Crossed Surface Flat Bands of Weyl Semimetal Superconductors

It has been noted that certain surfaces of Weyl semimetals have bound states forming open Fermi arcs, which are never seen in typical metallic states. We show that the Fermi arcs enable them to support an even more exotic surface state with crossed flat bands in the superconducting state. We clarify the topological origin of the crossed flat bands and the relevant symmetry that stabilizes the cross point. Our symmetry analysis is applicable to known candidate materials of time-reversal breaking Weyl semimetals. We also discuss their possible experimental verification by tunneling spectroscopy.

Figure 1

Schematic illustration of surface flat bands in the surface Brillouin zone of doped superconducting WSMs (a) with and (b) without magnetic mirror reflection symmetry, and (c) that in ${}^3\mathrm{He}\text{−}A$ phase. Crossed flat bands (a) occur with magnetic mirror reflection symmetry. The shaded circle (dots) indicates the Fermi surface (point nodes) projected on the surface BZ. The inserted signs at point nodes correspond to the signs of monopole charge. Arrow lines show the topological flows and are regarded as the zero energy flat bands. Red (green) color represents the zero energy Andreev bound state (Fermi arc). Simultaneously, the directions of the arrows show the chirality of the surface states: The zero energy flat band depicted by upward (downward) arrow has positive (negative) group velocity along the ${\overline{k}}_y$ axis.

Figure 2

(a) Energy dispersion $E({\overline{k}}_y,{\overline{k}}_z)$ of SABSs inside the projected Fermi surface near $(0,0,Q)$. (b) Quasiparticle spectra function at zero energy. Dashed line denotes the projected Fermi surface. $t=t_z=1$, $Q=\pi /2$, $\mu =0.3$, $\mathrm{\Delta }=0.001$, and $m=0.8$ are chosen for both (a) and (b).

Figure 3

(a) Projection of Fermi surfaces (dark region) on ${\overline{k}}_y-{\overline{k}}_z$ surface BZ and Chern number at a given $k_z$ in the BZ. The Chern number $C_1(k_z)$ changes when $k_z$ crosses a plane including a point node (red cross). The amount of change is given by the monopole charge of the point node. (b) Flat bands of SABSs and Fermi arcs (lines with arrows) in the surface BZ.

Figure 4

Normalized tunneling conductance as a function of bias voltage $(eV/\mathrm{\Delta })$ for $m$ equal to (a) 0.8 and (b) 0.2. (c) Relation between height of normalized ZBCP and $\chi$. Other parameters are as the same as in Fig. 2.