Scattering rate

We now want to study the consequences of such a model with respect to the optical properties of a composite medium. For such a purpose, we will consider the phenomenological Lorentz-Drude model, based on the classical dispersion theory, in order to describe qualitatively the various components [20]. Therefore, a Drude term defined by the plasma frequency and scattering rate, will describe the optical response of the bulk metal or will define the intrinsic metallic properties (i.e., Zm((a) in Eq.(6)) of the small particles, while a harmonic Lorentz oscillator, defined by the resonance frequency, the damping and the mode strength parameters, will describe the insulating host (i.e., /((0) in Eq.(6)). 

Fig. 7. Model calculations for the reflectivity (a) and the optical conductivity (b) for a simple (bulk) Drude metal and an effective medium of small metallic spherical particles in a dielectric host within the MG approach. The (bulk) Drude and the metallic particles are defined by the same parameters set the plasma frequency = 2 eV, the scattering rate hr = 0.2 eV. A filling factor/ = 0.5 and a dielectric host-medium represented by a Lorentz harmonic oscillator with mode strength fttOy, 1 = 10 eV, damping ftF] = I eV and resonance frequency h(H = 15 eV were considered for the calculations.

The main difference between the two models lies in the fitted scattering rate T (Table 2) which is considerably smaller, one order of magnitude, for the BM then for the MG model. Moreover, we also notice that (Op(a ) > (Oy,(aj.) and that cOp is slightly larger in BM compared to MG. According to the band structure... 

For the particular calculations shown in Figures 1 - 4, it was assumed that the scattering rates are relatively high and that they are the same for all layers and for both spin channels. Both the field and the current are assumed to be parallel to the layers which consist of 111 atomic planes. 

Figure 1 Non-local layer dependent conductivity for majority electrons for parallel alignment of the cobalt moments. The scattering rate is assumed to be high so that the electron lifetime is relatively short (4.8X10 sec).

An accurate calculation of the heat conductivity requires solving a kinetic equation for the phonons coupled with the multilevel systems, which would account for thermal saturation effects and so on. We encountered one example of such saturation in the expression (21) for the scattering strength by a two-level system, where the factor of tanh((3co/2) reflected the difference between thermal populations of the two states. Neglecting these effects should lead to an error on the order of unity for the thermal frequencies. Within this single relaxation time approximation for each phonon frequency, the Fermi golden rule yields, for the scattering rate of a phonon with Ha kgT,... 

In order to compute the lifetime of a phonon of energy E, one averages the Golden Rule scattering rate (7ig A /pCj )tanh(p /2) with respect to n(e, A), subject to the resonance condition E = y/EA + A [8, 11, 93]. This yields two contributions to the decay rate ... 

Wt vanishes identically for a nonabsorbing medium Ws is the rate at which energy is scattered across the surface A. Therefore, Wext is just the sum of the energy absorption rate and the energy scattering rate ... 

Fig. 20. (a) Temperature dependence of the upper critical field calculated within a two-band model for several impurity scattering rates yjmp (cm-1). (b) calculated Hc2(0)-vi.-ylmp curve illustrating the transition from the clean to the dirty limit. Dotted line Hc2(0)-y,mp dependence in the dirty limit. (Drechsler et al. 2000 Fuchs... 

Growing degree of substitutional disorder results in a reduction of the other above-mentioned quantities. However, the microscopic mechanism, which mediates disorder to Tc and to the other physical quantities, is not yet clarified. Typical scenarios for disorder effects could be the peak of the density of states at the Fermi level, N(Ef), may be broadened or the phonon spectrum may be modified by disorder (Manalo et al. 2001) or the scattering rate of the conduction electrons may increase. 

We have thus far considered the probability of superelastic scattering on a single orbit. To obtain the scattering rate, or autoionization rate, we simply multiply this probability by the orbital frequency, 1/n3.4 Once again we find that T oc 1/n3 and that T decreases with increasing Z. The scattering description we have just given is a two channel description. This picture, when many channels are present, forms the basis of multichannel quantum defect theory.5... 

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. 

---