Femtosecond valley polarization and topological resonances in transition metal dichalcogenides

We theoretically introduce the fundamentally fastest induction of a significant population and valley polarization in a monolayer of a transition metal dichalcogenide (i.e., $\mathrm{MoS_2}$ and $\mathrm{WS_2}$). This may be extended to other two-dimensional materials with the same symmetry. This valley polarization can be written and read-out by a pulse consisting of just a single optical oscillation with a duration of a few femtoseconds and an amplitude of $\sim0.2~\mathrm V/\mathrm{\AA}$. Under these conditions, we predict a new effect of {\em topological resonance}, which is due to Bloch motion of electrons in the reciprocal space where electron population textures are formed defined by non-Abelian Berry curvature. The predicted phenomena can be applied for information storage and processing in PHz-band optoelectronics.