  We report systematic theoretical studies of the inverse Faraday effect in
materials with massless Dirac fermions, both in two dimensions such as graphene
and surface states in topological insulators, and in three dimensions such as
Dirac and Weyl semimetals. Both semiclassical and quantum theories are
presented, with dissipation and finite size effects included. We find that the
magnitude of the effect can be much stronger in Dirac materials as compared to
conventional semiconductors. Analytic expressions for the optically induced
magnetization in the low temperature limit are obtained. Strong inverse Faraday
effect in Dirac materials can be used for the optical control of magnetization,
all-optical modulation, and optical isolation.
