Mott-type transition

Specific Electric Conductivity The specific electric conductivities a of LGS, LGN and LGT were measured using a four-point technique at temperatures between 795 and 1000 K on crystal slices cut perpendicular to the Z-axes. The temperature dependence of the conductivities in dielectric materials with a limited defect density are caused by localized electronic states, and thus the data yield a straight line in a plot of In c versus 1/T, the slope of which is a measure of the activation energy AE of the charge carriers in a Mott-type transition model. These activation energies were found to be 1.1 (LGS), 1.0 (LGN) and 0.9 (LGT) eV, respectively. The rather strong increase in electric conductivity (LGS 10 Q cm at 530°C, 5 X lO- Q- cm- at 730 °C LGT lO- fi- cm" at 600 °C, 8 x 10-"Q- cm- at 730 °C) appears to limit the high-temperature applications of these materials. 

In Fig. 6, it is seen that the metallic radius of americium metal is not obtained when applying the simplified Friedel-type model which, on the contrary, explains well the metallic radii of Pa, U, and, to some extent, of Np and Pu. Between Pu and Am we have indicated the Mott-like transition proposed by Johansson which was discussed in Chapt. A. This transition from itinerant to localized behaviour occurs because of the... 

For a transition of Mott type we shall show in Chapter 4, Section 3, neglecting the discontinuity resulting from long-range forces, that the transition should occur when 2zl = U. Near the transition the energy needed to excite an electron into the upper Hubbard band is U — 2zl. The wave function of an electron then falls off as e-fltr, where a=2m(I7 — 2zI)1/2/fc2. Thus the amount of spin in the sphere surrounding each atom will be made up from electrons on many of the surrounding atoms, and will clearly go to zero as [Pg.88]

The susceptibility is expected to appear as in Fig. 4.9. In the first edition of this book we quoted results due to Quirt and Marko (1973) on metallic Si P near the concentration for the metal-insulator transition that show just this behaviour. However, it is now clear (see Chapter 5) that the transition in Si P is not of Mott type, so this must be accidental. 

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. 

A prediction of theory (Chapter 4) is that when an insulator-metal transition of either band-crossing or Mott type occurs through a change of composition in an alloy, the zero-temperature conductivity should jump discontinuously from zero to a finite value. This seems to be the case for the alloys with Ti203. The alloys with titanium have a conductivity when metallic of order 104 1 cm-1 at... 

We now consider the nature of the transition. In compensated Si P the transition takes place in an impurity band for high concentrations of dopant this merges with the conduction band. In uncompensated Si P the many-valley structure of the conduction band leads to a kind of self-compensation so that N( F) is already finite at the transition (Chapter 5), and the transition is of Anderson type. Whether this is so for p-type material or for single-valley materials is not known. If not then the transition must be of Mott type (Chapter 4), occurring when B U. 

By adsorption of metal atoms, one can induce various reconstructed surfaces that show metal-insulator phase transitions. Some transitions apparently are of the Mott type [73], whereas the driving mechanism of others is still subject to discussion, particularly considering the role of defects. Glasslike, disordered states have been found, which are very similar to theoretical predictions for phase separation in correlated electron systems [105]. 

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... 

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. 

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. 

For the metals Co, Ni and Pd and perhaps others it appears to be a good approximation to assume, in spite of the hybridization, that part of the Fermi surface is s-like with mrff me, and part d-hke with meff me. The current is then carried by the former, and the resistance is due to phonon-induced s-d transitions. This model was first put forward by Mott (1935) and developed by many other authors (e.g. Coles and Taylor 1962) for reviews see Mott (1964) and Dugdale and Guenault (1966). Applications of the model have also been made to ordered alloys of the type Al6Mn, Al7Cr by Griiner et al (1974), where the width A of the d-band is the same as it would be for an isolated transitional-metal atom in the matrix, but most of the Fermi surface is assumed to be (s-p)-like. The behaviour of the disordered Pd-Ag alloy series is particularly interesting. The 4d-bands of the two constituents are well separated, as shown particularly by... 

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. 

In earlier work (see e.g. Mott 1987) the present author has attempted to combine the hypothesis that the Hubbard U determines the value of nc in doped semiconductors with the observation that the transition shows the properties of one of Anderson type (second order, cv = 0, quantum interference and interaction effects) by supposing that two Hubbard bands, separated by U, have small localized tails, as in Fig. 5.13, and that the transition occurs for a value of nc such... 

In the case discussed here a Mott transition is unlikely the Hubbard U deduced from the Neel temperature is not relevant if the carriers are in the s-p oxygen band, but if the carriers have their mass enhanced by spin-polaron formation then the condition B U for a Mott transition seems improbable. In those materials no compensation is expected. We suppose, then, that the metallic behaviour does not occur until the impurity band has merged with the valence band. The transition will then be of Anderson type, occurring when the random potential resulting from the dopants is no longer sufficient to produce localization at the Fermi energy. 

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