We propose an ultrafast all-optical anomalous Hall effect in two-dimensional (2D) semiconductors of hexagonal symmetry such as gapped graphene (GG), transition metal dichalcogenides (TMDCs), and hexagonal boron nitride (h-BN). To induce such an effect, the material is subjected to a sequence of two strong-field single-optical-cycle pulses: a chiral pump pulse followed within a few femtoseconds by a probe pulse linearly polarized in the armchair direction of the 2D lattice. Due to the effect of topological resonance, the first (pump) pulse induces a large chirality (valley polarization) in the system, while the second pulse generates a femtosecond pulse of the anomalous Hall current. The proposed effect is the fundamentally the fastest all-optical anomalous Hall effect possible in nature. It can be applied to ultrafast all-optical storage and processing of information, both classical and quantum.
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