Bulk Dirac cone and highly anisotropic electronic structure of $\mathrm{Ni}{\mathrm{Te}}_2$

Transition-metal dichalcogenides (TMDCs) hosting type-II Dirac fermions have attracted a great deal of research interest owing to their rich application capabilities. Here, we have systematically investigated the bulk and surface electronic structures of type-II Dirac semimetal $\mathrm{Ni}{\mathrm{Te}}_2$ by means of angle-resolved photoelectron spectroscopy (ARPES) combined with first-principles calculations. As a result, a bulk Dirac point located 150 meV below the Fermi energy is directly observed by using bulk-sensitive soft x-ray ARPES. Moreover, the measured Fermi surfaces of $\mathrm{Ni}{\mathrm{Te}}_2$ are found to be strongly anisotropic. The first-principles calculations, which match remarkably well with the experimental results, show that the energy position of the Dirac point crucially depends on a small variation of the structural parameters. Our work establishes $\mathrm{Ni}{\mathrm{Te}}_2$ as an ideal platform for further investigating the anisotropic magnetotransport associated with type-II Dirac fermions in TMDCs and paves the way for prospective applications.

Figure 1

Top (a) and side (b) views of the crystal structure of $\mathrm{Ni}{\mathrm{Te}}_2$. Green and yellow balls represent Ni and Te atoms, respectively. (c) Bulk and (001) surface Brillouin zone. The high-symmetry points of the BZ are marked with black dots, and the red dots indicate the bulk Dirac point position. (d) Calculated bulk band structure of $\mathrm{Ni}{\mathrm{Te}}_2$ with two different lattice parameters. Red and blue arrows denote the Dirac point positions with an experimental [16] and relaxed lattice parameter, respectively.

Figure 2

(a) and (b) $k_x–k_z$ and $k_y–k_z$ Fermi surface maps of $\mathrm{Ni}{\mathrm{Te}}_2$ along the $K$-Γ-$K$ and $M$–Γ–$M$ lines taken with photon energies ranging from 420 to 508 eV and 376 to 542 eV, respectively. The $k_z$ values are estimated by free-electron final-state models; the high-symmetry points as well as Dirac point positions are marked with purple, blue, and green dashed lines. Black dashed lines in (b) are included as guides for the eye. (c), (d) Calculated Fermi surface cuts in $k_x–k_z$ and $k_y–k_z$ planes corresponding to (a) and (b), respectively. Different color shows the different bulk band structure [see Fig. S2(a)]. (e)–(n) Photon energy-dependent band dispersions of $\mathrm{Ni}{\mathrm{Te}}_2$ along the $K$–Γ–$K$ line. The corresponding $k_z$ values are labeled in each panel, and $c^{*}=2\pi /c$. The two bands which form a type-II Dirac point are highlighted by red arrows (e); the red dashed lines in (m) are included as guides for the eye.

Figure 3

Calculated in-plane ($k_x–k_y$) bulk Fermi surface, where the different colors represent different $k_z$ values along the Γ–$A$ line of the bulk BZ [see Fig. S2(e)]. In-plane ($k_x–k_y$) constant energy surface maps of $\mathrm{Ni}{\mathrm{Te}}_2$ at $E-E_{\mathrm{F}}=0\mathrm{eV}$ [(f)–(j)] and at $E-E_{\mathrm{F}}=-0.5\mathrm{eV}$ [(k)–(o)] acquired with different photon energies.

Figure 4

VUV-ARPES spectra of $\mathrm{Ni}{\mathrm{Te}}_2$ along the $\overline{K}\overline{\mathrm{\Gamma }}\overline{K}$ (a)–(c) and $\overline{M}\overline{\mathrm{\Gamma }}\overline{M}$ (d)–(f) lines taken at 73, 114, and 140 eV, respectively. Calculated surface electronic structures, shown along the $\overline{K}\overline{\mathrm{\Gamma }}\overline{K}$ (g) and $\overline{M}\overline{\mathrm{\Gamma }}\overline{M}$ (h) lines. Shaded area corresponds to projected bulk states; red circles indicate the surface states. (i)–(l) $k_x–k_y$ constant energy surface maps near the Fermi level taken with a photon energy of 73 eV.