Electrons metal-insulator transition

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. 

It is well known that metallic electronic structure is not generally realised in low-dimensional materials on account of metal-insulator transition (or Peierls transition [14]). This transition is formally required by energetical stabilisation and often accompanied with the bond alternation, an example of which is illustrated in Fig. 4 for metallic polyacetylene [15]. This kind of metal-insulator transition should also be checked for CNT satisfying 2a + b = 3N, since CNT is considered to belong to also low-dimensional materials. Representative bond-alternation patterns are shown in Fig. 5. Expression of band structures of any isodistant tubes (a, b) is equal to those in Eq.(2). Those for bond-alternation patterned tube a, b) are given by. 

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. 

Figure 6.17. DOS diagrams showing schematically the electron density around the Fermi level for a free-electron metal, a transition metal, and an insulator.

Composites containing nanometer-sized metal particles of a controllable and uniform size in an insulating ceramic matrix are very interesting materials for use as heterogeneous catalysts and for magnetic and electronic applications. They show quantum size effects, particularly the size-induced metal-insulator transition (SIMIT) [1],... 

Kanoda K (2006) Metal-insulator transition in k-(ET)2X and (DCNQI)2M two contrasting manifestation of electron correlation. J Phys Soc Jpn 75 051007/1-16... 

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... 

The trisulphides (and triselenides) of Ti, Zr, Hf, Nb and Ta crystallize in onedimensional structures formed by MSg trigonal prisms that share opposite faces. Metal atoms in these sulphides are formally in the quadrivalent state, and part of the sulphur exists as molecular anions, M S2 S . TaSj shows a metal-insulator transition of the Peierls type at low temperatures (Section 4.9). NbSj adopts a Peierls distorted insulating structure suggesting the possibility of a transformation to a metallic phase at high temperatures, but does not transform completely to the undistorted structure. Electronic properties and structural transitions of these sulphides have been reviewed (Rouxel et al, 1982 Meerschaut, 1982 Rouxel, 1992). 

An early success of quantum mechanics was the explanation by Wilson (1931a, b) of the reason for the sharp distinction between metals and non-metals. In crystalline materials the energies of the electron states lie in bands a non-metal is a material in which all bands are full or empty, while in a metal one or more bands are only partly full. This distinction has stood the test of time the Fermi energy of a metal, separating occupied from unoccupied states, and the Fermi surface separating them in k-space are not only features of a simple model in which electrons do not interact with one another, but have proved to be physical quantities that can be measured. Any metal-insulator transition in a crystalline material, at any rate at zero temperature, must be a transition from a situation in which bands overlap to a situation when they do not Band-crossing metal-insulator transitions, such as that of barium under pressure, are described in this book. 

For disordered systems, then, a quite different form of metal-insulator transition occurs—the Anderson transition. In these systems a range of energies exists in which the electron states are localized, and if at zero temperature the Fermi energy lies in this range then the material will not conduct, even though the density of states is not zero. The Anderson transition can be discussed in terms of non-interacting electrons, though in real systems electron-electron interaction plays an important part. 

Metal-insulator transitions in both crystalline and non-crystalline materials are often associated with the existence of magnetic moments. Moments on atoms in a solid are of course an effect of correlation, that is of interaction between electrons, and their full discussion is deferred until Chapter 3. But even within the approximation of non-interacting electrons in crystalline solids, metal-insulator transitions can occur. These will now be discussed. 

The electrons in a solid interact both with one another and with the lattice vibrations. A theme of this book is the effect of the interaction between electrons in inducing magnetic moments and metal-insulator transitions. Interaction with phonons also has an important effect, particularly in some transitional-metal oxides. In this chapter both kinds of interaction are introduced. 

An important property of the Fermi surface is that the volume (in /c-space) that it encloses is not altered by the interaction between the electrons, unless long-range antiferromagnetic order is set up. This was first shown by Luttinger (1960). We shall make use of this theorem in Chapter 4, Section 3 in discussing metal-insulator transitions due to correlation. 

We discuss in this section the effect of short-range interaction on the Anderson-localized states of a Fermi glass described in Chapter 1, Section 7, and in particular the question of whether the states are singly or doubly occupied. Ball (1971) was the first to discuss this problem. In this section we consider an electron gas that is far on the metal side of the Wigner transition (Chapter 8) the opposite situation is described in Chapter 6, where correlation gives rise to a metal-insulator transition. We also suppose that Anderson localization is weak (cca 1) otherwise it is probable that all states are singly occupied. 

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. 

If we neglect the electron-hole interaction, as in Chapter 1, then a metal-insulator transition should occur when the two bands overlap. For infinite values of a, the separation in energy between the two bands should be just the Hubbard Uy so the transition occurs when... 

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