  We present a low-energy effective-mass theory to describe chiral orbital
current and anomalous magnetic moment in graphenes with band gap and related
materials. We show that a Bloch electron generally contains an anomalous
current density due to inter-band matrix elements, which describes a chiral
current circulation associated with magnetic moment. In gapped graphenes, the
chiral current is opposite between different valleys, and corresponding
magnetic moment accounts for valley splitting of Landau levels. In gapped
bilayer graphene, in particular, the valley-dependent magnetic moment is
responsible for divergence of paramagnetic susceptibility at the band bottom,
and full valley polarization is achieved in relatively small magnetic field
range. The formulation also applies to the gapped surface states of
three-dimensional topological insulator, where the anomalous current is related
to the magneto-electric response in spatially-modulated potential.
