The study of solid-state materials out of equilibrium is a highly active
research field in physics, encompassing both theoretical and
experimental approaches. The manipulation of electronic structures
with time-periodic light beams, as described by Floquet theory, gives rise
to exciting phenomena. In this Master’s thesis, we implement Floquet
theory in three materials with distinct electronic properties: Graphene,
known for its Dirac cones with almost linear dispersion; Black
Phosphorous, a semiconductor whose direct band gap size depends on
the sample thickness; and its monolayer version, Phosphorene. Using
numerical techniques, we explore various dynamical and topological
effects, including the occupation of instantaneous Floquet states, the
emergence of Berry curvature from gap openings in the band structure,
and light-induced orbital magnetization of the material. By changing
the physical parameters of the periodic light beam, we can control
these effects on ultrafast timescales. Finally, we propose experimental
techniques that could potentially measure these predicted effects,
providing a pathway for future research.