The sensitivity of the transition temperature to changes in α2 F(ω)

The transition temperature of a superconductor depends on α² F(ω), the spectral function of the effective interaction due to phonon exchange. We discuss how strongly the transition temperature is influenced by different frequency parts of α² F(ω). For this purpose the functional derivative δT _c /δα² F(ω) is calculated. It is shown that all frequency regions of α² F(ω) yield a positive contribution toT _c and that the most effective range covers frequencies, slightly above 2πT _c . The functional derivative is calculated numerically for several superconductors from their measured α² F(ω)-spectra. Finally, we discuss the change in transition temperature due to the softening of α² F(ω) which has been observed in amorphous superconductors.     

Tunneling-states model and the propagation characteristics of surface phonons in amorphous solids at low temperatures

The propagation characteristics of the surface phonon in an amorphous film are theoretically investigated at low temperatures based on the tunneling-states model. It is shown that the attenuation rate of the surface phonon is proportional to ω tanh ?ω/2k_BT and the relative velocity variation to ln (T/T₀) for the thickness of the amorphous film comparable to or larger than the surface phonon wavelength. Below 3K, our result can well account for recent measurements of the relative velocity variation by Hartemann et al.     

Electron-phonon interaction near a normal metal-superconductor boundary

Electron tunneling has been used to study the electron-phonon interaction in PbCd proximity effect samples by injecting electrons into Pb side. For Pb thicknesses ranging from 950 to 330 Å, the phonon structure occurs at the same energy as bulk Pb and the magnitude of the structure scales as T_c². The shape of the phonon spectral function, α²F(ω), remains essentially unchanged even though T_c has been depressed by 35%.     

Mössbauer effect of119Sn in amorphous superconducting metals

Mössbauer spectra for¹¹⁹Sn in crystalline and disordered Sn, as well as in crystalline and liquid-like amorphous Sn_1-x Cu _x (X=0.10?0.18), have been measured at 2.6 K≦T≦108 K. The Debye-Waller-Factor (DWF) obtained from the spectra is identical for the crystalline and for the disordered phase. The DWF of the amorphous phase is smaller than the DWF of the crystalline phase athigh temperatures, but it shows a stronger temperature dependence than the DWF of the crystalline phase and reaches the latter one at about 4 K. From this low-temperature result we conclude that the differences of the Eliashberg functionα ²(ω)F(ω) and of the superconducting transition temperatureT _c in these two phases cannot be related to changes in the phonon spectrumF(ω), but must result from changes of the interaction parameterα ² (ω). A comparison between DWF,α ² F, and specific heat data is performed. From the values for the isomeric shift of the Mössbauer line we can show that the hybridisation and covalency of the electronic bonds present in the crystalline and in the disordered phases are destroyed in the amorphous phase. Both, the DWF and the isomer shift demonstrate that the electronic properties of crystalline and amorphous Sn(Cu) differ appreciably. The electronic and superconducting properties of amorphous Sn(Cu) are similar to the properties of the high pressure phase of tin.     

奇点zph与超导临界温度级数

基于对复变函数F_α(y)=∫₀^(ω_ph-α)(ω²y)/(ω²y+1)g(ω)dω解析性质的分析,本文认为:在决定的收敛半径以外,吴杭生等提出的T_c级数解的部分和作为近似T_c公式仍可用于1/λ的适当范围。但它可能达到的精度依赖于谱形,一般来说是有限的。 关键词：     

Functional derivative of Tc with α2(ω)F(ω) for an anisotropic superconductor

The functional derivative δT_c/δα²(ω)F(ω) of the critical temperature (T_c) with the electron-phonon spectral density (α²(ω)F(ω)) gives information on the effectiveness of various phonon modes in enhancing T_c. For an anisotropic superconductor, it is found that δT_c/δα²(ω)F(ω) goes negative at some small but finite phonon energy. This contrasts with the isotropic case for which it is well known that the functional derivative is positive everywhere. Thus, very low energy phonons reduce T_c in an anisotropic superconductor which is similar to the known effects of static impurities that wash out anisotropy and hence reduce T_c.     

Equivalence of optimized conventional and proximity electron tunneling (PET) for niobium

A comparison is made of effective phonon spectra α²F(ω) obtained by a fully corrected proximity electron tunneling spectroscopy (PETS) on recrystallized foils of Nb with new results from “conventional” junctions of the form Ag-Al₂O₃-Nb. The latter show the largest strong coupling phonon structure ever observed for Nb and lead directly to an α²F(ω) in good agreement with PETS. This comparison suggests the equivalence of the two techniques if clean and highly ordered NS proximity structures are employed.     

McMillan-Rowell tunneling spectroscopy in the Nb-Zr system

We report the first full application of tunneling spectroscopy to a superconducting transition metal alloy: Nb_1?xZr_x at x = 0.25, corresponding to the maximum T_c in the Nb-Zr system. The spectral function α²F(ω) and related parameters, when compared to those for the Nb, confirm that the increase in T_c from 9.22 K (x = 0) to 10.8 K(x = 0.25) arises largely by softening of the effective phonon spectrum.     

Spatial-temporal dispersion of the kinetic coefficients near the Anderson transition

A generalization of the Vollhardt-Wölfle localization theory is proposed to make it possible to study the spatial-temporal dispersion of the kinetic coefficients of a d-dimensional disordered system in the low-frequency, long-wavelength range (ω?_F and q?k _F ). It is shown that the critical behavior of the generalized diffusion coefficient D(q,ω) near the Anderson transition agrees with the general Berezinskii-Gor’kov localization criterion. More precisely, on the metallic side of the transition the static diffusion coefficient D(q,0) vanishes at a mobility threshold λ _c common for all q: D(q, 0)∝t=(λ _c ?λ)/λ _c →0, where λ=1/(2π?_F τ) is a dimensionless coupling constant. On the insulator side, q≠0 D(q,ω)∝?iω as ω→0 for all finite q. Within these limits, the scale of the spatial dispersion of D(q,ω) decreases in proportion to t in the metallic phase and in proportion to ωξ ², where ξ is the localization length, in the insulator phase until it reaches its lower limit ～λ _F. The suppression of the spatial dispersion of D(q,ω) near the Anderson transition up to the atomic scale confirms the asymptotic validity of the Vollhardt-Wölfle approximation: D(q,ω)?D(ω) as |t|→0 and ω→0. By contrast, the scale of the spatial dispersion of the electrical conductivity in the insulator phase is of order of the localization length and diverges in proportion to |t|^?v as |t|→0.     

Direct measurement of the electron-phonon interaction in Pd,Mo and W by point-contact spectroscopy

The point-contact electron-phonon interaction function α²F has been obtained for the three transition metals Pd, Mo and W. The measured^Pα²F_p-spectra show clear structures which are in agreement with characteristic features in the phonon densities of states and calculated α²(ω)F(ω)-spectra.     

Phonons in disordered solids

The effects of crystalline disorder on the frequency distribution and lifetimes of phonons are investigated. As the disorder parameter g characterizing the scattering of normal modes is increased to g>g_c, the normal mode spectrum becomes unstable against arbitrarily small nonlinearities while the ground state (if any) becomes increasingly degenerate. The bandwidth of the acoustic phonon spectrum increases with g, from a value ω_Dat g = 0 to 1.24ω_D at g_c. The speed of sound at long wavelengths decreases with increasing g; at threshold (g_c) it has decreased by some 29.3% from its value at g = 0. For g < g_c the scattering lifetime of long-wavelength normal modes satisfies Rayleigh's law (1/τ = A(_g)ω⁴). At g_c the damping satisfies a different law: 1/τ = Bω². Similar effects are obtained for the optic mode phonons. For these reasons, it appears that g_c marks the threshold of amorphous behavior, although the regime g >g_c is beyond the scope of our model.     

Electron-phonon interaction in superconducting Nb

Acoustic phonon damping in Nb due to superconductivity is accurately measured by the inelastic neutron scattering technique. The phonon line widths can be characterized by the reduced parameters $\text{h}\text{?}\text{ω}{}_{\mathrm{p}}\text{/2Δ(0)}$ and T/T_c, and are in good qualitative agreement with the calculation by Bobetic based on the BCS theory.     

Electronic structure and phonon spectrum of binary iron-based superconductor FeSe in both nonmagnetic and striped antiferromagnetic phases

Using first-principles calculations, we investigate electronic structure and phonon spectrum of binary iron-based superconductor FeSe in both tetragonal nonmagnetic (NM) phase and orthorhombic striped antiferromagnetic (SAF) phase. It is found that the softening of atomic vibration modes and main electron-phonon coupling contribution from low-frequency Eliashberg spectral function α²F(ω) in SAF phase of FeSe lead to the enhancement of electron-phonon coupling strength λ_ep and logarithmically average frequency ω_ln. However, the obtained superconducting T_c in SAF phase just increases up to 0.34 K, even though Coulomb pseudopotential μ^∗ is limited to zero. As a result, our magnetic phonons calculation still rules out phonon mediated superconductivity, although the electron-phonon coupling through the spin channel play an important role in FeSe.     

Raman measurements of the superionic conductor AgI

Using the Raman technique, we have observed large abrupt reversible changes in the phonon spectrum at the transition temperature, T_c = 147°C, of the superionic conductor AgI. The defect nature of the high temperature phase completely breaks down the selection rules and allows the Raman measurements to give a measure of the frequency dependent conductivity, σ(ω), assuming a frequency independent matrix element. Similarities as well as differences in σ(ω) above and below T_c are shown.     

Electron-phonon interaction in NbB2: a comparison with MgB2

We present a comparison of electron-phonon interaction in NbB₂ and MgB₂, calculated using full-potential, density-functional-based methods in P6/mmm crystal structure. Our results, described in terms of (i) electronic structure, (ii) phonon density of states F(ω), (iii) Eliashberg function α²F(ω), and (iv) the solutions of the isotropic Eliashberg gap equation, clearly show significant differences in the electron-phonon interaction in NbB₂ and MgB₂. We find that the average electron-phonon coupling constant λ is equal to 0.59 for MgB₂ and 0.43 for NbB₂, leading to superconducting transition temperatures T_c at around 22 K for MgB₂ and 3 K for NbB₂.     

Albedo for an inhomogeneous half space

The Albedo is calculated for an inhomogeneous half-space by assuming that the single scattering albedo behaves like c(z) = c_oe^-(z/s). The modified Eddington method is used to obtain the outgoing flux and hence the albedo. Numerical calculations and comparisons with Pomraning et al. and with an improved version of the F_N- method indicate that the approach is reasonably accurate.     

非晶态超导体的2△0/(kBTc)和声子谱参量

提出了能够很好地描述非过渡金属无序和非晶态超导体的2Δ₀/(k_BT_c)与声子谱参量之间关系的一个公式:2Δ₀(k_BT_c=4.95[1-(T₀<ω>^1/2)/A(1/(λω₀)+1/(20λ<ω>)+1/(20<ω>))]。计算了大量已知声子谱的非晶和无序超导体的能隙2Δ₀对T_c的比,结果表明在百分之几的范围内与实验值符合。指出了非过渡金属和合金的非晶态超导体,既可以是一个2Δ₀/(k_BT_c)值远大于BCS理论值(3.53)的强耦合超导体,也可以是一个2Δ₀/(k_BT_c)值比BCS理论值还要小得多的弱耦合超导体。 关键词：     

Polisher density into Preston equation

For the polishing process, Preston (1927) [1] proposed wear, h, is proportional to the work given by a frictional force, f_fr, on the glass. He assumed f_fr does not depend on relative velocity, v, between the glass and the tool. Téllez et al. (2007) [2] found frictional force depends on v. We have experimentally found that f_dr depends on relative velocity, v, and concentration, ρ, of the polisher suspension. Then Preston equation has to be modified i.e. h = h(f_fr(v), ρ).     

Lattice dynamics of a disordered Ni1−xPtx system in the pseudo unit cell model

The phonon dispersion relations for a disordered Ni_1?xPt_x system have been derived using the pseudo unit cell model proposed by Varshney et al. The results are presented for a few values of x along the [00ζ] direction and compared with recent measurements of Kunitomi et al. Reasonable agreement is found between the calculated and measured dispersion curves at all concentrations. In particular the localised impurity mode for low Ni concentrations does not split off from the main phonon band, in agreement with experiment and in contrast with the mass defect CPA prediction.