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 $\mathrm{\Gamma }$ 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.