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Weyl semimetals are known to host massless surface states called Fermi arcs.These Fermi arcs are the manifestation of the bulk-edge correspondence intopological matter and thus are analogous to the topological chiral surfacestates of topological insulators. It has been shown that the latter, dependingon the smoothness of the surface, host massive Volkov-Pankratov(VP) states thatcoexist with the chiral ones. Here, we investigate these VP states in theframework of Weyl semimetals, namely their density of states andmagneto-optical response. We find the selection rules corresponding to opticaltransitions which lead to anisotropic responses to external fields. In thepresence of a magnetic field parallel to the interface, the selection rules andhence the poles of the response functions are mixed.

Dynamical conductivity of the Fermi arc and the Volkov-Pankratov states on the surface of Weyl semimetals