to achieve some predefined metastable target behavior can be formulated as an optimal control problem. We discuss several ways to formulate and solve this problem. We present, as examples, some applications in the context of material science, although the methods discussed here are valid for any quantum system (from molecules and nanostructures to extended periodic and non periodic quantum materials). In particular, we show how one can achieve the…