  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.
