Optical control of the valley Zeeman effect through many-exciton interactions

Charge carriers in two-dimensional transition metal dichalcogenides (TMDs), such as WSe$_2$, have their spin and valley-pseudospin locked into an optically-addressable index that is proposed as a basis for future information processing. The manipulation of this spin-valley index requires tuning its energy, typically through external magnetic field (B), which is cumbersome. Thus, other efficient routes like all-optical control of spin-valley index are desirable. Here, we show that many-body interactions amongst interlayer excitons in WSe$_2$/MoSe$_2$ heterobilayer induce a steady-state valley Zeeman splitting corresponding to B $\sim$ 6 Tesla. This anomalous splitting, present at incident powers as low as $\mu$Ws, increases with power and enhances, suppresses or even flips the sign of a B-induced splitting. Moreover, the $\it{g}$-factor of valley Zeeman splitting can be tuned by $\sim$ 30 $\%$ with incident power. In addition to valleytronics, our results are relevant for achieving optical non-reciprocity using two-dimensional materials.