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

Macroscopic degeneracy of zero-mode rotating surface states in 3D Dirac and Weyl semimetals under radiation