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The breaking of time-reversal symmetry is a crucial ingredient to topologicalbands. It can occur intrisically in materials with magnetic order, or beinduced by external fields, such as magnetic fields in quantum Hall systems, orcircularly polarized light fields in Floquet Chern insulators. Apart frompolarization, photons can carry another degree of freedom, orbital angularmomentum, through which time-reversal symmetry can be broken. In this Letter,we pose the question whether this property allows for inducing topologicalbands via a linearly polarized but twisted light beam. To this end, we study agraphene-like model of electrons on a honeycomb lattice interacting with atwisted light field. To identify topological behavior of the electrons, wecalculate their local markers of Chern number, and monitor the presence ofin-gap edge states. Our results are shown to be fully analogous to the behaviorfound in paradigmatic models for static and driven Chern insulators, andrealizing the state is experimentally straightforward. With this, our workestablishes a new mechanism for generating Fermionic topological phases ofmatter that can harness the central phase singularity of an optical vortexbeam.

Fermionic Chern insulator from twisted light with linear polarization