  A two-dimensional honeycomb lattice harbors a pair of inequivalent valleys in
the k-space electronic structure, in the vicinities of the vertices of a
hexagonal Brillouin zone, K}$_{\pm}$. It is particularly appealing to exploit
this emergent degree of freedom of charge carriers, in what is termed
"valleytronics", if charge carrier imbalance between the valleys can be
achieved. The physics of valley polarization will make possible electronic
devices such as valley filter and valley valve, and optoelectronic Hall
devices, all very promising for next-generation electronic and optoelectronic
applications. The key challenge lies with achieving valley imbalance, of which
a convincing demonstration in a two-dimensional honeycomb structure remains
evasive, while there are only a handful of examples for other materials. We
show here, using first principles calculations, that monolayer MoS_2, a novel
two-dimensional semiconductor with a 1.8 eV direct band gap, is an ideal
material for valleytronics by valley- selective circular dichroism, with
ensuing valley polarization and valley Hall effect.
