Narrow band systems

X-Ray absorption data in combination with atomic theory and solid-state band-structure theory can yield detailed information about the ground-state electronic structure of solids on an energy scale on the order of meV. This holds particularly true for correlated narrow-band systems, such as the rare-earth and transition-metal compounds. In broad-band materials, such as the... 

It has been seen in the previous section that the ratio of the onsite electron-electron Coulomb repulsion and the one-electron bandwidth is a critical parameter. The Mott-Hubbard insulating state is observed when U > W, that is, with narrow-band systems like transition metal compounds. Disorder is another condition that localizes charge carriers. In crystalline solids, there are several possible types of disorder. One kind arises from the random placement of impurity atoms in lattice sites or interstitial sites. The term Anderson localization is applied to systems in which the charge carriers are localized by this type of disorder. Anderson localization is important in a wide range of materials, from phosphorus-doped silicon to the perovskite oxide strontium-doped lanthanum vanadate, Lai cSr t V03. 

MiiUer-Hartmann, E., 1981, In Electron correlation and magnetism in narrow band systems, ed. T. Moriya (Springer, Berlin) p. 178. 

A striking similarity between the charge transfer salts and oxides is the importance of electron correlations,and hence the proximity of superconducting and magnetic states in the phase diagrams, as a function of band filling or structural modifications. This arises from the fact that both types of compound are narrow-band systems. 

T. Moriya, ed.. Electron Correlation and Magnetism in Narrow-Band Systems, Springer Series in Solid State Sciences 29, Springer, Heidelberg, 1981. 

Unlike the diode laser, the transfer function of many modulators is easily expressible in a simple analytical form. For example, the Mach-Zehnder transfer function is a simple raised cosine, 1 + cosrp, as shown by the solid curve in Fig. 9.55. Consequently, the linearity is a predictable function of the chosen bias point. For example, operating a Mach-Zehnder at /2 forces aU of the even-order distortion terms to zero. Using this bias point in a broad-band application means that the IM-free DR is determined by the odd-order distortion, which is dominated by the third-order term. Recall that for narrow-band systems the second-order distortion terms fall outside the pass band and consequently can be filtered out. Thus, for such applications the bias point can be moved away from /2 with no system consequence. One reason... 

Calculations for Ceo in the LDA approximation [62, 60] yield a narrow band (- 0.4 0.6 eV bandwidth) solid, with a HOMO-LUMO-derived direct band gap of - 1.5 eV at the X point of the fee Brillouin zone. The narrow energy bands and the molecular nature of the electronic structure of fullerenes are indicative of a highly correlated electron system. Since the HOMO and LUMO levels both have the same odd parity, electric dipole transitions between these levels are symmetry forbidden in the free Ceo moleeule. In the crystalline solid, transitions between the direct bandgap states at the T and X points in the cubic Brillouin zone arc also forbidden, but are allowed at the lower symmetry points in the Brillouin zone. The allowed electric dipole... 

Samples and reference substances should be dissolved in the same solvents to ensure that comparable substance distribution occurs in all the starting zones. In order to keep the size of the starting zones down to a minimum (diameter TLC 2 to 4 mm, HPTLC 0.5 to 1 mm) the application volumes are normally limited to a maximum of 5 xl for TLC and 500 nl for HPTLC when the samples are applied as spots. Particularly in the case of adsorption-chromatographic systems layers with concentrating zones offer another possibility of producing small starting zones. Here the applied zones are compressed to narrow bands at the solvent front before the mobile phase reaches the active chromatographic layer. 

The copper system appears to behave similarly to the silver system, and it may be used here in order to illustrate the idea of "selective, naked-cluster cryophotochemistry 150,151). A typical series of optical-spectral traces that illustrate these effects for Cu atoms is given in Fig. 15, which shows the absorptions of isolated Cu atoms in the presence of small proportions of Cu2, and traces of Cus molecules. Under these concentration conditions, the outcome of 300-nm, narrow-band photoexcitation of atomic Cu is photoaggregation up to the Cus stage. The growth-decay behavior of the various cluster-absorptions allows unequivocal pinpointing of UV-visible, electronic transitions associated with Cuj and Cus 150). With the distribution of Cui,2,3 shown in Fig. 15, 370-nm, narrow-band excitation of Cu2 can be considered. Immediately apparent from these optical spectra is the growth (—10%) of the Cu atomic-resonance lines. Noticeable also is the concomitant... 

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