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