  Breaking space-time symmetries in two-dimensional crystals (2D) can
dramatically influence their macroscopic electronic properties. Monolayer
transition-metal dichalcogenides (TMDs) are prime examples where the
intrinsically broken crystal inversion symmetry permits the generation of
valley-selective electron populations, even though the two valleys are
energetically degenerate, locked by time-reversal symmetry. Lifting the valley
degeneracy in these materials is of great interest because it would allow for
valley-specific band engineering and offer additional control in valleytronic
applications. While applying a magnetic field should in principle accomplish
this task, experiments to date have observed no valley-selective energy level
shifts in fields accessible in the laboratory. Here we show the first direct
evidence of lifted valley degeneracy in the monolayer TMD WS2. By applying
intense circularly polarized light, which breaks time-reversal symmetry, we
demonstrate that the exciton level in each valley can be selectively tuned by
as much as 18 meV via the optical Stark effect. These results offer a novel way
to control valley degree of freedom, and may provide a means to realize new
valley-selective Floquet topological phases in 2D TMDs.
