  The breaking of time-reversal symmetry is a crucial ingredient to topological
bands. It can occur intrisically 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 whether this property allows for inducing topological
bands via a linearly polarized but twisted light beam. To this end, we study a
graphene-like model of electrons on a honeycomb lattice interacting with a
twisted light field. To identify 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 new mechanism for generating Fermionic topological phases of
matter that can harness the central phase singularity of an optical vortex
beam.
