Metal Insulator Transition

The temperature dependence of conductivity r(T) for unoriented (CH)X is typical of an insulator. By increasing the orientation of chains/fibrils, a(T) becomes weaker both parallel and perpendicular to the chain axis [14]. Although oj / t l 100, the behavior of cr(T), and consequently the mechanism for charge transport, is nearly identical in both cases (oj and r ). Moreover, this indicates that weak interchain transport plays the limiting role in bulk charge transport properties. 

The role of the carrier density in M-I transitions is shown for an oriented sulfuric acid-polyparaphenylenevinylene (PPV-H2SO4) sample. The optical anisotropy of this oriented PPV sample, from dichroic ratio measurements at 1520 cm 1, is nearly 50 [15]. The value of pr continuously increases upon reducing the carrier density by systematically dedoping the sample, as shown in Fig. 3.4. However, it is difficult to locate the M I transition from the a vs. T plot alone. Instead, the W = d(ln r)/d(lnT) vs. T plot for the same data is shown in Fig. 3.5. If the system is in the metallic regime with a weak negative TCR, then W shows a positive temperature coefficient at low temperatures. Moreover, this ensures that there is a finite conductivity as T — 0. As pr increases, W(T) gradually moves from positive (metallic) to negative 

The metallic state in PPV-H2SO4 (o- 10000 S/cm, T /ctj 100, pr 2, crystalline fraction roughly 70%, crystalline coherence length roughly 80 A) can be described [13,15] by the localization-interaction model  

In oriented metallic conducting polymers, with large anisotropy in conductivity, the anisotropic diffusion coefficient factor should be taken into account in the above model. The robustness of this metallic state can be verified from the field dependence of conductivity at low temperatures. For example, in the case of sample E with oj 2 200 S/cm (see Fig. 3.4), which is just on the metallic side of the M-I transition, a field of 8 T can induce a transition to the insulating state, as shown in Fig. 3.7. The corresponding W vs. T plot (Fig. 3.7a) is consistent with the fact that the system has moved from the metallic to the critical/insulating side. This is a typical example 

The lack of agreement with experiments is often blamed on the electronic correlation effects. However, this is not always justified. The wave functions for localized and delocalized systems are very different, but the difference is often in the mathematical form of the orbitals rather than in the number of configurations in the wave function. It is necessary to specify which type of correlation effects are present and this will be attempted next. 

Boer and Verwey were committed to applying the band model. Obviously, the 3d of nickel is unfilled, and thus they expected a metal. After decades of futile attempts to improve the band model, John Hubbard took the pragmatic approach to simply add a positive number (U) to the unoccupied electronic levels, where the band gap appears experimentally (the Fermi level). Later, Neville Mott came up with an explanation. According to him, the system was indeed localized. The meaning of U is that energy is needed to transfer one electron from one site to the next. In NiO, we have to transfer one electron between two Ni + sites, to form NF and Ni +. 

It now appeared as justified to add U at the Fermi level. However, since the model was still the band model, not much was gained because the wave function is still incorrect. 

Transition metal crystals with oxygen ligands (for example, MnO, FeO, CoO, NiO, CuO, nickelates, and cuprates with a single valence state +2 on nickel and 

FIGURE 16.7 (See color insert) Nickel oxide (a) and aqueous solution of NiS04 (b). The green color is due to ligand field transitions in the Ni06 complex. 

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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. 

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],... 

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. 

Knight Shifts and Metal-Insulator Transition in Doped Silicon... 

Perhaps not surprisingly, the most thorough NMR studies of Knight shifts, Korringa relaxation, metal-insulator transitions, and the NMR of the dopant nuclei themselves have been carried out for doped silicon. Since few semiconductors other than PbTe, which presents a considerably more complicated case, have been studied in such detail, it is worthwhile here to summarize salient points from these studies. They conveniently illustrate a number of points, and can shed light on the behavior to be expected in more contemporary studies of compound semiconductors, which are often hindered by the lack of availability of a suite of samples of known and widely-varying carrier concentrations. 

We saw in Section 12.2.3.1 that the presence of additional chalcogen atoms in BEDT-TTF/TCNQ promotes interstack interactions, suppressing the Peierls distortion and imparting upon the salt increased dimensionality compared to TTF/TCNQ. The result of including a different chalcogen into the TTF/TCNQ structure is shown in Table 2. Despite losing donor efficiency compared to TTF (Table 1) the TCNQ complexes of m/trans-diselenadithiafulvalene (DSDTF, 55/56) and TSF show an improvement in conductivity when two or four selenium atoms are incorporated. The reduced metal-insulator transition suggests that this effect is also caused by a suppression of the Peierls distortion. Increased Se-Se interstack contacts add dimensionality to the structure and limit the co-facial dimerisation typical of Peierls distortion. Wider conduction bands are afforded from the improved overlap of diffuse orbitals. 

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. 

Mach-Zehnder interferometer, 144 Medical applications, 153 Metal-insulator transitions, 52 Monte Carlo procedure, 135 Multi-energy X-ray imaging, 131 Multilayer targets, 131 Multiphoton absorption, 85 Multiphoton ionization, 82 Multiple filamentation, 91, 92 Multipulse techniques, 152... 

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. 

N. F. Mott, Metal-Insulator Transitions, Taylor and Francis, London, 1974, p. 35 ff. 

Titanium dioxide crystallizes in several forms. The most important is the rutile form. This structure is also adopted by S11O2, MgF2, and ZnF2. A number of oxides that show metallic or metal-insulator transitions, for example, VO2, NbC>2, and Cr02, have a slightly distorted form of the structure. 

R Menon, CO Yoon, D Moses, and AJ Heeger, Metal-insulator transition in doped conducting polymers, in Handbook of Conducting Polymers, T.A. Skotheim, R.L. Elsenbaumer, and J.R. Reynolds, Eds., Marcel Dekker, New York, 1998, pp. 27-84. 

UIt) — (U/t) measures the deviation distance of the system away from the critical state with (U/t) = 12.5, which is exactly equal to the critical value for metal-insulator transition when the same order parameter U/t is used [92-94]. = q is the correlation length of the system with the critical expo-... 

After publication of the X-ray study, the charge transfer was obtained from the reciprocal-space position of the satellite reflections, which occur in the diffraction pattern at temperatures below the Peierls-type metal-insulator transition at 53 K (Pouget et al. 1976). Assuming that the gap in the band structure occurs at twice the Fermi wavevector, that is, at 2kF, the position of the satellite reflections corresponds to a charge transfer of 0.59 e, in excellent agreement with the direct integration. The agreement confirms the assumption that the gap in the band structure occurs at 2kF. 

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