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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 twostrong-field single-optical-cycle pulses: a chiral pump pulse followed within afew femtoseconds by a probe pulse linearly polarized in the armchair directionof the 2D lattice. Due to the effect of topological resonance, the first (pump)pulse induces a large chirality (valley polarization) in the system, while thesecond pulse generates a femtosecond pulse of the anomalous Hall current. Theproposed effect is the fundamentally the fastest all-optical anomalous Halleffect possible in nature. It can be applied to ultrafast all-optical storageand processing of information, both classical and quantum.

Anomalous Ultrafast All-Optical Hall Effect in Gapped Graphene