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We investigate the topological protection of surface states in Weyl andnodal-line semimetals by characterizing them as evanescent states when the bandstructure is extended to complex momenta. We find in this way a sequence ofexceptional points -that is, branch points with zero energy in the complexspectrum- allowing us to identify the set of surface states with complexmomentum 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 theway surface states decay. Type A semimetals have surface states with smallerpenetration length and oscillating decay while type B semimetals have longersimple exponential decays. The difference between both types reflects in theway the branch cuts in the spectrum accommodate in the complex plane. Thestability of the surface states stems in this approach from the complexstructure that develops around the exceptional points, with a topologicalprotection which is based on the fact that the branch cuts cannot be closed bysmall perturbations. We check this property when nodal-line semimetals areplaced under circularly polarized light, where we observe that the exceptionalpoints survive the effect of such a perturbation, though appropriate boundaryconditions for zero-energy surface states cannot be satisfied in general due tothe breakdown of time-reversal invariance by the radiation field.

Topological protection from exceptional points in Weyl and nodal line semimetals