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We investigate the valley depolarization due to the electron-hole exchangeinteraction in monolayer MoS$_{2}$. Both the long- and short-range parts of theintra- and inter-valley electron-hole exchange interactions are calculated. Wefind that both the long- and short-range exchange interactions can cause theinter- and intra-valley bright exciton transitions. With the intra-valleybright exciton transition channel nearly forbidden due to the large splittingof the valence bands, the inter-valley channel due to the exchange interactioncan cause the valley depolarization efficiently by the Maialle-Silva-Shammechanism [Phys. Rev. B {\bf 47}, 15776 (1993)]. With only the long-rangeexchange interaction, the calculations show good agreement with the recentvalley polarization experiments, including the time-resolved valleypolarization measurement, the pump-probe experiment and the steady-state PLpolarization measurement. We further show that for the A-exciton with large(small) center-of-mass momentum, the long-range exchange interaction can causethe {\em fast} ({\em slow}) inter-valley exciton transition.

Valley depolarization due to inter- and intra-valley electron-hole exchange interactions in monolayer MoS$_{2}$