Mott-Hubbard

First we consider the origin of band gaps and characters of the valence and conduction electron states in 3d transition-metal compounds [104]. Band structure calculations using effective one-particle potentials predict often either metallic behavior or gaps which are much too small. This is due to the fact that the electron-electron interactions are underestimated. In the Mott-Hubbard theory excited states which are essentially MMCT states are taken into account dfd -y The subscripts i and] label the transition-metal sites. These... 

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 1.19. Generic T-P phase diagram for BFS. The origin on the pressure axis is arbitrarily set for (TMTTF)2PF6. MH, Mott-Hubbard M, Metal SP, Spin-Peierls AF, Antiferromagnetic SDW, Spin-Density-Wave SC, Superconductor. Adapted from Auban-Senzier J6rome, 2003.

Iwasa Y, Takenobu T (2003) Superconductivity, Mott-Hubbard states, and molecular orbital order in intercalated fullerides. J Phys Condens Matter 15 R495-R519... 

In Sect. 4 and 5, the consequences of spin polarization in unsaturated 5f shells are analysed, and the Stoner and Mott-Hubbard theories briefly reviewed. In this way, concepts which are central for actinides, and which the reader may find only when perusing many textbooks (references of which are duly given) are adequately concentrated. 

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. 

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. 

The Case of Americium the Mott-Hubbard Transition and the Effects of 102... 

It is perhaps useful to distinguish the two ways in which the concept of a Mott-Hubbard transition is introduced in the discussion of actinide metals. 

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. 

The many-particle local point of view (Mott-Hubbard theory)... 

In the Mott-Hubbard theory on the other hand, it is shown that there exists an instability in the narrow-band electronic structure (Peierls instabihty ) and if the bandwidth decreases below a critical value, a sudden transition (Mott transition) takes place toward a complete localized situation. In this approach, it is assumed, in fact, that band magnetism does not exist and one has to deal only with 2 classes of materials... 

Evidence from Photoemission Spectroscopy for the Mott-Hubbard Transition. . . 230... 

Fig. 7 a-c. Schematic representation of final state screening models for lanthanide and d-metal core level responses (a) and c)) (c.b. means conduction band). In part b), the possible situations for light and heavy actinides (before and after the Mott-Hubbard transition) are also represented... 

Figure 17 is a clear illustration of the Mott-Hubbard transition in the actinide series the 5f emission occurs, for a-Pu, at Ep, indicating a high 5f-density of states pinned at the Fermi-level, whereas the 5 f emission occurs at lower energy for americium metal. In this case, therefore, a theoretical concept deduced indirectly from the physical properties of the two metals, finds direct (one might even say photographic ) confirmation in the photoemission spectra. 

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).

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