Mirror Protected Dirac Fermions on a Weyl Semimetal NbP Surface

The first Weyl semimetal was recently discovered in the NbP class of compounds. Although the topology of these novel materials has been identified, the surface properties are not yet fully understood. By means of scanning tunneling spectroscopy, we find that NbP’s (001) surface hosts a pair of Dirac cones protected by mirror symmetry. Through our high-resolution spectroscopic measurements, we resolve the quantum interference patterns arising from these novel Dirac fermions and reveal their electronic structure, including the linear dispersions. Our data, in agreement with our theoretical calculations, uncover further interesting features of the Weyl semimetal NbP’s already exotic surface. Moreover, we discuss the similarities and distinctions between the Dirac fermions here and those in topological crystalline insulators in terms of symmetry protection and topology.

Figure 1

(a) Illustrations of the two-dimensional Dirac cones (upper panel) and the Fermi surface (lower panel) in the first surface Brillouin zone (BZ) of NbP(001). High symmetry points are marked on the sketches. Red dotted lines are the Fermi-arc-derived surface contours. Dark blue regions are the surface states, which are “’trivial" in the context of Weyl physics, but feature interesting Dirac-cone-type electronic structures. (b) The surface electronic band structure along $\overline{X}\text{−}\overline{M}\text{−}\overline{Y}$. Two bands cross each other and form a Dirac node, indicated by the arrow. (c) A constant-current STM image on our high-quality NbP crystal’s (001) surface, showing the atomically ordered lattice with only one point defect in the $7.7\times 7.7{\mathrm{nm}}^2$ area. (d) A typical $dI/dV$ spectrum on NbP(001) surface far from defects.

Figure 2

(a) A Fourier-transformed $dI/dV$ map (50 mV) representing the QPI pattern on the NbP(001) surface. The four Bragg points are indicated by $B$. (b),(c) Energy-resolved QPI features along orthogonal directions taken along the purple and yellow dashed lines in (a), respectively. A Dirac-cone-shaped feature can be seen inside the white dashed rectangle. White lines in (c) serve as guides to the eye for the Dirac cones. (d) A series of QPI patterns at indicated energies, clipped from the white dashed rectangle in (a). Arrows indicate the positions of Dirac nodes.

Figure 3

(a) The theoretically calculated CEC at 250 meV above the Fermi level. High symmetry points in the first Brillouin zone are marked. The positions of the Dirac cones are indicated by the arrows. (b) A zoomed-in view of the area marked by the rectangle in (a), where a pair of Dirac cones are visible. A dominant scattering vector $Q$ links the two Dirac contours. (c) A numerically simulated QPI pattern at the same energy as (a). (d) The zoomed-in view of the central region of (c), indicated by a red rectangle. (e) The experimentally acquired QPI pattern. Its main features are well reproduced by our simulation in (d). The scattering vector $Q$ in (d) and (e) are same as in (b).