Effects of non-circular Polarization on Vortex-driven Dirac Materials

Within Floquet theory, two-dimensional massive Dirac-like materials exhibit vortex-bound states when irradiated with circularly polarized vortex light beams (VLB). Fermionic states trapped within the vortex possess well-defined angular momentum due to the symmetries present in the system. Their quasienergy spectrum replicates that of superconductors subjected to magnetic flux vortices. Within the one Floquet copy approximation, the spectrum is described by the Caroli-de Gennes Matricon equation [1]. These results were derived from clean systems illuminated by circularly polarized VLBs; however, the impact of deviations from full circular polarization was not considered. We study the effects of non-circular polarization on the quasienergy spectrum. To analyze this effect, we solve a model for a material irradiated with non-circularly polarized light with fixed intensity. To this effect, we introduce an oppositely circularly polarized beam as a perturbation. We demonstrate that for minimally distorted beams, bulk states begin to occupy the energy gap while the vortex states persist. As polarization approaches linearity, the gap further diminishes, leading the material to lose its dynamic insulating properties. For VLBs achieved in laboratory conditions, these deviations are negligible, preserving the gap and the presence of vortex states.