Lightwave topology for strong-field valleytronics

Modern light generation technology offers extraordinary capabilities for sculpting light pulses, with full control over individual electric field oscillations within each laser cycle. These capabilities are at the core of lightwave electronics - the dream of ultrafast lightwave control over electron dynamics in solids, on a few-cycle to sub-cycle timescale, aiming at information processing at tera-Hertz to peta-Hertz rates. Here we show a robust and general approach to valley-selective electron excitations in two-dimensional solids, by controlling the sub-cycle structure of non-resonant driving fields at a few-femtosecond timescale. Bringing the frequency-domain concept of topological Floquet systems to the few-fsec time domain, we develop a transparent control mechanism in real space and an all-optical, non-element-specific method to coherently write, manipulate and read selective valley excitations using fields carried in a wide range of frequencies, on timescales that can be much shorter than the valley lifetime, crucial for implementation of valleytronic devices.