Mott transition

Mott transition, 25 170-172 paramagnetic states, 25 148-161, 165-169 continuum model, 25 159-161 ESR. studies, 25 152-157 multistate model, 25 159 optical spectra, 25 157-159 and solvated electrons, 25 138-142 quantitative theory, 25 138-142 spin-equilibria complexes, 32 2-3, see also specific complex four-coordinated d type, 32 2 implications, 32 43-44 excited states, 32 47-48 porphyrins and heme proteins, 32 48-49 electron transfer, 32 45-46 race-mization and isomerization, 32 44—45 substitution, 32 46 in solid state, 32 36-39 lifetime limits, 32 37-38 measured rates, 32 38-39 in solution, 32 22-36 static properties electronic spectra, 32 12-13 geometric structure, 32 6-11 magnetic susceptibility, 32 4-6 vibrational spectra, 32 13 summary and interpretation... 

Lefebvre S, Wzietek P, Brown S, Bourbonnais C, Jerome D, Meziere C, Eourmigue M, Batial P (2000) Mott transition, antiferromagnetism, and unconventional superconductivity in layered organic superconductors. Phys Rev Lett 85 5420-5423... 

Ganin AY, Takabayashi Y, Jeglic P, Arcon D, Potocnik A, Baker PJ, Ohishi Y, McDonald MT, Tzirakis MD, McLennan A, Darling GR, Takata M, Rosseinsky MJ, Prassides K (2010) Polymorphism control of superconductivity and magnetism in CssCgo close to the Mott transition. Nature 466 221-225... 

Shimizu Y, Kurosaki Y, Miyagawa K, Kanoda K, Maesato M, Saito G (2005) NMR study of the spin-liquid state and Mott transition in the spin-frustrated organic system, k-(ET)2Cu2(CN)3. Synth Met 152 393-396... 

This constitutes a critical condition for the Mott-transition. The condition may be also written in terms of the charge density n ... 

To put it on a more quantitative basis, Johansson uses the expression for the critical point of the Mott transition as reformulated by Hubbard in terms of the bandwidth W[ and the polar state formation energy Uh (or effective intra-atomic correlation) (Eq. (36)). 

In Chap. E, photoelectron spectroscopic methods, in recent times more and more employed to the study of actinide solids, are reviewed. Results on metals and on oxides, which are representative of two types of bonds, the metallic and ionic, opposite with respect to the problem itineracy vs. localization of 5f states, are discussed. In metals photoemission gives a photographic picture of the Mott transition between Pu and Am. In oxides, the use of photoelectron spectroscopy (direct and inverse photoemission) permits a measurement of the intra-atomic Coulomb interaction energy Uh. 

The first part of the chapter is devoted to an analysis of these correlations, as well as to the presentation of the most important experimental results. In a second part the following stage of development is reviewed, i.e. the introduction of more quantitative theories mostly based on bond structure calculations. These theories are given a thermodynamic form (equation of states at zero temperature), and explain the typical behaviour of such ground state properties as cohesive energies, atomic volumes, and bulk moduli across the series. They employ in their simplest form the Friedel model extended from the d- to the 5f-itinerant state. The Mott transition (between plutonium and americium metals) finds a good justification within this frame. 

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... 

After a survey of the basic theory and some experimental aspects of photoelectron spectroscopy which are relevant to actinide solids, two systems are illustrated elemental actinide metals, in which the Mott transition between plutonium and americium is evidenced in a photographic way by photoemission, and strongly ionic oxides, in which the 5f localized behaviour is clearly seen, and indications of f-p or d-p covalent mixing are investigated. 

On the basis of the known electronic properties of actinides (which have been discussed elsewhere in this book), theoreticians had distinguished the 5f itinerant behaviour of light actinide metals from the 5 f localized behaviour of heavy actinide metals from Am on. The crossover, presented often as a Mott transition, had been predicted to occur between Pu and Am metal, due to the localized character of the 5f state in the latter. Photoemission spectroscopy demonstrates this phenomenon directly with the observation of a 5 f multiplet away from the Fermi level. The detailed description of this peak is certainly complicated, as often happens for response of localized states in photoemission on the other hand (Fig. 17) the contrast to the emission of Pu metal is convincing. 

The three basic ground state properties of the heavy actinides are more likely to follow those of the rare earths (Fig. 2 of Chap. A). The atomic volumes of the rare earth metals decrease monotonically with atomic number. This suggests, as will be explained more fully below, that the 4f electrons make little or no contribution to cohesion. They are said to be on the low density side of a Mott transition - with the notable exception of one of the phases of cerium. This is believed to be also the case for the second half of the actinide series ... 

The great vivacity of the debate centered around the above ideas, has triggered a flourishing of experimental efforts in all fields, attracting on actinides the attention of non-actinide scientists. Uranium systems have been, of course, the most studied, since they do not present all the characteristics of hazards and the needs of special protections the other actinides do. Nevertheless, attention should be given and is given to Pu and Am, where the Mott-transition of the 5 f metallic bond occurs. 

Hubbard (13) elucidated a mathematical description of the change from one situation to another for the simplest case of a half-filled s band of a solid. His result is shown in Figure 11. For ratios of W/U greater than the critical value of 2/ /3 then a Fermi surface should be found and the system can be a metal. This critical point is associated with the Mott transition from metal to insulator. At smaller values than this parameter, then, a correlation, or Hubbard, gap exists and the system is an antiferromagnetic insulator. Both the undoped 2-1 -4 compound and the nickel analog of the one dimensional platinum chain are systems of this type. At the far left-hand side of Figure 11 we show pictorially the orbital occupancy of the upper and lower Hubbard bands. 

Mott transition. Wigner (1938) introduced the idea of electron-electron interactions and suggested that at low densities, a free-electron gas should crystallize ... 

Many papers have been published on the theory of die Kondo effect, including some exact solutions. We recommend the 260 page review by Tsvelich and Weigmann (1983). Our aim in giving a simple non-mathematical account is to point out the similarity between the enhancement of the effective mass that occurs in crystalline metallic systems near to the conditions for a Mott transition (Chapter 4), and also to address the possible effects of free spins in doped semiconductors near the transition (Chapter 5). 

In this book we treat the discontinuous nature of the transition using an analysis introduced by Brinkman and Rice (1970a, b). This applies to bandcrossing transitions and transitions in an array of one-electron centres. We term the latter Mott transitions when the centres have a moment we do not limit the term to cases when the moment is that of a single spin, and indeed such cases are rare (Chapter 3). The insulating antiferromagnetic state is sometimes called a Mott insulator . A Mott transition can be accompanied by a change of structure (see Section 3 below). 

We turn now to an evaluation of nc, the concentration of centres at which the transition occurs. We remark first of all that an experimental value is difficult to obtain. We do not know of a crystalline system, with one electron per centre in an s-state, that shows a Mott transition. Figure 5.3 in the next chapter shows the well-known plot given by Edwards and Sienko (1978) for nc versus the hydrogen radius aH for a large number of doped semiconductors, giving ncaH=0.26. In all of these the positions of the donors are random, and it is now believed that for many, if not all, the transition is of Anderson type. In fluid caesium and metal-ammonia solutions the two-phase region is expected, but this is complicated by the tendency of one-electron centres to form diamagnetic pairs (as they do in V02). In the Mott transition in transitional-metal oxides the electrons are in d-states. 

It can be seen that e2 drops linearly at first, but has lower slope near the transition. There is no discontinuity, as would be expected for a Mott transition in a crystal (Chapter 4), and, as we believe, occurs (though broadened by temperature) in liquids such as fluid caesium (Chapter 10). The disorder here is greater than in a liquid metal because the orbitals of the electrons in the donors can overlap strongly. The present author (Mott 1978) has given conditions under which disorder can remove the discontinuity but this may not be relevant to such materials as Si P, because (Section 12) the Hubbard gap has disappeared, at any rate in many-valley semiconductors, at a concentration well below the transition,... 

Many authors have discussed a dielectric catastrophe and the Mott transition in terms of the Clausius-Mossotti relationship... 

Anderson type (though affected of course by long-range interaction). Until recently it was supposed by the present author that the former is the case. We must now favour, however, the latter assumption for many-valley materials (e.g. Si and Ge), the Hubbard gap opening up only for a value of the concentration n below nc. The first piece of evidence comes from a calculation of Bhatt and Rice (1981), who found that for many-valley materials this must be so. The second comes from the observations of Hirsch and Holcomb (1987) that compensation in Si P leads to localization for a smaller value of nc than in its absence. As pointed out by Mott (1988), a Mott transition occurs when B = U (B is the bandwidth, U the Hubbard intra-atomic interaction), while an Anderson transition should be found when B 2 V, where V is some disorder parameter. Since U e2/jcuH, where aH is the hydrogen radius, and K e2/jca, and since at the transition a 4aH, if the transition were of Mott type then it should be the other way round. 

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