Electrical resistivity of aluminum below 4.2 K

The resistivities of aluminum samples having resistance ratios ranging from 245 to 40 600 have been measured from 4.2 K down to the superconducting transition temperature ${T}_{c}=1.18$ K. No simple power law could describe the resistivity over this entire temperature range. In the vicinity of 4.2 K, the temperature-dependent portion of the resistivity $\ensuremath{\rho}(c,T)$ varied approximately as ${T}^{3}$. As the temperature was lowered, it approached a ${T}^{2}$ variation. Below 2.2 K the data were consistent with the form $\ensuremath{\rho}(c,T)=A{T}^{2}+B{T}^{5}$, with $A$ in the vicinity of 2.8 \textonehalf{} ${10}^{\ensuremath{-}15}$ \ensuremath{\Omega} m/${\mathrm{K}}^{2}$ and $B$ in the vicinity of 5 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}17}$ \ensuremath{\Omega} m/${\mathrm{K}}^{5}$. This is the form predicted for a combination of electron-electron and electron-phonon scattering in A1 in this temperature range, and the magnitude of $B$ is compatible with calculations for the electron-phonon component. Moreover, the coefficient $A$ was nearly independent of residual resistivity, grain size, dislocation density, sample thickness, and various other parameters tested, exactly as expected if it is associated with electron-electron scattering. On the other hand, the magnitude of $A$ is about 20 times larger than predicted for electron-electron scattering due to screened Coulomb repulsion, and also larger than expected on the basis of radiofrequency size effect and high-temperature Wiedemann-Franz ratio measurements on A1. The most likely resolution of these apparent contradictions lies in the importance of a phonon-mediated electron-electron attraction just above ${T}_{c}$, which MacDonald has recently argued increases the estimated magnitude of $A$ by about a factor of 20 at low temperatures but leaves it unchanged at high temperatures. Finally, the question of "saturation" in the magnitude of $\ensuremath{\rho}(c,T)$ as the residual resistivity ${\ensuremath{\rho}}_{0}(c)$ is increased, was investigated at both 1.87 K and 4.2 K. At 1.87 K saturation was clearly observed, in that the magnitude of $\ensuremath{\rho}(c,1.87 \mathrm{K})$ was the same to within experimental uncertainty for all of the samples studied. At 4.2 K, the data for all of the samples given a standard hydrogen anneal were consistent with saturation, but data for samples subjected to other treatments were not.

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