Generic Coexistence of Fermi Arcs and Dirac Cones on the Surface of Time-Reversal Invariant Weyl Semimetals

The hallmark of Weyl semimetals is the existence of open constant-energy contours on their surface—the so-called Fermi arcs—connecting Weyl points. Here, we show that, for time-reversal symmetric realizations of Weyl semimetals, these Fermi arcs, in many cases, coexist with closed Fermi pockets originating from surface Dirac cones pinned to time-reversal invariant momenta. The existence of Fermi pockets is required for certain Fermi-arc connectivities due to additional restrictions imposed by the six ${\mathbb{Z}}_2$ topological invariants characterizing a generic time-reversal invariant Weyl semimetal. We show that a change of the Fermi-arc connectivity generally leads to a different topology of the surface Fermi surface and identify the half-Heusler compound LaPtBi under in-plane compressive strain as a material that realizes this surface Lifshitz transition. We also discuss universal features of this coexistence in quasiparticle interference spectra.

Figure 1

(a) The BZ of a WSM as a collection of 2D insulators with zero (green) or nonzero (red) Chern numbers. Weyl nodes (blue spheres) separate planes with different Chern numbers. The bold frames indicate the TRI 2D insulators characterized by a ${\mathbb{Z}}_2$ invariant. (b) Typical low-energy surface spectrum of a TRI WSM with an additional surface Dirac cone: surface states are shown in red, whereas the surface projections of the 3D bulk Weyl cones are highlighted in blue. (c)–(d) Fermi arc connectivities in the surface BZ of a TRI WSM with four Weyl points indicated by their topological charge $\pm$. The surface projections of the 3D TRI planes are highlighted by dotted black ($\nu =0$) or dashed green ($\nu =1$) lines.

Figure 2

Fermi surfaces and JDOS for (010) surfaces in the tight-binding model with $a=b=1$, $t=1.5$, $\alpha =0.3$, $d=0.1$, $\lambda =0.5$, and $E_F=0$: (a),(c),(e) the first column shows the Fermi surfaces for different values of the parameter $\beta$. The bulk Weyl nodes are highlighted in blue and their topological charge is indicated. Surface states are highlighted in red. (b),(d),(f) The second column shows the corresponding JDOS spectra. In (f), the kidney-shaped features indicative of the coexistence of Fermi arcs and Dirac cones are clearly visible in the JDOS.

Figure 3

Surface Fermi surfaces of LaPtBi with (001) termination: shown is the surface spectral weight. The positions of the four Weyl-point projections are marked by grey dots. The panels (a)–(c) display the transition between different Fermi-arc connectivities by varying the Fermi level. Note that the connectivity shown in (c) requires the presence of an additional Fermi pocket around the origin which resembles Fig. 2. (d) A further increase of the Fermi level reveals that the Fermi pocket, indeed, originates from a Dirac cone around $\overline{\mathrm{\Gamma }}$.