Interactions lattice-electron

The electron-lattice interaction is introduced through the dependence of the electron hopping amplitude on the carbon-carbon bond length ... 

If the information of the potential of electron-lattice interactions, expressed by V, is incorporated into the expression of the electron mass, then the total energy of electron in the lattice can be... 

Besides magnetic perturbations and electron-lattice interactions, there are other instabilities in solids which have to be considered. For example, one-dimensional solids cannot be metallic since a periodic lattice distortion (Peierls distortion) destroys the Fermi surface in such a system. The perturbation of the electron states results in charge-density waves (CDW), involving a periodicity in electron density in phase with the lattice distortion. Blue molybdenum bronzes, K0.3M0O3, show such features (see Section 4.9 for details). In two- or three-dimensional solids, however, one observes Fermi surface nesting due to the presence of parallel Fermi surface planes perturbed by periodic lattice distortions. Certain molybdenum bronzes exhibit this behaviour. 

Here jtt is the chemical potential of electrons in the semiconductor (the electron-lattice interaction energy) and /if is the electrochemical potential of an electron in phase 5, normally known as the Fermi level (see Appendix A for explanation of the difference). Similarly, the inner potential of the membrane (3) is... 

The Jahn-Teller effect is associated with electron-lattice interactions. In particular, when the electronic states of the nondistorted molecule are degenerate, the Jahn-Teller effect removes this degeneracy by distorting the molecule. Orbital ordering can also lead to a cooperative Jahn-Teller distortion and three-dimensional ferromagnetic ordering. 

Keywords Electron-lattice interaction, phonons, Spin Peierls, Angle Resolved... 

Fig. 12 Complexity of the problem of marginal metallicity (adapted from ref. 27). The oxides discussed in this article fall somewhere in the three-dimensional space indicated here. The other factors include electron-lattice interaction, magnetic polaron and finite temperature effects.

Electrons, however, don t have a common velocity in fact, laws of physics say that in a current, they cannot. How then could one expect that electrons would run in such harmony Bardeen, who had independently visualized an electron-lattice interaction, sought to answer this and eventually realized that another ingredient was necessary to explain superconductivity. That ingredient, he suggested, was what is known as a condensation in velocity. 

Questions that had been of fundamental importance to quantum chemistry for many decades were addressed. When the existence of bond alternation in trans-polyacetylene was been demonstrated [14,15], a fundamental issue that dates to the beginnings of quantum chemistry was resolved. The relative importance of the electron-electron and electron-lattice interactions in Ti-electron macromolecules quickly emerged as an issue and continues to be vigorously debated even today. Aspects of the theory of one-dimensional electronic structures were applied to these real systems. The important role of disorder on the electronic structure and properties of these low dimensional metals and semiconductors was immediately evident. The importance of structural relaxation in the excited state (solitons, polarons and bipolarons) quickly emerged. 

A. Band structure, electron—lattice interaction, electron—electron interaction and disorder... 

In the diffuse X-ray measurements of TTF-TCNQ the superlattice reflection was found with the wave number 4kp = 0.59 b [56]. It is observed even at room temperature and suggests the absence of the interchain correlation above 49 K. A set of superlattice reflection was found below 49 K suggesting the formation of an ordered structure of three-dimension. This superstructure is ascribed to the molecular displacement caused by the Wigner crystal of electrons through the electron-lattice interaction [67]. The 4 p structure is considered to be formed predominantly on the TTF stacks. The 2kp superstructure is rather ascribed to TCNQ stacks. This is suggested [68] by detailed analyses of the results of X-ray, neutron, EPR and NMR measurements. 

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