  Stacking and twisting atom-thin sheets create superlattice structures with
unique emergent properties, while tailored light fields can manipulate coherent
electron transport on ultrafast timescales. The unification of these two
approaches may lead to ultrafast creation and manipulation of band structure
properties, which is a crucial objective for the advancement of quantum
technology. Here, we address this by demonstrating a tailored lightwave-driven
analogue to twisted layer stacking. This results in sub-femtosecond control of
time-reversal symmetry breaking and thereby band structure engineering in a
hexagonal boron nitride monolayer. The results practically demonstrate the
realization of the topological Haldane model in an insulator. Twisting the
lightwave relative to the lattice orientation enables switching between band
configurations, providing unprecedented control over the magnitude and location
of the band gap, and curvature. A resultant asymmetric population at
complementary quantum valleys lead to a measurable valley Hall current,
detected via optical harmonic polarimetry. The universality and robustness of
the demonstrated sub-femtosecond control opens a new way to band structure
engineering on the fly paving a way towards large-scale ultrafast quantum
devices for real-world applications.
