  Among topological materials, nodal loop semimetals (NLSMs) are arguably the
most topologically sophisticated, with their valence and conduction bands
intersecting along arbitrarily intertwined nodes. But unlike the well-known
topological band insulators with quantized edge conductivities, nodal loop
materials possess topologically nontrivial Fermi surfaces, not bands. Hence an
important question arises: Are there also directly measurable or even
technologically useful physical properties characterizing nontrivial nodal loop
topology? In this work, we provide an affirmative answer by showing, for the
first time, that nodal linkages protect the higher harmonic generation (HHG) of
electromagnetic signals. Specifically, nodal linkages enforce non-monotonicity
in the intra-band semi-classical response of nodal materials, which will be
robust against perturbations preserving the nodal topology. These
nonlinearities distort incident radiation and produce higher frequency peaks in
the teraHertz (THz) regime, as we quantitatively demonstrate for a few known
nodal materials. Since THz sources are not yet ubiquitous, our new mechanism
for HHG will greatly aid applications like material characterization and
non-ionizing imaging of object interiors.
