The metal-insulator transition

We have seen in the previous section that disorder results in the localisation of charge carriers and that the conductivity will fall as a consequence of this. There is a minimum metallic conductivity, which corresponds to the electron mean free path being equal to the lattice repeat distance. The occurrence of the mobility edge means that in an amorphous metal the conductivity can switch 

---

In this chapter the results of detailed research on the realistic electronic structure of single-walled CNT (SWCNT) are summarised with explicit consideration of carbon-carbon bond-alternation patterns accompanied by the metal-insulator transition inherent in low-dimensional materials including CNT. Moreover, recent selective topics of electronic structures of CNT are also described. Throughout this chapter the terminology "CNT stands for SWCNT unless specially noted. 

Electronic structures of SWCNT have been reviewed. It has been shown that armchair-structural tubes (a, a) could probably remain metallic after energetical stabilisation in connection with the metal-insulator transition but that zigzag (3a, 0) and helical-structural tubes (a, b) would change into semiconductive even if the condition 2a + b = 3N s satisfied. There would not be so much difference in the electronic structures between MWCNT and SWCNT and these can be regarded electronically similar at least in the zeroth order approximation. Doping to CNT with either Lewis acid or base would newly cause intriguing electronic properties including superconductivity. 

In the framework of CUORICINO [41] and CUORE [42] experiments (see Section 16.5), Ge crystal wafers of natural isotopic composition have been doped by neutron irradiation, and the heavy doping led to materials close to the metal insulator transition. Several series of NTD wafers with different doping have been produced [43], After an implantation and metallization process on both sides of the wafers, thermistors of different sizes can be obtained by cutting the wafers and providing electrical contacts. 

Fig. 8 Temperature dependence of din f>/d(T 1), i.e., slope of the Arrhenius plot as a function of temperature for (a) (EDT-TTFBr2)FeBr4 at various pressures - the data for 0, 5.8 and 10.1 kbar are vertically shifted up by 60, 40 and 20 K, respectively, for clarity (b) (EDO-TTFBr2)2GaCl4 and (EDO-TTFBr2)2FeCl4 at 11 kbar. TMl and TN are the metal-insulator transition temperature and the Neel temperature, respectively, hi (b) the metal-insulator transition is observed as two separate peaks...

Collier, C. P. Saykally, R. J. Shiang, J. J. Henrichs, S. E. Heath, J. R. 1997. Reversible tuning of silver quantum dot monolayers through the metal-insulator transition. Science 277 1978-1981. 

Remarkably, the Wigner distribution could be observed in a number of systems by physical experiments and computer simulations evading the whole quantum world from atomic nuclei to the hydrogen atom in a magnetic field to the metal-insulator transition (Guhr, Muller-Groeling and Weidenmuller, 1998). In this contribution we address the situation in QCD and in hadrons. 

Aleshin A, Kiehooms R, Menon R, Heeger AJ (1997) Electronic transport in doped poly (3,4-ethylenedioxythiophene) near the metal-insulator transition. Synth Met 90 61-68... 

OF-KEDF s with the DD AWF emerged, " and a scheme to treat highly inhomogeneous systems like realistic surfaces was tested with semiquantitative success. " An immediate application to the study of the metal-insulator transition in a 2-dimensional array of metal nanocrystal quantum dots (with 498 A1 atoms per simulation cell) further magnifies its promise. ... 

For the theme of this book, namely the metal-insulator transition, it is important to realize that if the lattice parameter becomes larger, v(q) will get progressively more negative, as shown in Fig. 1.12. Expansion of most metals will at first decrease the gap and then enlarge it in mercury it will increase it from the beginning. 

This factor g is of major importance in discussing the metal-insulator transition resulting from disorder. Using the model of Fig. 1.17, we take... 

Very direct evidence for the existence of bound spin polarons is provided by the work of Torrance et al (1972) on the metal-insulator transition in Eu-rich EuO At low temperatures, when the moments on the Eu ions are ferromagnetically aligned, the electrons in the oxygen vacancies cannot form spin polarons and are present in sufficient concentration to give metallic conduction. Above the Curie temperature the conductivity drops by a factor of order 10 , because the electrons now polarize the surrounding moments, forming spin polarons with higher effective mass. 

This section does not attempt a survey of this large subject. Its aim is only to show briefly how metallic Ni, Co and Fe differ from the transitional-metal oxides that are of particular interest to us in connection with the metal-insulator transition. The former are in our view in a sense more complicated, because the number of electrons in the d-band is in all cases non-integral, while in metallic oxides (such as V203 under pressure and Cr02) this is not the case. 

In principle, then, the zero-temperature free energy of the system, plotted against volume or (in an alloy) composition, both denoted by x, must show a kink as illustrated in Fig. 4.2 at the metal-insulator transition. If x is the volume and this is decreased by pressure then there will be a discontinuous change of volume between B and A. If x denotes the composition then between B and A the alloy will be unstable, and will in equilibrium separate into two phases. The behaviour... 

We are interested in the situation near the metal-insulator transition when U 2zl, and for this case, from (10),... 

A point of some interest is the value of the moment on each atom and the Neel temperature at the metal-insulator transition. Putting B=U in equation (6) of Chapter 3 shows that the moment is reduced by a factor of 1 — (4z) 1 and that the Neel temperature at the transition, since B=U, is given by... 

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. 

Fig. 63 Generalized phase diagram of the metal-insulator transition in V203 as a function of doping with Cr or Ti and as a function of pressure, showing the critical point...

Clearly the metal-insulator transition is by no means so sharp as predicted for a first-order change of phase, but much disorder broadening is observed in the Raman spectra (Lemos et al. 1980). 

In some of the metal-insulator transitions discussed here the use of classical percolation theory has been used to describe the results. This will be valid if the carrier cannot tunnel through the potential barriers produced by the random internal field. This may be so for very heavy particles, such as dielectric or spin polarons. A review of percolation theory is given by Kirkpatrick (1973). One expects a conductivity behaving like... 

---