Are the surface Fermi arcs in 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 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 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, 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. Of particular interest are 3D semimetals where the bulk electronic dispersion exhibits point nodes at the Fermi level and the low-energy physics are effectively described by a Weyl or Dirac Hamiltonian (9).A striking feature of 3D Weyl semimetals (WSMs), which necessarily break either time-reversal or inversion symmetry, is the existence (5) of topologically protected surface "Fermi arcs." Here the Fermi contour in the surface Brillouin zone breaks up into disconnected pieces, which connect the projection of two Weyl nodes with opposite chirality. The Fermi arcs have been recently observed in angle-resolved photoemission spectroscopy (ARPES) studies of noncentrosymmetric TaAs (10-15).Here we focus on another outstanding example, the Dirac semimetal (DSM), which is the 3D analog of graphene. In the presence of both time-reversal and inversion symmetries, the electronic excitations near each node are described by a four-component Dirac fermion, and a dispersion that is linear in all directions in k space (16)(17)(18). ARPES has clearly observed linearly dispersing bands near Dirac nodes in two DSM materials, Na 3 Bi (19, 20) and Cd 3 As 2 (21-23). The signatures of Fermi arcs by ARPES in Na 3 Bi (24) and by their peculiar quantum oscillations (25) in Cd 3 As 2 (26) have recently been reported. Although DSM can in principle appear in a system with spin rotational symmetry (27), here we focus on DSMs in spinorbit-coupled systems that are more closely related to material realizations.We can understand the Dirac fermions as two degenerate Weyl fermions with opposite chirality, where crystal symmetries forbid the two Weyl nodes from hybridizing and opening up a gap at each Dirac point (16,28). Given this picture of the bulk, it is natural to expect the surface states in a DSM (17, 18) as two copies of the chiral Fermi arc on the WSM surface: i.e., the "double Fermi arcs" shown schematically in Fig. 1A.In thi...

Topological Dirac semimetal phase in Pd and Pt oxides

“…Unlike WSMs, the Fermi arcs in 3D DSMs are not stable against symmetry-allowed perturbations. They can be continuously deformed into other forms without breaking any symmetry [28][29][30]. By further decreasing energy, we indeed observe a Lifshitz transition of the Fermi surface, which is shown on the right hand side of Fig.…”

“…Important questions arise for instances whether different forms of Fermi arcs in 3D DSMs can coexist and how they interact with each other [28][29][30]. To this end, a system with multiple pairs of DPs is urgently needed.…”

Triple Point Topological Metals

“…While the topological protection of the Fermi arcs of Weyl semimetals, in general, do not rely on crystalline symmetries [6], the Fermi arcs of Dirac semimetals are, in general, not protected away from TR symmetric planes k z ¼ 0, π and can be subject to hybridization [49]. Still, in Dirac semimetals Cd 3 As 2 and Na 3 Bi, closed surface Fermi contours, connecting the two DPs, are found both numerically and experimentally [7,10,50].…”

Weyl and Dirac semimetals in three-dimensional solids

“…Theory further suggests that measurement of ARPES intensities from these modes in a nonequilibrium state with applied fields E · B = 0 could be used in principle to visualize an induced chiral current in both the WSM or DSM states 5 (Behrends et al, 2016). Recent work has focused attention on the fragility Fermi arcs on the boundaries of DSMs Kargarian et al, 2016;Potter et al, 2014). The possibility of having double Fermi arcs on a DSM that are pinned to its Dirac nodes is problematic because these nodes are protected only by a bulk spatial (rotational) symmetry 6 .…”