  Motivated by recent experimental demonstrations of Floquet topological
insulators, there have been several theoretical proposals for using structured
light, either spatial or spectral, to create other properties such as flat band
and vortex states. In particular, the generation of vortex states in a massive
Dirac fermion insulator irradiated by light carrying nonzero orbital angular
momentum (OAM) has been proposed [Kim et al. Phys. Rev. B 105, L081301(2022)].
Here, we evaluate the orbital magnetization and optical conductivity as
physical observables for such a system. We show that the OAM of light induces
nonzero orbital magnetization and current density. The orbital magnetization
density increases linearly as a function of OAM degree. In certain regimes, we
find that orbital magnetization density is independent of the system size,
width, and Rabi frequency of light. It is shown that the orbital magnetization
arising from our Floquet theory is large and can be probed by magnetometry
measurements. Furthermore, we study the optical conductivity for various types
of electron transitions between different states such as vortex, edge, and bulk
that are present in the system. Based on conductance frequency peaks, a scheme
for the detection of vortex states is proposed.
