Light-Shaping of Valley States.

The established paradigm to create valley states, excitations at local band extrema ("valleys"), is through selective occupation of specific valleys via circularly polarized laser pulses. Here we show a second way exists to create valley states, not by valley population imbalance but by "light-shaping" in momentum space, i.e. controlling the of the distribution of excited charge at each valley. While noncontrasting in valley charge, such valley states are instead characterized by a valley current, identically zero at one valley and finite and large at the other. We demonstrate that these (i) are robust to quantum decoherence, (ii) allow lossless toggling of the valley state with successive femtosecond laser pulses, and (iii) permit valley contrasting excitation both with and without a gap. Our findings open a route to robust ultrafast and switchable valleytronics in a wide scope of 2d materials, bringing closer the promise of valley-based electronics.