Low-energy type-II Dirac fermions and spin-polarized topological surface states in transition-metal dichalcogenide NiTe$_2$

TL;DR

This study identifies low-energy type-II Dirac fermions and spin-polarized topological surface states in NiTe₂, revealing its potential for spintronics and ultrafast optoelectronic applications through combined experimental and theoretical analysis.

Contribution

The paper demonstrates the existence of a low-energy type-II Dirac semimetal state in NiTe₂ and characterizes its topological surface states with chiral spin texture, using spin-ARPES and ab initio calculations.

Findings

Dirac node near Fermi energy in NiTe₂

Topological surface states with chiral spin texture

Band inversions supporting Dirac cone surface states

Abstract

Using spin- and angle- resolved photoemission spectroscopy (spin-ARPES) together with ${\it ab~initio}$ calculations, we demonstrate the existence of a type-II Dirac semimetal state in NiTe$_2$. We show that, unlike PtTe$_2$, PtSe$_2$, and PdTe$_2$, the Dirac node in NiTe$_2$ is located in close vicinity of the Fermi energy. Additionally, NiTe$_2$ also hosts a pair of band inversions below the Fermi level along the $\Gamma-A$ high-symmetry direction, with one of them leading to a Dirac cone in the surface states. The bulk Dirac nodes and the ladder of band inversions in NiTe$_2$ support unique topological surface states with chiral spin texture over a wide range of energies. Our work paves the way for the exploitation of the low-energy type-II Dirac fermions in NiTe$_2$ in the fields of spintronics, THz plasmonics and ultrafast optoelectronics.

Full text

The discovery of topological semimetals has ushered in a new era of exploration of massless relativistic quasi-particles in crystalline solidsBansil et al. (2016); Hasan and Kane (2010); Armitage et al. (2018); Kong and Cui (2011). These arise as emergent quasi-particles in crystals with linearly dispersing bands in vicinity of a degenerate band crossing point (either accidental or symmetry-enforced) and are protected by crystalline symmetriesBradlyn et al. (2016). Double, triple and quadruple degeneracy of the band crossing leads to topologically protected WeylXu et al. (2015a); Huang et al. (2015); Lv et al. (2015); Xu et al. (2015b); Fang et al. (2012); Weng et al. (2015); Singh et al. (2012); Chang et al. (2017); Xu et al. (2017), triple pointLv et al. (2017); Gao et al. (2018); Zhu et al. (2016); Lv et al. (2017); Yu et al. (2017); Fulga and Stern (2017); Yang et al. (2017); Wang et al. (2017) and Dirac fermionsYoung et al. (2012); Young and Kane (2015); Wieder et al. (2016); Liu et al. (2014a, b); Neupane et al. (2014); Borisenko et al. (2014); Wang et al. (2012, 2013), respectively. In contrast to their high energy counter-parts, these emergent quasi-particles are not protected by Lorentz symmetry, and can also occur in a tilted form, giving rise to type-I and type-II Dirac fermions. Specifically, Na3BiWang et al. (2012); Liu et al. (2014b) and Cd3As2Wang et al. (2013); Liu et al. (2014a) are type-I Dirac semimetal (DSM), while the transition-metal dichalcogenides (TMDs) PtTe2Yan et al. (2017); Bahramy et al. (2017); Politano et al. (2018), PtSe2Zhang et al. (2017), and PdTe2Noh et al. (2017); Bahramy et al. (2017); Fei et al. (2017) are type-II DSM.

In group X Pd- and Pt- based dichalcogenides, the bulk Dirac node lies deep below the Fermi level ($\sim$0.6, $\sim$0.8 and $\sim$1.2 eV in PdTe2, PtTe2, and PtSe2, respectively) Yan et al. (2017); Bahramy et al. (2017); Politano et al. (2018); Zhang et al. (2017); Noh et al. (2017); Bahramy et al. (2017); Fei et al. (2017), hindering their successful exploitation in technology. In contrast, NiTe2 has been predicted to host type-II Dirac fermions in vicinity of the Fermi energy Xu et al. (2018). The so far performed experimental studies on NiTe2 have primarily focused on its crystal structure, and transport properties while its topological band structure remains unexplored Uchida and Kondoh (1956); Ettenberg et al. (1970); Guo and Liang (1986); Orders et al. (1982); Monteiro et al. (2017); Xu et al. (2018); Zhao et al. (2018); Liu et al. (2019). Motivated by this, we explored the electronic band structure of NiTe2 by means of spin- and angle-resolved photoemission spectroscopy (ARPES) in combination with density functional theory (DFT).

Our spin-resolved ARPES measurements explicitly demonstrate the existence of a pair of type-II Dirac nodes in NiTe2 along the $C_{3}$ rotation axis, lying just above (within 20 meV) the Fermi energy. Additionally, we show that NiTe2 also hosts a series of inverted band-gaps (IBG). Especially, one of the IBG below the Fermi level supports a Dirac cone in the surface states. Together, the bulk Dirac node and the pair of IBG in NiTe2 give rise to topological spin-polarized surface states over a wide range of energies. This non-trivial band morphology in NiTe2 originates primarily from the 5$p$-orbital manifold of the Te atoms modified by the intra-layer hybridization, trigonal crystal field splitting and spin-orbit coupling.

Bulk NiTe2 crystallizes in the CdI2 type trigonal structure (space group $P\bar{3}m1$, number 164). It has a layered structure with individual monolayer stacked together via weak van der Walls force. As shown in Fig. 1(a)-(b), each monolayer has three sub-layers, with the central Ni layer being sandwiched between two adjacent Te layers (Ni-Te bond length 2.60 Å). The observation of sharp spots in the low-energy diffraction pattern (LEED) in Fig. 1(c) confirms the high quality of the NiTe2 crystals cleaved along the (001) direction, along with the presence of six-fold symmetry. Surface cleanliness of the as-cleaved samples was checked by high-resolution electron energy loss spectroscopy and X-ray photoelectron spectroscopy. The details of crystal preparation and characterization, ARPES measurements and DFT calculations are presented in Sec. S1, S2 and S3, of the Supplementary material (SM) 222 Supplementary material detailing 1) Sample preparation and characterization, 2) computational details, 3) ARPES measurements, 4) Topological band inversions and 5) ARPES measurements with potassium doping, is available at https://bit.ly/2YWZf1o.

The electronic band structure of NiTe2 including spin-orbit coupling is shown in Fig. 2(a). It clearly depicts the presence of a pair of tilted band crossings along the $\Gamma-A$ direction. The presence of inversion and time-reversal symmetry mandates these bands to be doubly degenerate. Furthermore, the $\Gamma-A$ high-symmetry direction is the invariant subspace of the three fold rotation ($C_{3}$) symmetry, and a symmetry analysis reveals that the crossing bands have opposite rotation character. This prevents their hybridization, resulting in a pair of gapless quadruply degenerate type-II Dirac points. The type-II nature of the DSM phase is also confirmed by the fact that the Dirac point appears at the touching point of the electron and hole pocket, as highlighted in Fig. 2(b).

Our photon-energy dependent ARPES data, in part presented in Fig. 2(d-h), results in the $k_{z}$ dispersion presented in Fig. 2(c). Our experimental results are consistent with the DFT-based bulk band structure calculations. Extrapolating the fitted DFT band structure, we find that the Dirac cone is located just above ($\sim$20 meV) the Fermi energy. in contrast to other TMD-based type-II DSMs like PtTe2Yan et al. (2017); Bahramy et al. (2017); Politano et al. (2018), PtSe2Zhang et al. (2017), and PdTe2Noh et al. (2017); Bahramy et al. (2017); Fei et al. (2017). Our attempt to electronically dope the sample via alkali metal (potassium) deposition (see Fig. S6 in the SM Note (1)), and shift the Fermi energy above the Dirac point, revealed that only the surface states in NiTe2 are impacted by surface deposition. Bulk doing is needed to shift the bulk bands.

Extended energy range ARPES spectra for the two high-symmetry directions are shown in Fig. 3(c) and (d). These spectra are mainly dominated by the surface states, as seen from the comparison with the calculated band structure in Fig. 3 (e) and (f). In order to understand their origin, we note that there are two symmetry inequivalent Te atoms (Te1 and Te2) and a single Ni atom in an unit cell of NiTe2. The electronic configuration of Ni is $3s^{2}3d^{8}$ and that of Te is $4d^{10}5p^{4}$. We find that similar to other group-X TMDs Bahramy et al. (2017); Clark et al. (2019), the Te $5p$ orbital manifold in NiTe2, aided by the interplay between intra-layer hopping, crystal field splitting, and SOC strength, gives rise to most of the bulk Dirac nodes and multiple inverted band-gaps. To highlight this, we show the evolution of the $p$-orbital manifold of the Te atoms in Fig. 3(a). To start with (step I in Fig. 3(a)), strong intra-layer hybridization between the Te1 and Te2 $p$ orbitals results in bonding and anti-bonding states. These orbitals are further split (in step II), due to a strong trigonal crystal field generated by the layered crystal structure of NiTe2, separating $p_{z}$ from the $p_{x},p_{y}$ orbitals. Inclusion of SOC (step III) further splits the orbitals into $|J,|m_{J}|\rangle$ states. Step IV of Fig. 3(a) highlights the effect of the dispersion along the $\Gamma-A$ direction, and the formation of the bulk type-II Dirac point along with multiple band-inversions in the valance band.

The irreducible representation of some of these states at the at $\Gamma$ and $A$ points and along the $\Gamma-A$ high-symmetry line is shown in Fig. 3(b). The bulk Dirac point originates from the crossing of the $\Delta_{4}$ and $\Delta_{5,6}$ states along the $\Gamma-A$ direction. As discussed earlier, the doubly degenerate $\Delta_{4}$ and $\Delta_{5,6}$ bands have opposite rotation characters ($+1$ and $-1$, respectively) and, therefore, the Dirac point is protected from gap opening by any perturbation which respects the $C_{3}$ symmetry. Additionally, Fig. 3(b) also highlights the existence of a pair of IBGs in the valance band at the $A$ point. However, in comparison to PdTe2, the parity of the crossing bands at the $A$ point for NiTe2 is different and only the lower IBG supports a Dirac node in the surface states. See Sec. S5 in the SM Note (1) for a more detailed discussion and comparison of the topological band structure and surface states with PdTe2.

The Dirac-like conical crossing in the surface states of NiTe2 (at -1.4eV) is evident in the ARPES data taken along the two high-symmetry directions $\bar{K}-\bar{\Gamma}-\bar{K}$ and $\bar{M}-\bar{\Gamma}-\bar{M}$ as shown in Figs. 3(c) and (d). The dominant surface bands are indicated by the red arrows. In addition to the Dirac cone, several other surface states are present in NiTe2, owing to several band inversions below and above the Fermi level. Along the $\bar{M}-\bar{\Gamma}-\bar{M}$ direction, the surface states near the Fermi energy has its origin from a band inversion above the Fermi energy (see Fig. 3(b), and Fig. S3 in SM Note (1)) and the corresponding surface Dirac cone lies above the Fermi level. While its Dirac-like nature is significantly altered far away from the $\bar{\Gamma}$ point, we demonstrate its topological origin by displaying its chiral spin texture in Fig. 4. Similar surface states have also been observed in other Te-based TMDs like PtTe2 and PdTe2, while they are absent in the Se based compounds like PtSe2. This is a consequence of the avoided band inversion in PtSe2 resulting from the reduced interlayer hopping Yan et al. (2017); Clark et al. (2018).

Since these surface states have a topological origin, we now focus on the spin polarization of the bands using spin-polarized ARPES. In Fig. 4(a) we display the spin-resolved data superimposed directly onto the spin-integrated band structure shown earlier in Fig. 3(c) and (d). The measured spin polarization matches reasonably well with the calculated spin textures reported in Fig. 4(b) and (g). In the present dataset, the spin component is always perpendicular to the dispersion direction. The most prominent feature in Fig. 4(a)-(b) is the crossover of two opposite spin polarizations of almost equal magnitude for the surface state bands crossing at the $\Gamma$ point at a binding energy of $\sim-1.4$ eV. This confirms the helical nature of the spin-momentum locking in vicinity of the surface Dirac point, resulting from the IBG with the $Z_{2}=1$ topological order. In Fig. 4(c)-(e), we display the spin-polarized spectra and the spin polarization for the points marked by black arrows in Fig. 4(a). The measured polarization perpendicular to $\bar{\Gamma}-\bar{K}$ reaches almost $50\%$.

In the case of the bands along $\bar{M}-\bar{\Gamma}-\bar{M}$ direction of the surface BZ [Fig. 4 (f) and (g)], the polarization was measured for the electron-pocket-like surface states close to the Fermi energy. As discussed previously, although their shape is considerably different than a usual topological surface states, the clear spin polarization demonstrates their topological origin (see Fig. S3 of SM Note (1)). These indeed appear to be the most prominent spin-polarized features also in the calculated spin polarization perpendicular to the $\bar{\Gamma}-\bar{M}$ direction. The high values of the measured and calculated spin polarization indicates that NiTe2 belongs to the recently identified topological-ladder family of Pt/PdTe2 Bahramy et al. (2017); Clark et al. (2019).

To summarize, we have established the existence of type-II DSM phase in NiTe2 single crystals using spin-resolved ARPES measurements in conjunction with DFT-based ab-initio calculations. We show that, in contrast to similar class of materials like PtTe2, PdTe2, and PtSe2, where the Dirac point is buried deep in the valence band, the Dirac point in NiTe2 is located in vicinity of the Fermi energy. In addition to the bulk Dirac node, the Te $p$-orbital manifold in NiTe2 also gives rise to a series of IBGs with non-trivial $Z_{2}$ topological orders. Together, these give rise to topological Dirac nodes in the surface states characterized by the particular spin texture over a wide range of energies. Our findings establish NiTe2 as a prime candidate for exploration of Dirac fermiology and applications in TMD-based spintronic devices and ultrafast optoelectronics.

I acknowledgements

A.A. acknowledges funding support by Dept. of Sci- ence and Technology, Government of India, via DST Grant No. DST/NM/NS/2018/103(G), and from SERB Grant No. CRG/2018/002440. B.G. acknowledges CSIR for senior research fellowship. A. A. and B. G. acknowledges HPC- IIT Kanpur for its computational facilities. This work has been partly performed in the framework of the nanoscience foundry and fine analysis (NFFA-MIUR Italy, Progetti Internazionali) facility.

Note: B. G. and D. M. contributed equally to this work as first authors.