Insulators Mott-Hubbard

Liechtenstein AI, Anisimov VI, Zaanen J (1995) Density-functional theory and strong interactions orbital ordering in Mott-Hubbard insulators. Phys Rev B 52(8) R5467... 

Functional Theory and Strong Interactions Orbital Ordering in Mott-Hubbard Insulators. 

Figure 6.52 Schematic electron addition and removal spectra representing the electronic structure of transition-metal compounds for different regimes of the parameter values (a) charge-transfer insulator with U > A (b) Mott-Hubbard insulator A> U (From Rao et al, 1992).

Slater s band-theory treatment of Mott-Hubbard insulators... 

In our view (Mott 1972b), mixing the bands increases the tendency to moment formation and to Mott-Hubbard insulation, because, while U is... 

The addition of 2.5% Cr02 leads at intermediate temperature to a phase i n which only half the V ions are paired the others form a zig-zag chain (Marezio et al 1972, Pouget et al 1974). At low temperatures pairing takes place, and at higher temperatures the usual transition to the metallic rutile form. This intermediate phase has high susceptibility, and the zig-zag chains are interpreted as onedimensional Mott-Hubbard insulators above their Neel temperature. Since the transition temperature is little changed, this shows that U is the most important quantity in determining the gap. 

Matsumoto [98] tried to summarize the work done on the electronic structure of iron oxides and concluded that the about 2 eV in the bandgap of the hematite semiconductor measured in photoelectrochemistry indeed is based on the 3d band transition between the Fe3+ ions, which supports a Mott-Hubbard insulator. 

In Fig. 4 we show the molecular structures of [M(mnt)2] and perylene and the general scheme of the crystal structure of the a phases. The conduction band of the perylene system is a three-quarter-filled band, whereas the dithiolate chains are either Mott-Hubbard insulators or closed shell. The members of this series cover a number of the situations described above. 

The near-infrared reflectance provides the response to plasmon oscillations of the electron gas (which are uniform excitations). This region of the spectrum is, however, not sensitive to the strength of the short-range coulombic interactions, which prevent conductivity in a Mott-Hubbard insulating state. This is illustrated by the frequency-dependent conductivity cx((o) measured in various salts exhibiting very different values of the conductivity at room temperature (Fig. 27). The peak of the conductivity at the frequency w0 correlates with the metallic character namely, a low frequency of the peak position corresponds to a high dc conductivity and vice versa. The structures below 0)o are attributed to the coupling with intramolecular modes. 

Correlation effects are likely to be quite important in the compound 0(ET)2I3 since they also are narrowband conductors. However, the reason why these strong interactions do not materialize in a Mott-Hubbard insulator could be attributed to the absence of one-dimensional character for this system, which precludes establishment of a Mott-Hubbard localized state. 

Figure 7.1. The band gap is determined by the d-d electron correlation in the Mott-Hubbard insulator (a), where A > I/. By contrast, the band gap is determined by the charge transfer excitation energy in the charge transfer insulator (b), where U > A.

Unlike the Mott-Hubbard insulator MnO described above the band-gap in the isostruc-tural oxide NiO is much smaller than expected from intrasite Coulomb repulsion. Fujimori and Minami showed that this is owing to the location of the NiO oxygen 2p band - between the lower and upper Hubbard sub-bands (Fujimori and Minami, 1984). This occurrence can be rationalized by considering the energy level of the d band while moving from Sc to Zn in the hrst transition series. 

It has been seen in the previous section that the ratio of the onsite electron-electron Coulomb repulsion and the one-electron bandwidth is a critical parameter. The Mott-Hubbard insulating state is observed when U > W, that is, with narrow-band systems like transition metal compounds. Disorder is another condition that localizes charge carriers. In crystalline solids, there are several possible types of disorder. One kind arises from the random placement of impurity atoms in lattice sites or interstitial sites. The term Anderson localization is applied to systems in which the charge carriers are localized by this type of disorder. Anderson localization is important in a wide range of materials, from phosphorus-doped silicon to the perovskite oxide strontium-doped lanthanum vanadate, Lai cSr t V03. 

Systems exhibiting both strong disorder and electron correlation, so-caUed disordered Mott-Hubbard insulators, are difficult to evaluate. The description of electronic states in the presence of both disorder and correlation is still an unresolved issue in condensed matter physics. Whether disorder or the correlation is the predominant factor in controlling transport properties in a material depends on a complex... 

Hence, for Lai-xTiOs, both disorder and correlation are probably important. These phases are best considered disordered Mott-Hubbard insulators. 

Instabilities in a 1-D system, driven by a strong on-site electron-electron Coulomb repulsion U, lead to a Mott-Hubbard insulator [161], particularly for p = 1 systems this causes charge localization, and the crystal becomes insulating. For a chemist, a Mott-Hubbard insulator is like a NaCl crystal, where the energy barrier to moving a second electron onto the Cl site is prohibitively high, as is the cost of moving an electron off a Na site. 

When p = 1 (one electron per molecule) the electrons (or holes) are localized [23] any transport of charge puts two electrons on the same site, at a huge cost in energy thus a p=l system is a Mott-Hubbard insulator [161]. If Em + Id Aa 0 then interesting properties become possible [48]. 

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