  We report the observation of second harmonic generation with high conversion
efficiency $\sim 0.005\%$ in the terahertz regime from thin films of the
topological insulator Bi$_2$Se$_3$ that exhibit the linear photogalvanic
effect, measured via time-domain terahertz spectroscopy and terahertz emission,
respectively. As neither phenomena is observable from topologically trivial
In-doped Bi$_2$Se$_3$, and since no enhancement is observed when subject to
band bending, the efficient thickness-independent nonliear responses are
attributable to the Dirac fermions of topological surface states of
Bi$_2$Se$_3$. This observation of intrinsic terahertz second harmonic
generation in an equilibrium system unlocks the full suite of both even and odd
harmonic orders in the terahertz regime and opens new pathways to probing
quantum geometry via intraband nonlinear processes. We hope our work will
motivate the theoretical development of a full treatment of second harmonic
generation for probing the quantum geometry in various inversion-breaking
topological and twisted materials.
