Mott-Hubbard insulating state

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. 

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. 

Several physical parameters are summarized in Table 10.2. Since the bandwidths are comparable with or less than the effective on-site Coulombic repulsion, they are in the proximity of the Mott-Hubbard insulating state. The conduction electrons are strongly correlated in the metallic state to give rise to curious phenomena. As a result, there are many physical properties which are not fully understood yet. 

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. 

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... 

In the case of the CP state, where an unpaired electron exists at the M " site per dimer unit, no cell doubling occurs and so either a Mott-Hubbard insulator or a one-dimensional metal is expected. Conversely, the electronic structures of the CDW state and the ACP state are regarded as Peierls and spin-Peierls states, respectively [178,184,185]. The four states of the MMX complexes are distinguished by the valence states of the metal and the bond distances in the crystal structure. 

The LDA-I-U orbital-dependent potential (7.74) gives the energy separation between the upper valence and lower conduction bands equal to the Coulomb parameter U, thus reproducing qualitatively the correct physics for Mott-Hubbard insulators. To construct a calculation in the LDA-I-U scheme one needs to define an orbital basis set and to take into account properly the direct and exchange Coulomb interactions inside a partially filled d- f-) electron subsystem [439]. To realize the LDA-I-U method one needs the identification of regions in a space where the atomic characteristics of the electronic states have largely survived ( atomic spheres ). The most straightforward would be to use an atomic-orbital-type basis set such as LMTO [448]. 

Figure 7.1 Schematic density of states for (a) the Mott-Hubbard insulator and (b) the charge-transfer insulator. LHB and UHB indicate the lower Hubbard band and upper Hubbard band, respectively. represents the fermi level...

A concept related to the localization vs. itineracy problem of electron states, and which has been very useful in providing a frame for the understanding of the actinide metallic bond, is the Mott-Hubbard transition. By this name one calls the transition from an itinerant, electrically conducting, metallic state to a localized, insulator s state in solids, under the effect of external, thermodynamic variables, such as temperature or pressure, the effect of which is to change the interatomic distances in the lattice. 

When the cores are approached, the sub-bands split, acquiring a bandwidth, and decreasing the gap between them (Fig. 14 a). At a definite inter-core distance, the subbands cross and merge into the non-polarized narrow band. At this critical distance a, the narrow band has a metallic behaviour. At the system transits from insulator to metallic (Mott-Hubbard transition). Since some electrons may acquire the energies of the higher sub-band, in the solid there will be excessively filled cores containing two antiparallel spins and excessively depleted cores without any spins (polar states). 

A somewhat different interpretation has been given by Johansson who applied the Mott-Hubbard theory of localized versus itinerant electron behaviour also to compounds. This interpretation differs from the above one mainly in that it assumes complete localization for magnetic compounds, and that at a certain critical inter-atomic distance we have to switch our description from a metallic state to an insulating one for the 5 f electrons (see Eq. (42)). In Eq. (42), an is substituted by a convenient measure of the spatial extension of the 5 f orbital, the expectation values (analogous to (of Fig. 10) and Xmoh is calculated from the R j radii of actinide metals (Fig. 3). The result is given in Table 6. 

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