Mott-Hubbard localized states

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. 

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. 

In addition to Mott-Hubbard localization, there is another common source of electron localization, which arises when a lattice is under a random potential (e.g. a random distribution of alkali metal ions in alkali metal containing transition metal oxides). For a metal, a practical consequence of a random potential is to open a band gap at the Fermi level. Insulating states induced by random potentials are referred to as Anderson localized states (see Anderson Localization)) ... 

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. 

This transition has been emphasized by Mott for the case of localized impurity states in a semiconductor, forming a metallic band at some concentration of impurities (i.e. at some average distance between the impurities). It is referred to very often as the Mott (or Mott-Hubbard) transition. 

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. 

In the same paper, Brooks and Kelly have considered the possible contributions of 5 f orbitals to the bonding of UO2. While the hypothesis of an itinerant picture for these orbitals in the solids leads to a 35% higher atomic volume than the observed one, the assumption of a 5 f Mott-Hubbard spin-localized band, comprising seven states per atom (instead of 14) (see Chap. A) yields the correct value for this quantity. A certain amount of f-p hybridization is found as a weak and diffuse percentage of 5 f character in the predominantly 2p-6d valence band of this oxide. 

It is believed that electron correlation plays an important role with the anomalously high resistivity exhibited in marginal metals. Unfortunately, although the Mott-Hubbard model adequately explains behavior on the insulating side of the M-NM transition, on the metallic side, it does so only if the system is far from the transition. Electron dynamics of systems in which U is only slightly less than W (i.e. metallic systems close to the M-NM transition), are not well described by a simple itinerant or localized picture. The study of systems with almost localized electrons is still an area under intense investigation within the condensed matter physics community. A dynamical mean field theory (DMFT) has been developed for the Hubbard model, which enables one to describe both the insulating state and the metallic state, at least for weak correlation. 

There is one localized,unpaired spin per TCNQ molecule. This presumably follows from 1. if the disorder is sufficiently great as to give complete localization of the one-electron states to a single site or if one has a Mott-Hubbard metal to insulator transition and is in the strong-coup ling limit. However, as we shall see, one does not necessarily have one unpaired spin per site when the disorder potential and interaction are comparable. 

Finally, a a band on the itinerant-electron side of the Mott-Hubbard transition in the presence of localized t spins S = 3/2 signals covalent-mixing parameters X and therefore a cubic-field splitting (Eq. 5 of Goodenough, this volume) that approaches Aex- To test this deduction, hydrostatic pressure was used to induce a transition from the high-spin to the low-spin states in CaFeOs the transition was observed to occur at a pressure Pc 30 GPa [50]. 

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