Electrons near the Fermi surface

It was stated previously that the expressions for conductivity and mobility obtained from the simple Drude theory also held in the quantum mechanical treatment of electrons in simple metals. Since only the electrons near the Fermi surface are able to respond to an applied electric field, we must integrate the available states over the Fermi surface. We can write the current density as... 

Fig. 6.5 Scattering between filled and empty states near the Fermi surface. For the Fermi sphere of a free-electron gas the maximum number of such events occurs for q = 2kf. For a Fermi surface with flat regions the number of such events is dramatically enhanced for q = Q, the spanning wave vector.

It is usually assumed that the e-p coupling perturbs only the electronic states near the Fermi surface within the energy hco, where co is the phonon frequency. However, this is true only for the Holstein coupling. In the SSH... 

The electronic structure near the Fermi surface is crudely estimated in the tight binding approximation, where only the nearest neighbor overlap between the tt-orbitals is taken into account [125], The parameters (i.e. the tt-it overlap integral 7o 2.7 eV, and the lattice constant ao = 0.246 nm), are obtained from corresponding graphene calculations. For a graphene sheet [137],... 

Unlike other copper oxide superconductors which have higher cja ratio, the cj a ratio in the non-defective infinite-layer compound is close to 1. However, because of a lack of apical oxygen, the electronic structure is expected to be more anisotropic than all other high oxides, despite the similar c and a lattice constants of the unit cell. This supposition was recently confirmed by X-ray absorption spectroscopy (XAS) measurements [8.27], in which an anisotropic upper Hubbard band was reported. In this section, we will discuss the question of whether the electronic transitions near the Fermi surface behave anisotropically with respect to the a6-plane and the c-axis. 

Apparently in contradiction the photoemission spectra (see Fig. 5.3) exhibit a dominance of majority electrons near the Fermi level. However, keeping in mind the calculation of Wu et al. [50] one can now easily realize the distinct surface sensitivity of metastable de-excitation spectroscopy (MDS) which gives predominantly information from the topmost surface layer whereas in photoemission experiments the information depth is a few layers. 

The electron energy spectra of a clean Fe/W(l 10) film with a thickness of about 20 A and of O on such FeAV(l 10) films with an oxygen exposure of 3 L are shown in Fig. 5.22. The structure at high kinetic energies is caused by Fe kI electrons near the Fermi level. After dosing oxygen to the iron surface, the emission of these electrons is drastically reduced. 

The rest of this section is devoted to a discussion of amorphous semiconductors, which play a special role within the field of the electronic structures of disordered materials for two reasons. First, as discussed below, the transport properties of amorphous semiconductors are dominated by carriers within kT of the transition energy where the states are uniquely characteristic of disordered materials. Secondly, the amorphous semiconductors are all covalent, and it is the electronic structures of the covalent materials which should be most sensitive to disorder. Simple metals, where the electrons interact weakly with the atoms via small pseudopotentials are free-electron-like near the Fermi surface both as solids and liquids. Insulating materials with large band gaps but narrow bands again have electronic structures relatively insensitive to order. The covalent semiconductors correspond to intermediate cases of maximal sensitivity of electronic structure to atomic structure and composition. 

The theory indicates that the strength of the adsorption and bonding of reactants on catalyst snrfaces is closely related to the symmetry and spin state of reactants molecnlar or atomic orbitals, and depends on matching the energy levels of the reactants to those of the catalyst surface as well. Norskov and coworkers invoked a so-called d-band center theory based on a large body of experimental and theoretical results, which emphasizes that the density of d-band valence electrons near the Fermi level is an important factor affecting catalytic reactions [27], It is thus particularly attractive to be able to modulate metallic NP reactivity by controlling (1) their location (inside vs. outside CNTs), (2) CNT diameter, and (3) CNT helicity (metallic vs. saniconductor). 

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