🔬 materials science

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

By combining advanced photoemission and absorption spectroscopy with cluster model calculations, this study quantifies the electronic parameters of NiTe $_2$ to reveal that a negative charge-transfer energy and finite on-site Coulomb repulsion drive its classification as a moderately correlated type-II Dirac semimetal, distinguishing it from strongly correlated insulators like NiO.

Original authors: A. R. Shelke, C. -W. Chuang, S. Hamamoto, M. Oura, M. Yoshimura, N. Hiraoka, C. -N. Kuo, C. -S. Lue, A. Fujimori, A. Chainani

Published 2026-02-26

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: A. R. Shelke, C. -W. Chuang, S. Hamamoto, M. Oura, M. Yoshimura, N. Hiraoka, C. -N. Kuo, C. -S. Lue, A. Fujimori, A. Chainani

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a material called NiTe₂ (Nickel Telluride) as a bustling, high-speed highway for electrons. Scientists have long known this material is special because it acts like a Dirac Semimetal—a rare state of matter where electrons behave like massless particles, zipping around at incredible speeds. This makes it a hot candidate for future super-fast electronics and quantum computers.

However, there was a big debate in the scientific community: How "social" are the electrons in this material?

Team 1 said: "The electrons are loners. They don't care about each other. We can describe them perfectly with simple, independent rules."
Team 2 said: "No way! The electrons are very social (correlated). They constantly bump into and influence each other, and we need complex rules to explain them."

This paper acts as the referee, using high-tech "microscopes" (spectroscopy) to settle the score. Here is the story of what they found, explained simply.

1. The Two Neighbors: Nickel and Tellurium

Think of the NiTe₂ crystal as a neighborhood.

Nickel (Ni) atoms are the "hosts" of the party. They have electrons in their "d-orbitals" (let's call these their living rooms).
Tellurium (Te) atoms are the "neighbors." They have electrons in their "p-orbitals" (their gardens).

In a normal metal, the living room electrons stay in the living room. But in NiTe₂, the neighbors (Te) are so generous that they start lending their garden electrons to the hosts (Ni). In fact, they are so generous that the hosts end up with more electrons than they started with!

2. The "Rent" and the "Fence" (The Key Concepts)

To understand the physics, the authors looked at two main forces:

The "Fence" (On-site Coulomb Energy, $U_{dd}$ ): Imagine a fence around the Nickel's living room. If two electrons try to squeeze into the same small space, they repel each other. The strength of this repulsion is the "fence."
- In a very stubborn material like Nickel Oxide (NiO), the fence is tall and strong (High $U$ ). Electrons hate being together, so they stay put.
- In NiTe₂, the fence is lower (Medium $U$ ). The electrons are a bit more relaxed, but the fence is still there.
The "Rent" (Charge Transfer Energy, $\Delta$ ): This is the cost for an electron to move from the neighbor's garden (Te) into the host's living room (Ni).
- Positive Rent: It costs energy to move in. (Like in NiO).
- Negative Rent: It's actually profitable to move in! The neighbor is so eager to give away electrons that the host gets them for "free" (or even gets paid). NiTe₂ has negative rent.

3. The Big Discovery: The "Goldilocks" Zone

The researchers measured these forces and found something surprising:

NiTe₂ is a "Negative Charge-Transfer" material: The "Rent" is negative. The Tellurium neighbors are dumping electrons onto the Nickel hosts. This is why the Nickel atoms end up with about 9.1 electrons instead of the expected 8. They are "overcrowded" with extra guests.
But the Fence is still there: Even though the rent is negative, the "Fence" (repulsion) is still strong enough ( $U > |\Delta|$ ) to keep the Nickel's living room electrons from completely taking over the whole house.

Why does this matter?
If the fence were too weak (or non-existent), the electrons would just mix chaotically, and the material would act like a normal, messy metal.
If the fence were too strong, the electrons would freeze in place, and the material would be an insulator (like NiO).

NiTe₂ is in the "Goldilocks" zone:

The Negative Rent brings in extra electrons, creating a unique, crowded electronic environment.
The Moderate Fence pushes the Nickel's own electrons away from the main highway (the Fermi level).
The Result: This specific push-and-pull clears the highway for the Tellurium's electrons to flow freely. Because the Tellurium atoms are heavy, their electrons have a special "spin" property that causes the energy bands to invert (flip inside out).

4. The Analogy: The Traffic Jam that Creates a Superhighway

Imagine a city intersection (the Fermi level).

In a normal metal, cars (electrons) are everywhere, moving randomly.
In an insulator, the road is blocked; no cars can move.
In NiTe₂, the "Negative Rent" is like a construction crew bringing in a massive fleet of new cars (extra electrons).
However, the "Moderate Fence" acts like a traffic cop who says, "Okay, you can have all these new cars, but the old Nickel cars must move to the side streets."
This clearing of the main road allows the new cars (Tellurium electrons) to flow in a perfectly organized, frictionless line. Because of the heavy nature of Tellurium, this flow creates a Dirac Cone—a special shape in the energy map that allows electrons to travel without resistance, like light.

The Verdict

The paper concludes that electron correlations (the social interactions) are absolutely essential to understanding NiTe₂. You cannot explain why it is a topological semimetal by ignoring the electrons' relationships.

NiO is a "Strongly Correlated Insulator": The fence is huge, and the rent is high. Electrons are stuck.
NiTe₂ is a "Moderately Correlated Topological Metal": The rent is negative (generous neighbors), but the fence is just strong enough to organize the chaos into a perfect, topological highway.

Without this specific balance of "generous neighbors" and a "moderate fence," NiTe₂ wouldn't be the exotic, topological material we need for the quantum computers of the future.

1. Problem Statement

NiTe $_2$ is a layered transition metal dichalcogenide (TMD) identified as a Type-II Dirac semimetal (DSM). While Angle-Resolved Photoemission Spectroscopy (ARPES) and band structure calculations have confirmed its topological nature, there is significant controversy regarding the role of electron correlations in its electronic structure:

Conflicting Views: Some studies suggest NiTe $_2$ is a weakly correlated system where standard Density Functional Theory (DFT) suffices. Conversely, recent studies suggest strong correlations are essential for describing Te 5p-derived bands.
The Nickel Paradox: Ni is divalent in NiTe $_2$ (due to Te dimerization, Te $_2^{2-}$ ), similar to NiO. NiO is a well-known strongly correlated Charge Transfer (CT) insulator. However, NiTe $_2$ is a Pauli paramagnetic metal.
The Gap: There is a lack of quantitative experimental data on the key electronic parameters—specifically the on-site Coulomb energy ( $U_{dd}$ ) and the charge-transfer energy ( $\Delta$ )—for NiTe $_2$ . It remains unclear how these parameters compare to NiO and how they influence the material's topological properties (specifically the band inversion mechanism).

2. Methodology

The authors employed a multi-faceted experimental and theoretical approach to quantify electronic parameters:

Sample Preparation: High-quality single crystals of NiTe $_2$ were grown via chemical vapor transport.
Spectroscopic Techniques:
- Soft and Hard X-ray Photoemission Spectroscopy (SXPES/HAXPES): Used to probe core levels (Ni 2p, Te 3d, Te 3p) and valence bands with varying surface/bulk sensitivity.
- X-ray Absorption Spectroscopy (XAS): Measured at the Ni $L_{2,3}$ -edges to probe unoccupied states.
- Resonant Photoemission Spectroscopy (Res-PES): Performed at the Ni $2p-3d$ resonance to isolate the Ni 3d partial density of states (PDOS) and identify two-hole correlation satellites.
Theoretical Modeling:
- Charge Transfer (CT) Cluster Model: Calculations were performed using the QUANTY code. A NiL $_6$ cluster (Ni $^{2+}$ with 6 Te ligands) was used.
- Cini-Sawatzky Method: Applied to experimental data to extract the on-site Coulomb energy ( $U_{dd}$ ) by comparing the single-particle PDOS with the two-hole correlation satellite.
- Comparative Analysis: NiO was used as a benchmark reference for a strongly correlated CT insulator.

3. Key Contributions

Quantification of $U_{dd}$ : The study provides the first experimental determination of the Ni 3d on-site Coulomb energy in NiTe $_2$ ( $U_{dd} = 3.7$ eV) using the Cini-Sawatzky method.
Identification of Negative Charge Transfer: Through cluster model fitting of XAS and core-level spectra, the authors determined that NiTe $_2$ possesses a negative charge-transfer energy ( $\Delta = -2.8$ eV), contrasting sharply with the positive $\Delta$ of NiO.
Resolution of Correlation Debate: The work clarifies that NiTe $_2$ is a moderately correlated system, not weakly correlated as some DFT studies suggested, nor as strongly correlated as NiO.
Mechanism for Topology: The paper establishes that the specific balance of $U_{dd}$ and $\Delta$ is the critical factor enabling NiTe $_2$ to be a topological Dirac semimetal.

4. Key Results

Electronic Parameters

Parameter	NiTe $_2$	NiO (Reference)	Significance
On-site Coulomb Energy ( $U_{dd}$ )	3.7 eV	7.0 eV	NiTe $_2$ has significantly reduced electron-electron repulsion compared to NiO.
Charge Transfer Energy ( $\Delta$ )	-2.8 eV	+6.0 eV	NiTe $_2$ is a negative- $\Delta$ material; NiO is a positive- $\Delta$ insulator.
Hybridization ( $T_{eg}$ )	1.8 eV	2.4 eV	Hybridization is weaker in NiTe $_2$ (due to longer Ni-Te bond), ruling out hybridization as the cause for reduced $U_{dd}$ .
Ground State Configuration	~57% $d^9L^1$ , ~23% $d^{10}L^2$	~85% $d^8$	NiTe $_2$ has a dominant ligand-hole character ( $d^{n+1}L^1$ ), while NiO is dominantly $d^n$ .
Effective $d$ -count ( $d_n$ )	9.1	8.14	The Ni site in NiTe $_2$ gains nearly one extra electron due to charge transfer from ligands.

Spectroscopic Findings

Valence Band: The Fermi level ( $E_F$ ) lies within the Te 5p ligand bands, not the Ni 3d bands. This is consistent with the negative $\Delta$ scenario where the lowest energy excitations are $p \to p$ type (ligand to ligand).
Resonant PES: The Ni 3d PDOS peak is observed at ~1.9 eV binding energy, while a two-hole correlation satellite appears at ~7.9 eV. The energy difference yields $U_{dd} = 3.7$ eV.
Core Levels: The Ni 2p core-level spectra and L-edge XAS were successfully simulated only when using the negative $\Delta$ and reduced $U_{dd}$ values, confirming the validity of the cluster model.

Theoretical Implications (ZSA Scheme)

The authors place NiTe $_2$ in the Zaanen-Sawatzky-Allen (ZSA) phase diagram:

Condition: $U_{dd} > |\Delta|$ (3.7 eV > 2.8 eV).
Consequence: Although $\Delta$ is negative (implying ligand holes are lower in energy), the finite repulsive $U_{dd}$ is strong enough to push the Ni 3d states away from the Fermi level.
Topological Result: This separation ensures that the states near $E_F$ are primarily Te 5p-derived. Because these Te 5p states are strongly spin-orbit coupled, they undergo band inversion, creating the Type-II Dirac cone.
Counter-factual: If $U_{dd}$ were negligible ( $U_{dd} \ll |\Delta|$ ), the system would become a Mott-Hubbard metal with $d \to d$ excitations, destroying the band inversion and the topological nature.

5. Significance

Fundamental Physics: The study resolves the "correlation paradox" in NiTe $_2$ , demonstrating that it is a moderately correlated negative-charge-transfer metal. It highlights that electron correlations are not just a perturbation but a fundamental requirement for the material's topological phase.
Design Principle: It establishes a design rule for topological semimetals in TMDs: a finite, moderate repulsive $U_{dd}$ combined with a negative $\Delta$ is necessary to push $d$ -states away from $E_F$ and allow $p$ -state band inversion.
Methodological Advance: The successful application of the Cini-Sawatzky method combined with cluster model calculations provides a robust framework for quantifying electronic parameters in complex topological materials where standard DFT fails.
Material Applications: Understanding the electronic structure of NiTe $_2$ is crucial for its emerging applications in superconductivity (pressure-induced and topological), the Josephson diode effect, and electrocatalysis.

In summary, the paper proves that NiTe $_2$ is a topological Dirac semimetal specifically because of its moderate electron correlations and negative charge-transfer character, which together facilitate the necessary band inversion in the Te 5p manifold.