Role of on-site Coulomb energy and negative-charge transfer in a Dirac semi-metal NiTe$_2$

Angle-resolved photoemission spectroscopy (ARPES) combined with band structure calculations have shown that the layered transition metal dichalcogenide(TMD) NiTe$2$ is a type-II Dirac semimetal. However, conflicting conclusions were reported regarding the role of electron correlations in NiTe$2$. We study core-levels and valence band electronic structure of single crystal NiTe$2$ using soft and hard x-ray photoemission spectroscopy(SXPES, HAXPES), X-ray absorption spectroscopy(XAS) and Ni $2p-3d$ Resonant-PES to quantify electronic parameters in NiTe$2$. The Ni $3d$ on-site Coulomb energy ($U{dd}$) is quantified from measurements of the Ni $3d$ single particle density of states(DOS) and the two-hole correlation satellite. The Ni $2p$ core level and $L$-edge XAS spectra are analyzed by charge-transfer (CT) cluster model calculations using the experimental $U{dd}$, and it shows that NiTe$2$ exhibits a negative CT energy $Δ$. A comparative analysis of NiO $L$-edge XAS confirms its well-known strongly correlated CT insulator character, with a larger $U{dd}$ and positive $Δ$. The $d$-$p$ hybridization strength $T{eg}$ for NiTe$2$$<$NiO, and shows that $T{eg}$ is not responsible for reducing $U{dd}$ in NiTe\textsubscript{2} compared to NiO. The negative-$Δ$ and a reduced $U_{dd}$ leads to the increase in $d^n$ count on the Ni site in NiTe${2}$ by nearly one electron. However, importantly, since $U{dd}$$>$$|Δ|$, a finite repulsive $U_{dd}$ results in pushing $d$-states away from Fermi level and this is required to make NiTe$_{2}$ a moderately correlated Dirac semi-metal with band inversion in the $p$-$p$ type lowest energy excitations.

💡 Research Summary

This work provides a comprehensive experimental and theoretical investigation of the electronic correlations in the layered transition‑metal dichalcogenide NiTe₂, a material that has been identified as a type‑II Dirac semimetal by angle‑resolved photoemission spectroscopy (ARPES) and band‑structure calculations. While previous ARPES studies reported the Dirac point a few tens of meV above or below the Fermi level, the role of electron‑electron interactions, especially within the Ni 3d manifold, remained ambiguous. To resolve this, the authors combined soft‑ and hard‑x‑ray photoemission spectroscopy (SXPES and HAXPES), Ni L‑edge X‑ray absorption spectroscopy (XAS), and Ni 2p–3d resonant PES on high‑quality single crystals grown by chemical vapor transport.

Core‑level spectra of Te 3d, Te 3p and Ni 2p were measured with photon energies of 1.5 keV (SXPES) and 6.5 keV (HAXPES). The Te core levels appear as sharp, symmetric peaks with weak plasmon satellites (~19.7 eV higher binding energy). The Ni 2p spectra show the expected spin‑orbit doublet (3/2 at ~853.6 eV, 1/2 at ~870.9 eV) together with a pronounced charge‑transfer (CT) satellite about 8 eV above the Ni 2p 3/2 main line, indicating strong hybridization with Te ligands. Least‑squares fitting using asymmetric Voigt/Doni­ach‑Sunjic line shapes and Gaussian plasmon components yields precise binding‑energy positions and full‑widths, confirming the metallic nature of Ni and the absence of surface oxidation.

The key quantitative parameter, the on‑site Coulomb repulsion U_dd for Ni 3d electrons, was extracted from two independent measurements. First, Ni 2p–3d resonant PES provided the Ni 3d partial density of states (PDOS) and a two‑hole correlation satellite. Applying the Cini‑Sawatzky analysis to the energy separation between the single‑particle peak and the satellite gave U_dd = 3.7 eV. Second, a charge‑transfer multiplet cluster model (NiL₆ octahedron) was employed to simulate the Ni L₃,₂ XAS and Ni 2p core‑level spectra using the QUANTY code. By fixing U_dd at the experimentally determined value and varying the charge‑transfer energy Δ, the hybridization strength T_eg, and the crystal‑field splitting 10 Dq, the calculated spectra reproduced the experimental line shapes only when Δ = –2.8 eV (negative charge‑transfer) and T_eg was smaller than in the benchmark NiO system.

For comparison, the same analysis was performed on NiO, a prototypical charge‑transfer insulator. NiO exhibits U_dd ≈ 7.0 eV, Δ ≈ +6.0 eV, and a larger T_eg, confirming its strong correlation and positive charge‑transfer character. The contrast demonstrates that NiTe₂ lies in a distinct regime: the negative Δ indicates that the ligand‑hole configuration |3d⁹L¹⟩ is energetically favored over the nominal |3d⁸⟩ state, effectively increasing the Ni 3d electron count by roughly one electron. Nevertheless, because U_dd remains larger than |Δ|, a finite repulsive interaction still pushes the Ni 3d-derived bands away from the Fermi level. This subtle balance yields a “moderately correlated” electronic structure in which the low‑energy excitations are of p‑type (Te 5p → Te 5p) character, consistent with the Zaanen‑Sawatzky‑Allen (ZSA) scheme for a p‑type charge‑transfer system.

The authors argue that this moderate correlation is essential for the realization of the type‑II Dirac semimetal state in NiTe₂. The Dirac point arises from a band inversion between Te 5p states; the presence of a finite U_dd prevents the Ni 3d bands from crossing the Fermi level, thereby preserving the p‑p band inversion and the tilted Dirac cone. This explains why pure DFT calculations, which neglect explicit correlation, require ad‑hoc energy shifts (e.g., –60 meV and +100 meV) to match ARPES dispersions. Incorporating the experimentally determined U_dd and Δ into GW or DFT+U frameworks should naturally reproduce the observed band velocities and the small electron‑hole pockets.

Beyond the fundamental insight into correlation effects, the study has broader implications. NiTe₂ displays exceptionally high conductivity (∼10⁶ S m⁻¹ at 2 K) and Pauli paramagnetism, and it exhibits pressure‑induced superconductivity, a giant Josephson‑diode effect, and catalytic activity for hydrogen evolution. Understanding the balance of U_dd, Δ, and hybridization provides a quantitative basis for tuning these properties via chemical substitution, strain, or external pressure. Moreover, the methodology—combining bulk‑sensitive HAXPES, resonant PES, and charge‑transfer cluster modeling—offers a template for investigating other topological semimetals where subtle correlation effects may be hidden from surface‑sensitive ARPES alone.

In summary, the paper establishes that NiTe₂ is a moderately correlated Dirac semimetal characterized by a reduced on‑site Coulomb energy (U_dd = 3.7 eV) and a negative charge‑transfer energy (Δ = –2.8 eV). The negative Δ increases the Ni 3d occupancy, while the finite U_dd keeps the d‑states away from the Fermi level, enabling a p‑type band inversion that underlies the type‑II Dirac dispersion. These findings reconcile conflicting ARPES reports, clarify the role of electronic correlations, and set the stage for more accurate theoretical modeling and targeted functionalization of NiTe₂ and related topological materials.