Band structure general

More importantly, massless charge carriers in graphene can give rise to a room temperature quantum Hall effect (QHE) that was exclusively observed in two-dimensional electron gas (2DEG) systems earlier. The QHE on graphene is different from conventional cases of semiconductor heterostructures because of the unique band structure. Generally, the Hall resistance as a function of concentration of electrons produces a series of plateaus at jh/2eB, which is referred to as integer... 

Based on measurements in the UV-visible region, the interband transitions (band structures) can be characterized. As the band structure generally varies... 

The primary reason for interest in extended Huckel today is because the method is general enough to use for all the elements in the periodic table. This is not an extremely accurate or sophisticated method however, it is still used for inorganic modeling due to the scarcity of full periodic table methods with reasonable CPU time requirements. Another current use is for computing band structures, which are extremely computation-intensive calculations. Because of this, extended Huckel is often the method of choice for band structure calculations. It is also a very convenient way to view orbital symmetry. It is known to be fairly poor at predicting molecular geometries. 

The documentation is clearly written and generally adequate, although some of the less frequently used functions and utilities were not documented. The user should have a basic understanding of band structure theory before attempting to read the documentation. 

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. 

Two Hell UPS spectra of poly(3-hexylthiophene), or P3HT, compared with the DOVS derived from VEH band structure calculations 83], arc shown in Figure 5-14. The general chemical structure of poIy(3-a ky thiophcne) is sketched in Figure 5-4. The two UPS spectra, were recorded at two different temperatures, +190°C and -60 "C, respectively, and the DOVS was derived from VEH calculations on a planar conformation of P3HT. Compared to unsubslitutcd polythio-phene, the main influence in the UPS spectra due to the presence of the hexyl... 

The SCF method for molecules has been extended into the Crystal Orbital (CO) method for systems with ID- or 3D- translational periodicityiMi). The CO method is in fact the band theory method of solid state theory applied in the spirit of molecular orbital methods. It is used to obtain the band structure as a means to explain the conductivity in these materials, and we have done so in our study of polyacetylene. There are however some difficulties associated with the use of the CO method to describe impurities or defects in polymers. The periodicity assumed in the CO formalism implies that impurities have the same periodicity. Thus the unit cell on which the translational periodicity is applied must be chosen carefully in such a way that the repeating impurities do not interact. In general this requirement implies that the unit cell be very large, a feature which results in extremely demanding computations and thus hinders the use of the CO method for the study of impurities. 

The description derived above gives useful insight into the general characteristics of the band structure in solids. In reality, band structure is far more complex than suggested by Fig. 6.16, as a result of the inclusion of three dimensions, and due to the presence of many types of orbitals that form bands. The detailed electronic structure determines the physical and chemical properties of the solids, in particular whether a solid is a conductor, semiconductor, or insulator (Fig. 6.17). 

A group of scientists have studied current transients in biased M-O-M structures.271,300 The general behavior of such a system may be described by classic theoretical work.268,302 However, the specific behavior of current transients in anodic oxides made it necessary to develop a special model for nonsteady current flow applicable to this case. Aris and Lewis have put forward an assumption that current transients in anodic oxides are due to carrier trapping and release in the two systems of localized states (shallow and deep traps) associated with oxygen vacancies and/or incorporated impurities.301 This approach was further supported by others,271,279 and it generally resembles the oxide band structure theoretically modeled by Parkhutik and Shershulskii62 (see. Fig. 37). 

The band structure that appears as a consequence of the periodic potential provides a logical explanation of the different conductivities of electrons in solids. It is a simple case of how the energy bands are structured and arranged with respect to the Fermi level. In general, for any solid there is a set of energy bands, each separated from the next by an energy gap. The top of this set of bands (the valence band) intersects the Fermi level and will be either full of electrons, partially filled, or empty. 

For a discussion on general properties for the three-connected nets (the A1B2 and ThSi2 structures and their transition metal derivatives) see Zheng and Hoffmann (1989). Characteristic band structures were presented for these two compounds and their derivative structures (CaCuGe, LaPtSi) and other three-connected nets... 

The empirical approach [7] was by far the most fruitful first attempt. The idea was to fit a few Fourier coefficients or form factors of the potential. This approach assumed that the pseudopotential could be represented accurately with around three Fourier form factors for each element and that the potential contained both the electron-core and electron-electron interactions. The form factors were generally fit to optical properties. This approach, called the Empirical Pseudopotential Method (EPM), gave [7] extremely accurate energy band structures and wave functions, and applications were made to a large number of solids, especially semiconductors. [8] In fact, it is probably fair to say that the electronic band structure problem and optical properties in the visible and UV for the standard semiconductors was solved in the 1960s and 1970s by the EPM. Before the EPM, even the electronic structure of Si, which was and is the prototype semiconductor, was only partially known. 

CNTs can exhibit singular electronic band structures and can show metallic and semiconducting behavior. As a general rule, n.m tubes with n-m being an integer multiple of 3 are metallic, while the remaining tubes are semiconducting. 

However, it became evident in the post-war period that, valuable as they were, these band-structure concepts could not be applied even qualitatively to key systems of industrial interest notably steels, nickel-base alloys, and other emerging materials such as titanium and uranium alloys. This led to a resurgence of interest in a more general thermodynamic approach both in Europe (Meijering 1948, Hillert 1953, Lumsden 1952, Andrews 1956, Svechnikov and Lesnik 1956, Meijering 1957) and in the USA (Kaufman and Cohen 1956, Weiss and Tauer 1956, Kaufman and Cohen 1958, Betterton 1958). Initially much of the work related only to relatively simple binary or ternary systems and calculations were performed largely by individuals, each with their own methodology, and there was no attempt to produce a co-ordinated framework. 

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