  We investigate the development of novel surface states when 3D Dirac or Weyl
semimetals are placed under circularly polarized electromagnetic radiation. We
find that the hybridization between inverted Floquet bands opens in general a
gap, which closes at so-called exceptional points found for complex values of
the momentum. This corresponds to the appearance of midgap surface states in
the form of evanescent waves decaying from the surface exposed to the
radiation. We observe a phenomenon reminiscent of Landau quantization by which
the midgap surface states get a large degeneracy proportional to the radiation
flux traversing the surface of the semimetal. We show that all these surface
states carry angular current, leading to an angular modulation of their charge
that rotates with the same frequency of the radiation, which should manifest in
the observation of a macroscopic chiral current in the irradiated surface.
