Do the Fermi arcs in Weyl systems survive disorder?

Weyl semimetals exhibit topological surface states due to nodes in their Brillouin zone, but the semimetallic phase does not survive nonperturbative disorder effects. We, therefore, study the effect of quenched disorder on the surface states, finding evidence of surface-bulk hybridization. But the key question here is the topological robustness of the surface chiral properties in the presence of short-ranged disorder. We investigate this with numerically exact calculations on a lattice model exhibiting Weyl Fermi arcs on its surface. We find that the Fermi arc surface states, in addition to having a finite lifetime from disorder broadening, hybridize with nonperturbative bulk rare states giving them finite spectral weight in the bulk and making them no longer exponentially bound to the surface (i.e. they lose their purely surface spectral character). Thus, we provide strong numerical evidence that the Weyl Fermi arcs are not topologically protected from disorder. Nonetheless, the surface chiral velocity is robust and survives in the presence of strong disorder, persisting all the way to the Anderson localized phase by forming local current loops into the bulk that live within the localization length of the surface.