Pseudogaps and metal-insulator transitions

For the subject matter of this book, it is of particular interest to consider the situation for a non-crystalline system analogous to that of crystalline ytterbium or strontium under pressure, namely that when a valence and conduction band are separate or overlap slightly. If the degree of overlap can be changed by varying the mean distance between atoms, the composition or the coordination number then a metal-insulator transition can occur. Many examples will be discussed in this book, particularly amorphous films of composition (Mgi- )j(By3, liquid mercury at low densities, and liquid tellurium alloys in which the coordination number changes with temperature. The transition is, we believe, of Anderson type. 

If a conduction and valence band overlap slightly then a pseudogap or minimum in the density of states (Fig. 1.32) is expected, as first suggested by Mott (1966). As long as the overlap is small, one would expect the density of states, all 

As in previous sections, we introduce the Mott -factor, though here we must define it as being proportional to the density of states at the Fermi level, and normalized so that 

We emphasize that the use of g in these equations may be justified only if /—a, because of the Edwards cancellation theorem (Section 6). We should expect a metal-insulator transition to occur for some value of in the neighbourhood of For several liquid systems there is experimental evidence that the interference term in (52) is absent. Thus for liquid TeTl alloys, with variation of composition and temperature, for a less than the Ioffe-Regel value e2/3hai the conductivity is proportional to the square of the Pauli paramagnetic susceptibility and then to 2. These results are due to Cutler (1977). Warren (1970a, b, 1972a, b) examined 

Mott (1985,1989a) proposed that in liquids all collisions are inelastic, so that l—Li and the interference term in (52) vanishes. Thus, in a sense, rmin exists for liquids (see Chapter 10). We have to ask, however, whether localization exists under these conditions. The same problem exists in certain amorphous solids, where strong phonon interaction leads over a certain temperature range to the relation Lx a. We find that, as the energy drops into a region of small density of states, increases and the normal localization condition again becomes valid. 

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