Mott insulators, electronic conductivity

Since the discovery of the first organic conductors based on TTF, [TTF]C1 in 1972 [38] and TTF - TCNQ in 1973 [39], TTF has been the elementary building block of hundreds of conducting salts [40] (1) charge-transfer salts if an electron acceptor such as TCNQ is used, and (2) cation radical salts when an innocent anion is introduced by electrocrystallization [41]. In both cases, a mixed-valence state of the TTF is required to allow for a metallic conductivity (Scheme 5), as the fully oxidized salts of TTF+ cation radicals most often either behave as Mott insulators (weakly interacting spins) or associate into... 

In this section we discuss the properties of an electron in the conduction band of an antiferromagnetic insulator. This may be a simple Mott insulator, but, since the experimental evidence is related to them, we first discuss materials like EuSe, where the europium ion has seven 4f-electrons and electrons can be introduced into the conduction band by doping with GdSe the ion Gd2 + has the same number of f-electrons but one more electron in an outer shell, so a Gd ion acts as a donor. 

Sufficiently cold atoms can be trapped in optical lattices, formed by a three-dimensional overlap of standing laser waves in x-, y-, and z-directions. If the kinetic energy of the atoms is lower than the potential energy minima of such lattices they are trapped in these minima and cannot leave their fixed positions. Such a state is called a Mott insulator (in analogy to the situation in solid state physics explained by Sir Nevil Mott where a Mott insulator describes a situation where electrical conductivity should be possible according to the band structure but the repulsive interaction between the electrons prevents electron transport). The potential well depth can be tuned by changing the intensity of the three laser beams. 

It was realized quite early that the parent, undoped, compounds should be viewed as Mott insulators. More recent studies of the doping dependence have revealed the generic features between cuprates and other classes of Mott insulators. The principal trends in the evolution of the in-plane electronic conductivity with doping are in accord with the results of the calculations performed for Mott-Hubbard systems as will be described in sect. 3. 

Mott insulators are a class of materials that should conduct electricity imder conventional band theories, but are insulators when measmed (particularly at low temperatures). This effect is due to electron-electron interactions which are not considered in conventional band theory. Mott insulators are of growing interest in advanced physics research, and are not yet fully imderstood. They have applications in thin-film magnetic hetero structures and high-temperature superconductivity, for example. 

A Mott insulator may become conducting after doping. If green NiO is doped with colorless Li20, a black substance appears with the formula Li Nq, 0. In other words, Li+ substitutes Ni + in some sites. To maintain electroneutrality, some NF+ sites have to be oxidized to Ni + (in air). Li+ and 0 cannot conduct electricity, so this has to be done by the nickel ions. In addition to the Mott reaction, where Ni+ and NF+ are created, conductivity may now be obtained by electron exchange between Ni + and Ni + in an Cg orbital with the same spin. At room temperature, the conductivity increases proportional to the number of NF+ sites when the latter number is small. The blackness is obviously due to intervalence transitions. The latter transitions tend to be broad and apparently cover most of the visible spectrum. 

The same result is obtained for other doped Mott insulators. The conductivity is low if the rate of ET is low. In CuO and NiO, the number of antibonding Og electrons is changed hence, there is a large difference in some bond lengths between different oxidation states and, consequently, a large reorganization energy. 

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