  We theoretically propose a gigantic orbital Edelstein effect in topological
insulators and interpret the results in terms of topological surface currents.
We numerically calculate the orbital Edelstein effect for a model of a
three-dimensional Chern insulator as an example. Furthermore, we calculate the
orbital Edelstein effect as a surface quantity using a surface Hamiltonian of a
topological insulator, and numerically show that it well describes the results
by direct numerical calculation. We find that the orbital Edelstein effect
depends on the local crystal structure of the surface, which shows that the
orbital Edelstein effect cannot be defined as a bulk quantity. We propose that
Chern insulators and Z_2 topological insulators can be a platform with a large
orbital Edelstein effect because current flows only along the surface. We also
propose candidate topological insulators for this effect. As a result, the
orbital magnetization as a response to the current is much larger in
topological insulators than that in metals by many orders of magnitude.
