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Final-state effect on x-ray photoelectron spectrum of nominally $d^1$ and $n$-doped $d^0$ transition metal oxides

We investigate the x-ray photoelectron spectroscopy (XPS) of nominally $d^1$ and $n$-doped $d^0$ transition metal oxides including NbO$_2$, SrVO$_3$, and LaTiO$_3$ (nominally $d^1$), as well as $n$-doped SrTiO$_3$ (nominally $d^0$). In the case of single phase $d^1$ oxides, we find that the XPS spectra (specifically photoelectrons from Nb $3d$, V $2p$, Ti $2p$ core levels) all display at least two, and sometimes three distinct components, which can be consistently identified as $d^0$, $d^1$, and $d^2$ oxidation states (with decreasing order in binding energy). Electron doping increases the $d^2$ component but decreases the $d^0$ component, whereas hole doping reverses this trend; a single $d^1$ peak is never observed, and the $d^0$ peak is always present even in phase-pure samples. In the case of $n$-doped SrTiO$_3$, the $d^1$ component appears as a weak shoulder with respect to the main $d^0$ peak. We argue that these multiple peaks should be understood as being due to the final-state effect and are intrinsic to the materials. Their presence does not necessarily imply the existence of spatially localized ions of different oxidation states nor of separate phases. A simple model is provided to illustrate this interpretation, and several experiments are discussed accordingly. The key parameter to determine the relative importance between the initial-state and final-state effects is also pointed out.