Fermi wave length

Fig. 2-10. Profile of electron density and electronic potential energy across a metal/vacuum interface calculated by using the jellium model of metals MS = jellium surface of metals Xf = Fermi wave length p. - average positive charge density P- s negative charge density V = electron exchange and correlation energy V, - kinetic energy of electrons. [From Lange-Kohn, 1970.]...

The question may arise whether the self-energy effects are important in the normal state. These are known to be smaller than the inelastic backscattering nonlinearities in the ballistic regime [18]. If we decrease the contact size d or the elastic mean free path li in order to make the inelastic contribution negligible, the latter parameters become comparable to the Fermi wave length of charge carriers and the strong nonlinearities connected with localization occur, which masks the desired phonon structure [19]. 

The drop in the work function for cesium suboxides is explained as being caused by a quantum size effect. 47) The electronic structure of the suboxides is discussed in terms of a simple stractural model with clusters occupied by the 0 ions. The interior of the clusters is highly repulsive for the conduction electrons and the clusters are separated within a Fermi wave length. These model calculations lead to a decrease in work function with respect to Cs by 0.1 and 0.9 eV for CS7O and Csj 103, respectively. 

Transport of electrons along conducting wires surrounded by insulators have been studied for several decades mechanisms of the transport phenomena involved are nowadays well understood (see [1, 2, 3] for review). In the ballistic regime where the mean free path is much longer than the wire lengths, l 3> d, the conductance is given by the Sharvin expression, G = (e2/-jrh)N, where N (kpa)2 is the number of transverse modes, a, is the wire radius, a Fermi wave vector. For a shorter mean free path diffusion controlled transport is obtained with the ohmic behavior of the conductance, G (e2/ph)N /d, neglecting the weak localization interference between scattered electronic waves. With a further decrease in the ratio /d, the ohmic behavior breaks down due to the localization effects when /d < N-1 the conductance appears to decay exponentially [4]. 

The required 2D nearly free electron gas is realized in Shockley type surface states of close-packed surfaces of noble metals. These states are located in narrow band gaps in the center of the first Brillouin zone of the (lll)-projected bulk band structure. The fact that their occupied bands are entirely in bulk band gaps separates the electrons in the 2D surface state from those in the underlying bulk. Only at structural defects, such as steps or adsorbates, is there an overlap of the wave functions, opening a finite transmission between the 2D and the 3D system. The fact that the surface state band is narrow implies extremely small Fermi wave vectors and consequently the Friedel oscillations of the surface state have a significantly larger wave length than those of bulk states. 

Fermi energy relative to the bottom of the CB). The Fermi level wave lengths are in general incommensurable with the crystal s interatomic or interplanar distances as a result, the magnetic ground states of the rare-earth intermetallics and pure metals have complicated spatial distributions, ferromagnetic, antiferromagnetic, helical, etc. 

This is perhaps most easily seen by considering a ID chain in the form of a ring of length L. If there are n electrons, the Fermi wave vector kp = +irn/2L. 

We may also compare the polar energies. This is particularly simple in the context of the empty-core model. Then, in gallium arsenide, for example, we may expect the unscreened pseudopotential (both Z and r ) for both gallium and arsenic to be the same as in each pure material. The screening depends only upon the Fermi wave number, and since the bond length does not change appreciably in an isoelectronic series, the entire denominator should be the same for... 

For steady electron tunneling conditions a small bias U must be applied between sample and tip. A tunnel current of a few nA indicates that the distance between probe and sample is of the order of some 10 A, that is, typical wave lengths of the valence and conduction electrons close to the Fermi level. With crystalline materials the wave lengths of the electrons contributing to the tunnel current depend on the effective mass m and on the relative energy with respect to the bottom of the bulk or surface band Eq from which the tunnel electrons originate ... 

In the weak-coupling limit unit cell a (, 0 7a for fra/u-polyacetylene) and the Peierls gap has a strong effect only on the electron states close to the Fermi energy eF-0, i.e., stales with wave vectors close to . The interaction of these electronic states with the lattice may then be described by a continuum, model [5, 6]. In this description, the electron Hamiltonian (Eq. (3.3)) takes the form ... 

The criterium that the mean free path should be larger than the superconducting coherence length must be met. This is a very strict condition that implies also that the impurity interband scattering rate yab should be very small yah (1/2 )(KB/ft)Tc. Therefore most of the metals are in the dirty limit where the interband impurity scattering mixes the electron wave functions of electrons on different spots on bare Fermi surfaces and it reduces the system to an effective single Fermi surface. 

Figure 1. Band structure for all-trans conformation of unsubstituted polysilane calculated by using the LCAO-LDF method, cr-like bands are denoted with solid lines, u-like bands are denoted with dashed lines. The Fermi level is denoted as f. k represents the wave vector, and a is the length of the unit cell.

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