Are the double Fermi arcs of Dirac semimetals topologically protected?

Abstract

Motivated by recent experiments probing anomalous surface states of Dirac semimetals (DSMs) Na${}_3$Bi and Cd${}_3$As${}_2$, 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 in a minimal $4$-band model with a pair of Dirac nodes at $\mathbf{k}=(0,0,\pm Q)$, where gapless states on the side surfaces are protected only near $k_z=0$. 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 Na${}_3$Bi and Cd${}_3$As${}_2$. Generically, the arcs deform into a Fermi pocket, similar to {the surface states of a topological insulator (TI), and this 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 ARPES and quantum oscillation experiments.

Main text of published version, experimental implications are discussed

References in corpus (14)

• Topological Insulators with Inversion Symmetry
• Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs
• Theoretical Discovery/Prediction: Weyl Semimetal states in the TaAs material (TaAs, NbAs, NbP, TaP) class
• Observation of Weyl nodes in TaAs
• Discovery of a Weyl Fermion semimetal state in NbAs
• Classification of stable three-dimensional Dirac semimetals with nontrivial topology
• Two-dimensional Dirac fermions in a topological insulator: transport in the quantum limit
• Topological origin of subgap conductance in insulating bilayer graphene
• Topology of crystalline insulators and superconductors
• Quantum transport evidence for a three-dimensional Dirac semimetal phase in Cd3As2
• Anomalous conductivity tensor in the Dirac semimetal Na_3Bi
• Emergent topological phenomena in thin films of pyrochlore iridates
• Space group constraints on weak indices in topological insulators
• Classification of crystalline topological semimetals with an application to Na${}_3$Bi

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