Evidence for the constancy of $U$ in the Mott transition of V${}_2$O${}_3$

We have performed high-resolution hard-x-ray photoemission spectroscopy for the metal-insulator transition (MIT) system (V${}_{1-x}$Cr${}_x$)${}_2$O${}_3$ in the paramagnetic metal, paramagnetic insulator, and antiferromagnetic insulator phases. The quality of the spectra enables us to conclude that the on-site Coulomb energy $U$ does not change through the MIT, which eliminates all but one theoretical MIT scenario in this paradigm material.

Figure 1

Entire valence-band spectra of (V${}_{1-x}$Cr${}_x$)${}_2$O${}_3$ ($x=0$ and 0.015) in the PM and AFI phases (top), those in the PM and PI phases (middle), and those in the PI and AFI phases (bottom). Inset shows the schematic phase diagram of (V${}_{1-x}$Cr${}_x$)${}_2$O${}_3$.

Figure 2

High-resolution HAXPES spectra of (V${}_{1-x}$Cr${}_x$)${}_2$O${}_3$ ($x=0$ and 0.015) near $E_F$ in the PM and AFI phases (a), those in the PM and PI phases (b), and those in the PI and AFI phases (c). (d) The difference between the AFI and PI spectra (open circle), which is estimated by averaging the two results for the $x=0$ and 0.015 AFI spectra. The thick solid line is the smoothed difference.

Figure 3

Left panel: Photon energy dependence of the V $3d$ spectral weight near $E_F$ for V${}_2$O${}_3$ taken by HAXPES and SXPES in the PM phase (a), the AFI phase (b), and the PI phase (c). Solid lines in (a), (b), and (c) show the bulk component extracted from the PES spectra taken at 700 and 60 eV (Ref. 24) (700 and 220 eV) photons in the PM (AFI and PI) phase. Right panel: Comparison of the extracted bulk spectra between AFI and PI phases after normalization by the integrated intensity (d). In (e) and (f), the extracted LHB of the AFI phase is evaluated by the procedure mentioned in the text in detail.

Figure 4

Comparison of the extracted LHB of the AFI phase evaluated by the three types of the subtraction procedures mentioned in the text in detail.