Bloch electrons

Mobility measurements show that the carriers once created do not have an activated mobility, despite the narrow conduction bands calculated. This, combined with the observed and calculated anisotropy of mobility, suggests that the carriers may be treated as conventional Bloch electrons (39). 

In chemical usage [23, Section 14.11] an electron is said to be delocalized if its molecular orbital cannot be ascribed to a two-center bond otherwise it is localized. It is, however, always possible, but perhaps rarely convenient, to describe the electron distribution in a molecule with delocalized orbitals only. The situation in a covalent insulator such as diamond is similar to the molecular case. There are four valence electrons per atom, and four neighbors. Therefore, it is possible to describe the structure with four two-center, two-electron bonds, and localized Wannier orbitals. But keep in mind that the only physical reality is the resulting charge distribution. This reality can also be described by freely moving Bloch electrons. 

By now, we have identified three important ingredients in the cuprate superconductivity strong on-site Coulomb repulsion, small polaron formation, and spin-vortex formation. With all these ingredients, however, the conventional transport theory based on Bloch electrons will predict that the system is an insulator. In order to... 

Bloch electrons in a perfect periodic potential can sustain an electric current even in the absence of an external electric held. This infinite conductivity is limited by the imperfections of the crystals, which lead to deviations from a perfect periodicity. The most important deviation is the atomic thermal vibration from the equilibrium position in the lathee however, electric perturbations can also promote this type of vibration. A quantitative treatment of the external electric perturbation of a crystal, therefore, starts with the observation of the change in the lattice vibrations [1] ... 

Finally, the energy and the wave vector of the Bloch electrons can be related to... 

In the case of an electric potential applied to the metal, as in electrocatalysis, U(r) = U(r) + eV. However, the modified energy is the total energy, so the kinetic operator has to be also modified in an unknown form. We define the Bloch electrons as those obeying the periodic Schrodinger equation and the free electrons as those obeying a zero periodic potential. 

Using Equation 6.D.21, we can obtain the rate of propagation of the planar waves of the Bloch electrons given by the band index n and the wave vector k. 

The physics behind statement (10) is explained most easily by considering the special case Av = constant. The electronic states l > belonging to Aq are then Bloch electrons and we have to consider the change in free energy to second order... 

These predictions have been verified by experiments on low-energy helium atom scattering by metal surfaces [112]. The helium atom repels the Bloch electrons, because their wave function must become distorted to preserve orthogonality to the wave functions of the closed shells of helium. The repulsion potential appears in practise to be proportional to the local free electron density. Thus a helium atom scatters like a ping-pong ball from the electron cloud of the metal, and this allows to probe the distribution of electrons in the cloud, that is, the profile of the electronic tail and its lateral corrugation that usually follows the periodicity of the surface crystal plane [112]. 

As a proper reference for the RIn3 compounds, the electronic structure was investigated for Lalns by various theoretical methods. An analysis of the partial density of states revealed that the Bloch states in the lowest three bands consist dominantly of the In s state, and those in the upper part of the valence band consist mainly of the In p and La d states. The Fermi level lies in the vicinity of a sharp peak in the density of states. The Fermi surface consists of two sheets of bands 6 and 7 (Hasegawa 1982). The band 7 electron Fermi surface is essentially a sphere, which is centered at the R point and bulges slightly toward the M point and contains 0.38 electrons per primitive cell. The band 6 hole Fermi surface looks quite complex and contains the same number of holes as electrons, because Laln3 has an even number of Bloch electrons per primitive cell and thus is a compensated metal. 

The situation is different if the generalized k-f interactions are considered. In that case the elastic scattering may be different for the ground state and the excited state. The periodic part (V) of the elastic scattering processes is taken into account by the introduction of the Bloch electrons. It is... 

Furthermore, the coupling of the quasiparticle surface phonon with other quasiparticles such as Bloch electrons, magnons, plasmons, or polaritions are important ongoing research topics that lead in many cases beyond the well-established single-particle picture. Here, Section 8.2.5.2 could only give a small impression on phonon coupling issues. 

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