  We demonstrate that high-harmonic generation (HHG) in solids dominantly
originates from strongly localized surface states through non-perturbative
processes. Measurements reveal that HHG from bulk states is suppressed by at
least 1-2 orders of magnitude due to the lack of phase matching, when generated
perturbatively, or by at least 3-4 orders of magnitude, when generated
non-perturbatively. We derive a theory that fully supports this observation and
quantitatively describes the generation of harmonics from the surface states as
well as from interfaces between solids; it also predicts a much weaker
generation of harmonics from the bulk states. Our results pave the way for the
development of very high repetition rate high harmonic sources for vacuum
ultraviolet spectroscopy and high precision frequency comb metrology using
surface states from solids.
