Mott-Hubbard metal

Mott-Hubbard metal-insulator transition in the nanocrystal ensemble wherein the Coulomb gap closes at a critical distance between the particles. 

The electronic structure of bulk VO has been calculated by different band structure methods [110-114] and using correlated electron procedures [115]. This Mott-Hubbard metal, which forms a rocksadt type lattice, is the simplest of all single valence oxides of vanadium and has been treated theoretically already a long time ago. As an example, Neckel et al. [114] have published results from self-consistent APW calculations for the experimentally known lattice geometry... 

This study led to the observation of a reversible Mott-Hubbard metal-insulator transition in the nanocrystal ensemble wherein the coulomb gap closes at a critical distance between the particles. Tunnelling spectroscopic measurements on Aims of 2.6 nm Ag nanocrystals capped with decanethiol reveal a coulomb blockade behavior attributable to isolated nanocrystals [203]. On the other hand, nanocrystals capped with hexane and pentane thiol exhibit characteristics of strong interparticle quantum mechanical exchange (see Figure 4.28). Similar behavior was observed... 

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. 

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... 

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.

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. 

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. 

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).

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. 

A fundamental question is whether the transition between localized and itinerant electronic behavior is continuous or discontinuous. Mott (1949) was the first to point out that an on-site electrostatic energy Ua > Wr, is needed to account for the fact that NiO is an antiferromagnetic insulator rather than a metal. Hubbard (1963) subsequently introduced U formally as a parameter into the Hamiltonian for band electrons his model predicted a smooth transition from a Pauli paramagnetic metal to an antiferromagnetic insulator as the ratio W/U decreased to below a critical value of order unity. This metal-insulator transition is known as the Mott-Hubbard transition. 

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