Dirty limit

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... 

An unexpected concentration dependence is found for the parameter which describes, according to eq. (8), the deviation of the field dependence of the electronic specific heat in the mixed state from the linear law expected (Nohara et al. 1997) for isotropic s-wave superconductors in the dirty limit. The large deviations from this linear y(H) law observed... 

Fig. 60. Concentration dependence of various properties of polycrystalline Y(Ni xPt )2B2C obtained by specific heat measurements transition temperature Tc exponent a and parameter Hc2 from eq. (6) upper critical field Hc2(0) at T =0, where the dotted line schematically describes the dirty limit corresponding to the isotropic single band case (in reality there is a finite intersection with the field-axis for the dotted asymptotic line, see Shulga and Drechsler 2002) exponent fi of eq. (8) for the curvature of the electronic specific heat in the mixed state and Sommerfeld constant xn (after Lipp et al. 2001).

Fig. 61. Magnetic field dependence of the specific heat contribution y(H) of the vortex core electrons in the mixed state for Y(Nio.7sPto.25)2B2C. The dashed line is a fit according to eq. (8) with /) = 0.17, the solid line corresponds to the y(H)

We studied odd, s-wave, triplet superconductivity that may arise in S/F multilayered structures with a non-collinear orientation of magnetizations. It was assumed that the orientation of the magnetization is not affected by the superconductivity (e.g. the energy of the magnetic anisotropy is much larger than the superconducting energy). The analysis was carried out in the dirty limit (Jr -C 1) when the Usadel equation is applicable. 

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 61 Specific-heat contribution y (H) of the vortex-core electrons in the mixed state (normalized by the Sommerfeld parameter y ) of the YxLui xNi2B2C samples from Figure 60 as function of the applied magnetic field. The dotted straight line y(H) H corresponds to the usual s-wave behavior in the dirty limit. 

An unexpected concentration dependence is found for the parameter ft which describes, according to Eq. (8), the deviation of the field dependence of the electronic specific heat in the mixed state from the expected linear law (Nohara et al., 1997) for isotropic s-wave superconductors in the dirty limit. The large deviations from this linear y(H) law observed for YNi2B2C become smaller in the quasi-dirty limit, however, they do not completely disappear. It has been pointed out by Lipp et al. (2001) that for intermediate deviations from linearity of y (H), i.e. for = 0.15-0.3, the specific heat data of borocarbides at low magnetic fields can be discussed in the context of the conventional s-wave picture as well as within the... 

Thus, in the dirty limit C << 4 the parameter zero temperature, thus, Eq. (5) at small W has no solution and the superconducting transition is absent. 

In pure metals the electron-phonon interaction is inversely proportional to the number of thermal phonons Te-ph 7 [1]. This result is valid for pure limit 97- / 1 qr is thermal phonon wave vector, / is the electron mean free path) [2,3]. In dirty limit qt / 1) electrons mostly scatter from defects and impurities and the electron-phonon interaction demonstrates more complicated behavior. According to the theoretical analysis made by Thouless [4] and Reizer [3] the relaxation time is proportional to T Te.pf x T ) in the case of full phonon drag of scattering centers. 

T is the temperature. This means that our system is in the dirty limit at subkelvin temperatures. 

The microwave absorption of the paired boson superconductor is calculated in the extremely local (or dirty) limit (6). We find that it is sharply different from that of the Mattis-Bardeen (8) behavior characteristic of a BCS superconductor. In particular, we find that the ratio os(<<>)/on is strongly temperature dependent and... 

Here r measures the (almost T-independent) distance from the quantum critical point, F denotes the characteristic energy scale of the fluctuations and c, are constants. The frequency magnetic coq vanishes at the ordering vector Q of the magnetic stmcture. In the dirty limit the variation with temperature of the resistivity is given by... 

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