Are the surface Fermi arcs in Dirac semimetals topologically protected?
Significance In recent years there has been a surge of interest in quantum materials with topologically protected properties that are robust against the effects of disorder and other perturbations. An interesting example is the newly discovered three dimensional analog of graphene, called Dirac semimetals. These were expected to have highly unusual conducting states on their surfaces. We show here that the surface states of Dirac semimetals do not exhibit the expected topological robustness and, quite generally, get deformed into states that are of a rather different character. Our theoretical results not only have conceptual importance in the field of topological quantum materials but also make clear predictions that can be tested in several experiments. Motivated by recent experiments probing anomalous surface states of Dirac semimetals (DSMs) Na3Bi and Cd3As2, we raise the question posed in the title. We find that, in marked contrast to Weyl semimetals, the gapless surface states of DSMs are not topologically protected in general, except on time reversal invariant planes of surface Brillouin zone. We first demonstrate this finding in a minimal four band model with a pair of Dirac nodes at k=(0,0, Q) where gapless states on the side surfaces are protected only near kz=0. We then validate our conclusions about the absence of a topological invariant protecting double Fermi arcs in DSMs, using a K theory analysis for space groups of Na3Bi and Cd3As2. Generically, the arcs deform into a Fermi pocket, similar to the surface states of a topological insulator, and this pocket can merge into the projection of bulk Dirac Fermi surfaces as the chemical potential is varied. We make sharp predictions for the doping dependence of the surface states of a DSM that can be tested by angle resolved photoemission spectroscopy and quantum oscillation experiments.
Proceedings of the National Academy of Sciences