  We investigate the valley depolarization dynamics and valley Hall effect of
exciton due to the electron-hole exchange interaction in mono- and bilayer
MoS$_2$ by solving the kinetic spin Bloch equations. The effect of the exciton
energy spectra by the electron-hole exchange interaction is explicitly
considered. For the valley depolarization dynamics, in the monolayer MoS$_2$,
it is found that in the strong scattering regime, the conventional motional
narrowing picture is no longer valid, and a novel valley depolarization channel
is opened. For the valley Hall effect of exciton, in both the mono- and bilayer
MoS$_2$, with the exciton equally pumped in the K and K' valleys, the system
can evolve into the equilibrium state where the valley polarization is parallel
to the effective magnetic field due to the exchange interaction. With the drift
of this equilibrium state by applied uniaxial strain, the exchange interaction
can induce the {\it momentum-dependent} valley/photoluminesence polarization,
which leads to the valley/photoluminesence Hall current. Specifically, the
disorder strength dependence of the valley Hall conductivity is revealed. In
the strong scattering regime, the valley Hall conductivity decreases with the
increase of the disorder strength; whereas in the weak scattering regime, it
saturates to a constant, which can be much larger than the one in Fermi system
due to the absence of the Pauli blocking.
