Effects of Non-Circular Polarization on Vortex-driven 2D Dirac Materials

In previous studies, it was discovered that two-dimensional materials hosting massive Dirac-like fermions exhibit behavior similar to superconductors when subjected to a circularly polarized vortex light beam, creating an l-flux-quanta vortex. In this scenario, fermionic states become trapped within the vortex, possessing well-defined angular momentum, and the energy spectrum adheres to the Caroli-de Gennes relation [1]. These results were derived under the assumption of clean systems illuminated by circularly polarized light. However, the impact of deviations from full circular polarization, as well as the presence of impurities, has yet to be explored [2]. This presentation will focus on how deviations from full circular polarization influence the energy spectrum. To analyze this effect, we introduce an oppositely circularly polarized beam as a perturbation. While the first-order energy corrections vanish, the second-order corrections introduce selection rules with non-trivial coupling between states. We demonstrate that for minimally distorted beams, bulk states begin to occupy the energy gap while the vortex states persist. As the polarization approaches linearity, the gap further diminishes, leading the material to lose its insulating properties. In this regime, it is impossible to distinguish vortex states from the background.