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Stacking and twisting atom-thin sheets create superlattice structures withunique emergent properties, while tailored light fields can manipulate coherentelectron transport on ultrafast timescales. The unification of these twoapproaches may lead to ultrafast creation and manipulation of band structureproperties, which is a crucial objective for the advancement of quantumtechnology. Here, we address this by demonstrating a tailored lightwave-drivenanalogue to twisted layer stacking. This results in sub-femtosecond control oftime-reversal symmetry breaking and thereby band structure engineering in ahexagonal boron nitride monolayer. The results practically demonstrate therealization of the topological Haldane model in an insulator. Twisting thelightwave relative to the lattice orientation enables switching between bandconfigurations, providing unprecedented control over the magnitude and locationof the band gap, and curvature. A resultant asymmetric population atcomplementary quantum valleys lead to a measurable valley Hall current,detected via optical harmonic polarimetry. The universality and robustness ofthe demonstrated sub-femtosecond control opens a new way to band structureengineering on the fly paving a way towards large-scale ultrafast quantumdevices for real-world applications.

Lightwave-controlled band engineering in quantum materials