Band theory Peierls

It is the Peierl s instability that is believed to be responsible for the fact that most CPs in their neutral state are insulators or, at best, weak semiconductors. Hence, there is enough of an energy separation between the conduction and valence bands that thermal energy alone is insufficient to excite electrons across the band gap. To explain the conductive properties of these polymers, several concepts from band theory and solid state physics have been adopted. For electrical conductivity to occur, an electron must have a vacant place (a hole) to move to and occupy. When bands are completely filled or empty, conduction can not occur. Metals are highly conductive because they possess unfilled bands. Semiconductors possess an energy gap small enough that thermal excitation of electrons from the valence to the conduction bands is sufficient for conductivity however, the band gap in insulators is too large for thermal excitation of an electron accross the band gap. 

About one decade after the development of band theory, two Dutch industrial scientists at the NV Philips Corporation, Jan Hendrik de Boer (1899-1971) (de Boer was later associated with the Technological University, Delft) and Evert Johaimes Willem Verwey (1905-1981), reported that many transition metal oxides, with partially filled bands that band theory predicted to be metallic, were poor conductors and some were even insulating (de Boer and Verwey, 1937). Rudolph Peierls (1907-1995) first pointed out the possible importance of electron correlation in controlling the electrical behavior of these oxides (Peierls, 1937). Electron correlation is the term applied to the interaction between electrons via Coulombs law. 

The recent experimental confirmation of the existence of one-dimensional metallic systems has led to a rapid increase in the experimental and theoretical study of these conducting systems. The objective of this section is to acquaint the reader with the physical basis of the concepts currently being used to explain the experimental results. Emphasis is given to the development of one electron band theory because of its central importance in the description of metals and understanding the effects of lattice distortion (Peierls transition), electron correlation, disorder potentials, and interruptions in the strands. It... 

The tight-binding band theory and the accompanying Peierls instability discussion assumed that all electrons move independently of each other in a perfect uniform lattice. Electron-electron Coulomb repulsion, disorder, and interruptions in the strands alter the band theory results. These effects are important for the understanding of one-dimensional metals and are now introduced. 

ABSTRACT. The general concepts of quasi-one-dimensional conducting polymers are introduced including the role of band theory, electron-phonon interactions, the Peierls ground state, and commensurability. The dominant defect states present upon doping, solitons, polarons and bipolarons, are discussed. Application of these concepts to polyaniline is made with emphasis on the mechanism for the insulator-to-metal transition. 

In the Mott-Hubbard theory on the other hand, it is shown that there exists an instability in the narrow-band electronic structure (Peierls instabihty ) and if the bandwidth decreases below a critical value, a sudden transition (Mott transition) takes place toward a complete localized situation. In this approach, it is assumed, in fact, that band magnetism does not exist and one has to deal only with 2 classes of materials... 

Before the discovery of antiferromagnetism, it was pointed out that, according to the Wilson theory of metals and insulators (Chapter 1), nickel oxide should be a metal—whereas it is a transparent insulator. The nickel ions should have eight d-electrons, and the only splitting of the d-band to be expected is into the eg and t2g bands, with four and six electrons. Peierls explained in 1938 how this... 

Theoretical studiesof the Peierls distortion showthat within mean field theory its presence can be a function of temperature (261, 347, 349). This leads to a transition from a band metal to a band semiconductor/insulator as the temperature is lowered below the transition temperature, Tp, termed the Peierls transition. The characterization of the metal-insulator transition in KsPt(CN)4-Bro.3(H20)s as a Peierls transition has triggered much of the increased work on the theory of the Peierls transition. 

Conjngated polymers differ from crystalline semiconductors and metals in several aspects and are often treated theoretically as a one-dimensional system. The formation of the band gap is explained taking into account either electron-phonon interactions or electron-electron interactions among 7t-electrons. If electron-phonon interaction dominates in real 7t-conjugated polymers, these systems could be treated using Peierls theory. In contrast, when electron-electron interactions dominate, the Hubbard model could be used to explain the physical properties of polymers. 

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