Fermi-crossing Type-II Dirac fermions and topological surface states in NiTe2

Abstract

Transition-metal dichalcogenides (TMDs) offer an ideal platform to experimentally realize Dirac fermions. However, typically these exotic quasiparticles are located far away from the Fermi level, limiting the contribution of Dirac-like carriers to the transport properties. Here we show that NiTe₂ hosts both bulk Type-II Dirac points and topological surface states. The underlying mechanism is shared with other TMDs and based on the generic topological character of the Te p-orbital manifold. However, unique to NiTe₂, a significant contribution of Ni d orbital states shifts the energy of the Type-II Dirac point close to the Fermi level. In addition, one of the topological surface states intersects the Fermi energy and exhibits a remarkably large spin splitting of 120 meV. Our results establish NiTe₂ as an exciting candidate for next-generation spintronics devices.

Figure 1

(a) Crystal structure of 1T-NiTe₂ (space group: P-3m1), composed of hexagonal basal planes (ab-planes) of Ni-atom (red sphere) coordinated to the Ni-atom at the centre and triangular layers with inequivalent Te atomic site (blue sphere) above (Te-1) and below (Te-2) the basal plane along the (001)-direction. The hopping parameters between 2-site Te p-orbitals are categorised as intra-layer hopping (t₁ = t₂), interlayer hopping (t₃) within the unit cell and between two unit cells (t₄). (b) Brillouin zone. (c) Hierarchy of p-orbital derived energy levels at Γ and A-point showing the inverted band gaps (IBG), Dirac points (BDP: circled) and topological states. The symmetry of the states are labelled with IREPs (Γ_i, A_j, Δ_k) and parity (+/−). Inspired from Ref.^,. Figure made using Adobe Illustrator .

Figure 2

(a) Electronic DFT bulk band structures with orbital character of bands. Type-II Dirac fermion formed by crossing of band 1 and 2 near Fermi level. (b) Density of states (DoS) showing dominant contribution of Te p-bands at the Fermi Level compared to Ni d-bands. Above Fermi level, the DoS spectra is scaled up by factor of 2. (c) Band dispersion along the Γ-A direction with inverted band gaps (IBG) and bulk Dirac points (BDP) marked, (d) and (e) Zoomed-in dispersion and measured photon-energy dispersion with linear horizontal polarization along the Γ-A direction. A non-dispersive feature is marked with an arrow, which does not match with bulk DFT calculation. Figures made using Igor and Adobe Illustrator.

Figure 3

Spectral band dispersion along in-plane L′–A–L (a–c) and H′–A–H (d, e) direction, probed with photon energy hν = 99 eV (a) experimental ARPES data with linear horizontal polarization, supercell calculation integrated along k_z with (b) bulk DFT and (c) slab surface. Arrows mark the position of the topological surface states (TSS). The overlaid dotted red lines in (a, d) represent the calculated bulk DFT bands. Figures made using Igor and Adobe Illustrator.

Figure 4

(a) In-plane dispersion of TSS0 forming electron pockets labelled as ε and γ and (b) the non-dispersive behaviour of TSS0 surface state close to the Fermi level in the photon-energy dependence. (c) Fermi surface measured with horizontal polarization of light and photon energy, hν = 23 eV, which corresponds to the A-plane. The region under the red dotted box is magnified by a factor of 5 to show the electron pockets α (Band 2), ε and γ (TSS0) and the bulk bands. (Inset: calculated bulk Fermi surface consisting of the circular α electron pocket and bands forming hexagonal contour, in good agreement with measured data). (d) and (e) Slab calculation with projected spin components of the topological surface states. TSS2 shows finite <S_x> and <S_y> components normal to H′–A–H and L′–A–L direction, respectively. TSS0 has finite spin component <S_y> normal to L′–A–L (note that TSS0 is hybridized with bulk in all other regions of the plots, so no further conclusions about surface state spin texture can be made). Figures made using Igor and Adobe Illustrator.