Electron backscattering is introduced as mechanism to enhance high-harmonic generation in solid-state like systems with broken translational symmetry. As a paradigmatic example we derive for a finite chain of $N$ atoms the harmonic cut-off through backscattering of electrons in the conduction band from the edges of the chain. We also demonstrate a maximum in the yield of the high harmonics from the conduction band if twice the quiver amplitude of the driven electrons equals the length of the chain. High-harmonic spectra as a function of photon energy are shown to be equivalent if the ratio of chain length to the wavelength of the light is kept constant. Our quantum results are corroborated by a (semi-)classical trajectory model with refined spatial properties required to describe dynamics with trajectories in the presence of broken translational symmetry.
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