  We investigate the topological protection of surface states in Weyl and
nodal-line semimetals by characterizing them as evanescent states when the band
structure is extended to complex momenta. We find in this way a sequence of
exceptional points -that is, branch points with zero energy in the complex
spectrum- allowing us to identify the set of surface states with complex
momentum signaling the decay into the 3D semimetal. From this point of view,
Weyl and nodal-line semimetals can be classified in two types depending on the
way surface states decay. Type A semimetals have surface states with smaller
penetration length and oscillating decay while type B semimetals have longer
simple exponential decays. The difference between both types reflects in the
way the branch cuts in the spectrum accommodate in the complex plane. The
stability of the surface states stems in this approach from the complex
structure that develops around the exceptional points, with a topological
protection which is based on the fact that the branch cuts cannot be closed by
small perturbations. We check this property when nodal-line semimetals are
placed under circularly polarized light, where we observe that the exceptional
points survive the effect of such a perturbation, though appropriate boundary
conditions for zero-energy surface states cannot be satisfied in general due to
the breakdown of time-reversal invariance by the radiation field.
