The nexus between negative charge-transfer and reduced on-site Coulomb energy in correlated topological metals

TL;DR

The study tackles why CoTe$_2$ and NiTe$_2$, both topological Dirac Type-II metals, do not exhibit the expected correlation-induced d-band narrowing. Using resonant photoemission and CT cluster-model calculations, the authors quantify $U_{dd}$ and the charge-transfer energy $\Delta$, finding moderate $U_{dd}$ values ($3.0$ eV for CoTe$_2$ and $3.7$ eV for NiTe$_2$) with negative $\Delta$, in contrast to CoO/NiO. They demonstrate that the reduced $U_{dd}$ arises from negative $\Delta$ and Te polarizability rather than weaker $d$-$p$ hybridization, positioning the Te $5p$ states around $E_F$ and enabling $p$-$p$ type excitations that drive band inversion and topological behavior. The work establishes a direct link between negative $\Delta$, reduced $U_{dd}$, and the electronic structure required for topological metallic states in correlated materials, suggesting routes to tune Dirac features via bandwidth and doping.

Abstract

The layered $3d$ transition metal dichalcogenides (TMDs) CoTe$_2$ and NiTe$_2$ are topological Dirac Type-II metals. Their $d$-bands do not exhibit the expected correlation-induced band narrowing seen in CoO and NiO. We address this conundrum by quantifying the on-site Coulomb energy $U_{dd}$ via single-particle partial density of states and the two-hole correlation satellite using valence band resonant photoemission spectroscopy (PES), and obtain $U_{dd}$ = 3.0 eV/3.7 eV for CoTe$_2$/NiTe$_2$. Charge-transfer (CT) cluster model simulations of the measured core-level PES and x-ray absorption spectra of CoTe$_2$ and CoO validate their contrasting electronic parameters:$U_{dd}$ and CT energy $Δ$ are (3.0 eV, -2.0 eV) for CoTe$_2$, and (5.0 eV, 4.0 eV) for CoO, respectively. The $d$-$p$ hybridization strength $T_{eg}$ for CoTe$_2$$<$CoO, and indicates that the reduced $U_{dd}$ in CoTe$_2$ is not due to $T_{eg}$. The increase in $d^n$-count$\sim$1 by CT from ligand to Co site in CoTe$_2$ is due to a negative-$Δ$ and reduced $U_{dd}$. Yet, only because $U_{dd}$$>$$\big|Δ\big|$, CoTe$_{2}$ becomes a topological metal with $p$$\rightarrow$${p}$ type lowest energy excitations. Similarly, we obtain a negative-$Δ$ and reduced $U_{dd}$ in NiTe$_2$ compared to NiO. The study reveals the nexus between negative-$Δ$ and reduced $U_{dd}$ required for setting up the electronic structure framework for achieving topological behavior via band inversion in correlated metals.

Figures (14)

• Figure 1: (a). The Co 2p-3d resonant-PES valence band intensity map plotted as a function of incident photon energies ($h\nu$ = 770-803 eV) versus binding energy (BE = -1.2 to 45.8 eV). (b) The Co $L_3$- and $L_2$-edge XAS plotted as a function of $h\nu$(top x-axis). (c) Valence band spectra (BE = -1.2 to 35.0 eV) measured at select $h\nu$ values (labelled $a$-$z$) across the $L_3$- and $L_2$-edges of Fig. 1(b). (d) The kinetic energy of the Resonant Raman - $L_3VV$ Auger peak plotted as a function of $h\nu$(top axis), and also relative to the XAS $L_3$ peak energy(bottom x-axis).
• Figure 2: (a) The CoTe$_2$ off-resonant ($h\nu$ = 772.85 eV, maroon, $\medcirc$; $h\nu$ = 6.5 keV, blue, $\medcirc$) and on-resonant ($h\nu$ = 778.55 eV, dark blue, $\medcirc$) near $E_F$ spectra (normalized at 0.8 eV BE). (b) Co 3d PDOS (maroon, $\medbullet$) obtained by subtracting an integral background (gray line) from off-resonant spectrum($h\nu$ = 772.85 eV (maroon, $\medcirc$). The average $U_{dd}$ is the energy between self-convoluted Co $3d$ PDOS peak(red line) and the Resonant Raman peak ($h\nu$ = 777.15 eV; green, $\medcirc$), which becomes the LVV Auger peak.
• Figure 3: (a) Co 2p PES core levels and (b) Co L3,2-edge XAS of CoTe2 compared with charge transfer cluster model calculations. (c) Co 2p PES core levels and (d) Co L3,2-edge of CoO compared with charge transfer cluster model calculations.
• Figure 4: Plots of $d^n$-count vs. $T_{eg}$ for selected values of $\Delta$ and $U_{dd}$: (a) CoTe$_2$ and CoO (b) NiTe$_2$ and NiO, identify regions of effective negative-$\Delta$ (A) and effective positive-$\Delta$ (B, C). Squares($\square$) indicate optimal values which reproduce experimental spectra (Fig. 3).
• Figure 5: Schematic electronic structure of materials representing: (a) a Mott-Hubbard insulator with $U_{dd}$$<$$\Delta$. A further reduction of $U_{dd}$ would result in a Mott-Hubbard metal if the lower(occupied) and upper(unoccupied) Hubbard $d$-bands overlap. (b) a positive-$\Delta$ charge-transfer insulator with $U_{dd}$$>$$\Delta$ and p$\rightarrow$d type lowest energy excitations (c) an effective negative-$\Delta$ metal with $U_{dd}$$>$$|\Delta_{eff}|$ and $E_F$ positioned within the ligand-$p$ band states, facilitating band inversion with p$\rightarrow$p-type lowest energy excitations to make it a correlated topological metal. Note that for Mott-Hubbard and positive-$\Delta$ materials, the ground state $|\psi_0$$>$ has a dominantly $|d^{n}$$>$ character, while for an effective negative-$\Delta$ material, $|\psi_0$$>$ has a dominantly $|d^{n+1}\underline{L}^1$$>$ character, where $\underline{L}^1$ is a hole in the ligand $p$ band.