Insulating states

As mentioned previously, the negative magnetoresistance (MR) in metallic (CH) and PPV samples is quite sensitive to the extent of disorder [2, 3]. Even in the case of well-oriented metallic samples of (CH) and PPV, a marginal increase in disorder can easily suppress the quantum interference process involved in the WL contribution to negative MR [1135]. As disorder increases and the system moves toward the critical and insulating regimes, the posi- 

The Curie term in x(.T) is rather dominant, at low temperatures, for systems in the critical and insulating regimes. The temperature-independent Pauli term is usually observed at T 100 K. However, the x(T) is not as sensitive as o(I) and MR for identifying the metallic, critical, and insulating regimes near the M-I transition [2]. 

Nevertheless, many conjugated polymers undergo a transition from such a nonlinear excitation state to a metallic state at high 

These nonmetallic behaviors arise from the disorder of the sample, originating from a combination of molecular-scale disorder and mesoscale inhomogeneity. Such disorder suppresses the intrinsic metallic properties of conducting polymers, complicating their electronic properties. Indeed, it is well known that sufficient disorder causes the localization of the states, thereby inducing the metal-insulator (M-I) transition in spite of the finite density of states at the Fermi level [1125,1156,1157]. In such a system, the charge dynamics are expected to be inherently different from those of traditional metals. 

However, although the linear and nonlinear optical properties of conjugated polymers have been investigated for over a decade. 

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Dynamic properties. On the basis of cyclic voltammetry, Diaz et al. (1981) showed that thin films of polypyrrole on an electrode immersed in acetonitrile could be repeatedly driven between the conducting and insulating states, as shown by the stability of the cyclic voltammograms of the films (see Figure 3.73). 

The competition between these two terms produces a large variety of electronic structures in molecular systems. The condition l U favors itinerant metallic states, whereas the condition t stabilizes localized insulating states. In the latter case, the Hubbard Hamiltonian is reduced to the Heisenberg Hamiltonian... 

Komatsu T, Kojima N, Saito G (1997) Ambient-pressure superconductivity of k -(BEDT-TTF)2Cu2(CN)3 realized by a carrier-doping into a Mott-insulating state. Synth Met 85 1519-1520... 

Figure 3. For the half filhng case all the probabilities are equal for U = 0. For Uc 9 we have a transition from the metallic to the insulator state which is of first order at half filling and second order for other concentration as seen for n = 0.48.

There are two competing mechanisms to produce an insulating state for the half-filled o band. One is through valency disproportionation, and this is the case for BaBiOs, i.e., 2BiIV — Bira + Biv. If BiIV had not disproportionated in BaBiOj, we would expect this compound to be metallic because it would have a half-filled band. Many have been confused by this disproportionation description because of confusion about the meaning of valent states as opposed to real charges. We will come back to the subject later. 

In what follows we should bear in mind that the generation of a diamagnetic metallic state (irrespective of whether it is a superconductor or not) will not be favored by a half-filled band of electrons. Either a Peierls distortion or the generation of an antiferromagnetic insulating state will result, with a ferromagnet being less likely for the reasons discussed. Superconductivity in these materials is in fact only observed if electrons are removed, or (less commonly to date) added to the half-filled band. Considerable effort is underway to theoreti-... 

Figure 6.51 Phase diagram for transition-metal compounds in the f//t and A/t space showing the parameter ranges for metallic and insulating states (after Sarma et al., 1992).

In materials in which a metal-insulator transition takes place the antiferromagnetic insulating state is not the only non-metallic one possible. Thus in V02 and its alloys, which in the metallic state have the rutile structure, at low temperatures the vanadium atoms form pairs along the c-axis and the moments disappear. This gives the possibility of describing the low-temperature phase by normal band theory, but this would certainly be a bad approximation the Hubbard U is still the major term in determining the band gap. One ought to describe each pair by a London-Heitler type of wave function... 

We emphasize that, in the insulating state, the gap is given by U- j(B1+ B2), and that it depends on the existence of moments and not on whether or not they are ordered. The gap is not related to the crystal structure. Indeed, if the crystal structure is such as to predict a gap, no antiferromagnetic lattice can form, unless the gap resulting from the Hubbard U is greater than that derived from the crystal structure. 

Impurity conduction can also be studied in compensated semiconductors, i.e. materials containing acceptors as well as donors, the majority carriers (or the other way round). For such materials, even at low concentrations, activated hopping conduction can occur (Chapter 1, Section 15), some of the donors being unoccupied so that an electron can move from an occupied to an empty centre. Here too a metal-insulator transition can be observed, which is certainly of Anderson type, the insulating state being essentially a result of disorder. 

The resistivities of the mixed crystals are shown in Fig. 6.22. It can be seen that (as indeed follows from the phase diagram, Fig. 6.20) the transition to the insulating state occurs with larger x for increasing temperature, probably because of the high entropy of the AF insulator above its Neel temperature. 

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