  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.
