  For gapped graphene, we predict that an intense ultrashort
(single-oscillation) circularly-polarized optical pulse can induce a large
population of the conduction band and a large valley polarization. With an
increase in the bandgap, the magnitude of the valley polarization gradually
increases from zero (for the native gapless graphene) to a value on the order
of unity. The energy bandwidth of the electrons excited into the conduction
band can be very large ($\gtrsim 10$ eV for a reasonable pulse amplitude of
$\sim 0.5$ $\mathrm{V/\AA}$). These phenomena are due to the effect of
topological resonance: the matching of the topological (geometric) phase and
the dynamic phase. Gapped graphene with tunable bandgap can be used as a
convenient generic model of two-dimensional semiconductors with honeycomb
generic lattice structures and broken inversion symmetry, such as transition
metal dichalcogenides.
