  High-harmonic generation (HHG) in the two topological phases of a finite,
one-dimensional, periodic structure is investigated using a self-consistent
time-dependent density functional theory (TDDFT) approach. For harmonic photon
energies smaller than the band gap, the harmonic yield is found to differ up to
fourteen orders of magnitude for the two topological phases. This giant
topological effect is explained by the degree of destructive interference in
the harmonic emission of all valence-band (and edge-state) electrons, which
strongly depends on whether topological edge states are present or not. The
combination of strong-field laser physics with topological condensed matter
opens up new possibilities to electronically control strong-field-based light
or particle sources or---vice versa---to steer by all optical means topological
electronics.
