Deformation and stability of surface states in Dirac semimetals

The unusual surface states of topological semimetals have attracted a lot of attention. Recently, we showed [Proc. Natl. Acad. Sci. USA 113, 8648 (2016)] that for a Dirac semimetal (DSM) arising from band inversion, such as Na₃Bi and Cd₃As₂, the expected double Fermi arcs on the surface are not topologically protected. Quite generally, the arcs deform into states similar to those on the surface of a strong topological insulator. Here we address two questions related to deformation and stability of surface states in DSMs. First, we discuss why certain perturbations, no matter how large, are unable to destroy the double Fermi arcs. We show that this is related to a certain extra (particle-hole) symmetry, which is nongeneric in materials. Second, we discuss situations in which the surface states are completely destroyed without breaking any symmetry or impacting the bulk Dirac nodes. We are not aware of any experimental or density functional theory (DFT) candidates for a material which is a bulk DSM without any surface states, but our results clearly show that this is possible.