Calculated point-contact electron-phonon spectral functions for the alkali metals

The electron-phonon spectral functions $\alpha {}_{}{}^2{}_{}{}^{}F$, $\alpha {}_{}{}^2{}_{}{}^{}F_{\mathrm{tr}}^{}{}_{}{}^{}$, and $\alpha {}_{}{}^2{}_{}{}^{}F_p^{}{}_{}{}^{}$ and the corresponding coupling parameters $\lambda$, ${\lambda }_{\mathrm{tr}}$, and ${\lambda }_p$ central to the theories of superconductivity, transport, and point-contact spectroscopy are calculated for the alkali metals. It is found that the frequently made assumption ${\lambda }_p\sim \lambda$ is a very poor one. For example: ${\lambda }_p<\frac{\lambda }{2}$ for K, while ${\lambda }_p>2\mathrm{}\lambda$ for Cs. The dependence of the point-contact spectral function $\alpha {}_{}{}^2{}_{}{}^{}F_p^{}{}_{}{}^{}$ on the orientation of the crystalline axes relative to the contact is investigated. It is found that the very anisotropic lattice dynamics of the alkali metals lead to an anisotropy of only a few percent in ${\lambda }_p$. The anisotropy in $\alpha {}_{}{}^2{}_{}{}^{}F_p^{}{}_{}{}^{}$ at a given frequency can be a few times larger than this, but we find no significant anisotropy in either peak positions or heights.