Electronic states instability

Electronic properties of CNTs, in particular, electronic states, optical spectra, lattice instabilities, and magnetic properties, have been discussed theoretically based on a k p scheme. The motion of electrons in CNTs is described by Weyl s equation for a massless neutrino, which turns into the Dirac equation for a massive electron in the presence of lattice distortions. This leads to interesting properties of CNTs in the presence of a magnetic field including various kinds of Aharonov-Bohm effects and field-induced lattice distortions. 

The SSH model (Eq. (3.2)) is, essentially, the model used by Peierls for his discussion of the electron-lattice instability [33]. Its ground state is characterized by a non-zero expectation value of the operator. 

Liehr, A. D., and C. J. Ballhausen Inherent configurational instability of octahedral inorganic complexes in Eg electronic states. Ann. Phys. 3, 304 (1958). 

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. 

From the three decay times, which each measurement provides, the main point of interest how is the type I quantity T. It characterizes the dynamics of the relevant electronic state of the cluster size under investigation. The data, therefore, allow us to determine directly the photodissociation probabilities 1/r 1 of the observed clusters excited at the energies of the photon irradiation. The corresponding results reflect the stability of the clusters, as graphically presented in Fig. 26. For all measured cluster sizes the fragmentation probabilities at E = 2.00 eV are smaller than those for the other photon energies (figs. 26a, b). For E = 2.00 eV and E = 2.94 eV the curves of the dependence of the photodissociation probability on the cluster size have similar shapes. In Fig. 26b both curves show a particular instability for Kg, which... 

The necessary and sufficient condition of instability (lack of minimum of the AP) of high-symmetry configurations of any polyatomic system is the presence of two or more electronic states, degenerate (except 2-fold spin degeneracy) or pseudodegenerate, which interact sufficiently strong under the nuclear displacements in the direction of instability . 

Linear molecules are the only exception to the Jahn-Teller effect. But linear molecules may also have instabilities in their degenerate electronic states and this is called the Renner-Teller effect. It was first described by Renner in a theoretical paper on the degenerate first excited electronic state of carbon dioxide [86], It took more than twenty years to find the first experimental evidence of this effect, in the electronic absorption spectrum of the NH2 radical [87], The NH2 radical has one electron on an orbital and thus a n electronic state... 

The electronic properties of organic conductors are discussed by physicists in terms of band structure and Fermi surface. The shape of the band structure is defined by the dispersion energy and characterizes the electronic properties of the material (semiconductor, semimetals, metals, etc.) the Fermi surface is the limit between empty and occupied electronic states, and its shape (open, closed, nested, etc.) characterizes the dimensionality of the electron gas. From band dispersion and filling one can easily deduce whether the studied material is a metal, a semiconductor, or an insulator (occurrence of a gap at the Fermi energy). The intra- and interchain band-widths can be estimated, for example, from normal-incidence polarized reflectance, and the densities of state at the Fermi level can be used in the modeling of physical observations. The Fermi surface topology is of importance to predict or explain the existence of instabilities of the electronic gas (nesting vector concept see Chapter 2 of this book). Fermi surfaces calculated from structural data can be compared to those observed by means of the Shubnikov-de Hass method in the case of two- or three-dimensional metals [152]. 

Our recent observation (jO of electronic state fluorescence from laser-excited PuFe(g) and NpFe(g) has marked the beginning of systematic studies of the photophysics and photochemistry of transuranic hexafluorides and has provided the key to further exploration of the complex vibronic structure characteristic of these compounds. While the photochemistry of UFe has been the object of numerous investigations, only a few remarks are found in the literature concerning the electronic state photochemistry of the transuranic hexafluorides. Given the dense electronic energy level structures of PuFe and NpFe and their relative instability in comparison with UFe, we can anticipate that their photochemistry will involve a rich and complex set of interactions. The work we report here deals primarily with PuF6(g). We turn first to a very brief review of PuFe studies... 

The surface relaxation on both SrTiOs (001) terminations has been calculated by various numerical approaches [45,189-193]. The surface rumpling is usually reasonably accounted for, but all calculations predict an inward relaxation for the Ti02 termination, in contradiction to experiments [194-196]. A particular attention has been focused on the energy of surface states, since the first study based on non-self-consistent calculations predicted that they were located deep in the gap [197,198]. All subsequent self-consistent calculations have contradicted this prediction [191,192,199,200], in agreement with photoemission and EELS results [201,202]. When calculated [191,192], the surface energy is rather low, an indication that no surface instability takes place, and there is no evidence of anomalous filling of electronic states. 

It follows that the evaluation of the extent to which one-dimensional physics is relevant has always played an important part in the debate surrounding the theoretical description of the normal state of these materials. One point of view expressed is that the amplitude of in the b direction is large enough for a FL component to develop in the ab plane, thereby governing most properties of the normal phase attainable below say room temperature. In this scenario, the anisotropic Fermi liquid then constitutes the basic electronic state from which various instabilities of the metallic state, like spin-density-wave, superconductivity, etc., arise [29]. Following the example of the BCS theory of superconductivity in conventional superconductors, it is the critical domain of the transition that ultimately limits the validity of the Fermi liquid picture in the low temperature domain. 

What thus really makes one dimension so peculiar resides in the fact that the symmetry of the spectrum for the Cooper and Peierls instabilities refer to the same phase space of electronic states [108]. The two different kinds of pairing act as independent and simultaneous processes of the electron-electron scattering amplitude which interfere with and distort each other at all order of perturbation theory. What comes out of this interference is neither a BCS superconductor nor a Peierls/density-wave superstructure but a different instability of the Fermi liquid called a Luttinger liquid. 

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