In this Letter, terahertz high harmonic generation processes in topological
insulators of the bismuth and antimony chalcogenides family are investigated.
Field conversion efficiencies are determined and clean cubic and quintic
power-law scaling is observed for third and fifth harmonics, up to driving
terahertz fields of 140 kV/cm. This is in contrast to all previous experiments
on terahertz harmonics generation in Dirac materials where a non-perturbative
regime has been observed already at few 10s kV/cm driving fields. Our nonlinear
THz spectroscopy experiments are complemented by THz pump - optical probe
measurements showing distinctly different relaxation dynamics of the carriers
in the topologically-protected Dirac states at the surfaces and the bulk. The
THz-induced dynamics of surface states reveal ultrafast relaxation that
prevents accumulation effects, and results in a clear perturbative regime of
THz harmonics generation that is different to graphene or Dirac semimetals with
their slower relaxation times in the few ps regime