The breaking of time-reversal symmetry is a crucial ingredient to topological bands. It can occur intrinsically in materials with magnetic order, or be induced by external fields, such as magnetic fields in quantum Hall systems or circularly polarized light fields in Floquet Chern insulators. Apart from polarization, photons can carry another degree of freedom, orbital angular momentum, through which time-reversal symmetry can be broken. In this Letter we pose the question of whether this property allows for inducing topological bands via a linearly polarized but twisted light beam. To this end we study a graphenelike model of electrons on a honeycomb lattice interacting with a twisted light field. To identify the topological behavior of the electrons, we calculate their local markers of Chern number and monitor the presence of in-gap edge states. Our results are shown to be fully analogous to the behavior found in paradigmatic models for static and driven Chern insulators, and realizing the state is experimentally straightforward. With this, our work establishes a mechanism for generating fermionic topological phases of matter that can harness the central phase singularity of an optical vortex beam.

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• Angular momentum of light
• Chern insulators
• Optical vortices
• Quantum simulation
• Floquet systems