Mott-Hubbard metal-insulator transition

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

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... 

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. 

It is, however, not the JTD that turn these systems into insulators but strong correlations. The nature of metal-insulator transitions in these systems is one of the most debated points at present. Experimentally, a metal-insulator transition can be induced by relatively modest pressure in Rb4C60 and in the compound with the smallest lattice parameters (Na2C60) a residual metallic character can be detected. These behaviors support the idea that these compounds lie on the border of a Mott-Hubbard transition. We still observe typical molecular excitations of JT-distorted C60 on the metallic side of the transition, suggesting a possible coexistence. 

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. 

Figure 5. The metal-insulator transition in the doped semiconductor (Si P) and a divided metal. Here t/jc is the Mott-Hubbard correlation energy in the doped semiconductor, and t/dus is the corresponding charging energy of the divided metal.

There are, in principal, two independent paths to a metal —> insulator transition in Mott-Hubbard systems [5], both of which are characterized by the disappearance of the squared plasma frequency associated with the free carriers, cOp n/m ... 

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). 

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. 

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