Multiple tunable real-space degeneracies in graphene irradiated by twisted light

We report the theoretical discovery of multiple real-space degenerate Floquet-Bloch states in monolayer graphene coherently driven by twisted circularly polarized light. Using Floquet theory, we characterize the real-space structure of quasienergies and Floquet modes in terms of the orbital angular momentum and radial vortex profile of light. We obtain the effective real-space Floquet Hamiltonian and show it supports crossings of Floquet modes, especially at high-symmetry K and Γ points of graphene, localized at rings around the vortex center. At specific frequencies, the vortex bound states form a multiply degenerate structure in real space. This structure is purely dynamically generated and controlled by the frequency and tuned by the intensity of twisted light. We discuss the experimental feasibility of observing and employing multiple real-space degeneracies for coherent optoelectronic quantum state engineering.