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We theoretically study the topological robustness of the surface physicsinduced by Weyl Fermi-arc surface states in the presence of short-rangedquenched disorder and surface-bulk hybridization. This is investigated withnumerically exact calculations on a lattice model exhibiting Weyl Fermi-arcs.We find that the Fermi-arc surface states, in addition to having a finitelifetime from disorder broadening, hybridize with nonperturbative bulk rarestates making them no longer bound to the surface (i.e. they lose their purelysurface spectral character). Thus, we provide strong numerical evidence thatthe Weyl Fermi-arcs are not topologically protected from disorder. Nonetheless,the surface chiral velocity is robust and survives in the presence of strongdisorder, persisting all the way to the Anderson-localized phase by forminglocalized current loops that live within the localization length of thesurface. Thus, the Weyl semimetal is not topologically robust to the presenceof disorder, but the surface chiral velocity is.

Do the surface Fermi arcs in Weyl semimetals survive disorder?