  In this Letter, a tunable valley polarization is investigated for honeycomb
systems with broken inversion symmetry such as transition-metal dichalcogenide
MX2 (M = Mo, W; X = S, Se) monolayers through elliptical pumping. As compared
to circular pumping, elliptical pumping is more universal and effective method
to create coherent valley polarization. When two valleys of MX2 monolayers are
doped or polarized, a novel anomalous valley orbital magnetic moment Hall
effect driven by opposite Berry curvatures at different valleys is predicted
and can generate orbital magnetic moment current without the accompaniment of a
charge current, opening a new avenue for exploration of valleytronics and
orbitronics. Valley orbital magnetic moment Hall effect is expected to obscure
spin Hall effect and is tunable under elliptical pumping.
