  Twisted Bilayer Graphene at the magic twist angle features flat energy bands,
which lead to superconductivity and strong correlation physics. These unique
properties are typically limited to a narrow range of twist angles around the
magic angle with a small allowed tolerance. Here we report on a mechanism that
enables flattening of the band-structure using coherent optical illumination,
leading to emergence of flat isolated Floquet-Bloch bands. We show that the
effect can be realized with relatively weak optical beams at the
visible-infrared range (below the material bandwidth) and persist for a wide
range of small twist angles, increasing the allowed twist tolerance by an order
of magnitude. We discuss the conditions under which these bands exhibit a
non-zero Chern number. These optically induced flat bands could potentially
host strongly-correlated, non-equilibrium electronic states of matter.
