  Inversion symmetry breaking allows contrasted circular dichroism in different
k-space regions, which takes the extreme form of optical selection rules for
interband transitions at high symmetry points. In materials where band-edges
occur at noncentral valleys, this enables valley dependent interplay of
electrons with light of different circular polarizations, in analogy to spin
dependent optical activities in semiconductors. This discovery is in perfect
harmony with the previous finding of valley contrasted Bloch band features of
orbital magnetic moment and Berry curvatures from inversion symmetry breaking
[Phys. Rev. Lett. 99, 236809 (2007)]. A universal connection is revealed
between the k-resolved optical oscillator strength of interband transitions,
the orbital magnetic moment and the Berry curvatures, which also provides a
principle for optical measurement of orbital magnetization and intrinsic
anomalous Hall conductivity in ferromagnetic systems. The general physics is
demonstrated in graphene where inversion symmetry breaking leads to valley
contrasted optical selection rule for interband transitions. We discuss
graphene based valley optoelectronics applications where light polarization
information can be interconverted with electronic information.
