Sub-cycle valleytronics: control of valley polarization using few-cycle linearly polarized pulses

So far, selective excitation of a desired valley in the Brillouin zone of a hexagonal two-dimensional material has relied on using circularly polarized fields. We theoretically demonstrate a way to induce, control, and read valley polarization in hexagonal 2D materials on a few-femtosecond timescale using a few-cycle, linearly polarized pulse with controlled carrier-envelope phase. The valley pseudospin is encoded in the helicity of the emitted high harmonics of the driving pulse, allowing one to avoid additional probe pulses and permitting one to induce, manipulate and read the valley pseudospin all-optically, in one step. High circularity of the harmonic emission offers a method to generate highly elliptic attosecond pulses with a linearly polarized driver, in an all-solid-state setup.