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Psi-k | Ab initio (from electronic structure) calculation ... · $8) «íkðÕøòìeöeùvú¯ðòñâìêí 0$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $- ûhï C

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Page 1: Psi-k | Ab initio (from electronic structure) calculation ... · $8) «íkðÕøòìeöeùvú¯ðòñâìêí 0$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $- ûhï C

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Page 24: Psi-k | Ab initio (from electronic structure) calculation ... · $8) «íkðÕøòìeöeùvú¯ðòñâìêí 0$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $- ûhï C

(d1-d2LI ) hybridization (Uozumi et al., 1993). Cluster-model analysis has revealed considerable weight ofcharge-transfer configurations, d3LI ,d4LI 2, . . . , mixed intothe ionic d2 configuration, resulting in a net d-electronnumber of nd.3.1 (Bocquet et al., 1996). This value isconsiderably larger than the d-band filling or the formald-electron number n52 and is in good agreement withthe value (nd53.0) deduced from an analysis of core-core-valence Auger spectra (Sawatzky and Post, 1979).If the above local-cluster CI picture is relevant to experi-ment, the antibonding counterpart of the split-off bond-ing state is predicted to be observed as a satellite on thehigh-binding-energy side of the O 2p band, although itsspectral weight may be much smaller than the bondingstate [due to interference between the d2→d1

1e andd3LI →d2LI 1e photoemission channels; see Eq. (3.12)].Such a spectral feature was indeed observed in an ultra-violet photoemission study by Smith and Henrich (1988)and in a resonant photoemission study by Park andAllen (1997). In spite of the strong p-d hybridizationand the resulting charge-transfer satellite mechanism de-scribed above, it is not only convenient but also realisticto regard the d1-d2LI bonding band as an effective V 3dband (lower Hubbard band). The 3d wave function isthus considerably hybridized with oxygen p orbitals andhence has a relatively small effective U of 1–2 eV (Sa-watzky and Post, 1979) instead of the bare value U;4 eV. Therefore the effective d bandwidth W becomescomparable to the effective U : W;U . With these factsin mind, one can regard V2O3 as a model Mott-Hubbardsystem and the (degenerate) Hubbard model as a rel-evant model for analyzing the physical properties ofV2O3.

The time-honored phase diagram for doped V2O3 sys-tems, (V12xCrx)2O3 and (V12xTix)2O3 , is reproducedin Fig. 70. The phase boundary represented by the solidline is of first order, accompanied by thermal hysteresis(Kuwamoto, Honig, and Appel, 1980). In a Cr-dopedsystem (V12xCrx)2O3 , a gradual crossover is observedfrom the high-temperature paramagnetic metal (PM) to

FIG. 69. Photoemission spectra of V2O3 in the metallic phasetaken using photon energies in the 3p-3d core excitation re-gion. From Shin et al., 1990.

FIG. 68. Corundum structure of V2O3.

FIG. 70. Phase diagram for doped V2O3 systems,(V12xCrx)2O3 and (V12xTix)2O3. From McWhan et al., 1971,1973.

1147Imada, Fujimori, and Tokura: Metal-insulator transitions

Rev. Mod. Phys., Vol. 70, No. 4, October 1998

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Page 26: Psi-k | Ab initio (from electronic structure) calculation ... · $8) «íkðÕøòìeöeùvú¯ðòñâìêí 0$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $- ûhï C

−4 −2 0 2 4 6 8

Energy (eV)

a1g

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Inte

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U = 4.5 eV

U = 5.0 eV

U = 5.5 eV

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Page 27: Psi-k | Ab initio (from electronic structure) calculation ... · $8) «íkðÕøòìeöeùvú¯ðòñâìêí 0$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $- ûhï C

-3 -2.5 -2 -1.5 -1 -0.5 0 0.5

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Mo et al.’02Schramme et al.’00

0 1 2 3 4 5 6

E (eV)

LDALDA+DMFT(QMC)

Mueller et al’97

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