Paper detail

On the Question of Coincidence Between Energy Gaps and Kohn Anomalies

Recently, neutron scattering spin echo measurements have provided high resolution data on the temperature dependence of the linewidth $Γ({\bf q},T)$ of acoustic phonons in conventional superconductors Pb and Nb. [P. Aynajian, et al, Science 319, 1509 (2008)]. At low temperatures the merging of the $2Δ(T)$ structure in the linewidth with a peak associated with a low lying $\hbarω_{\bf q_{KA}}$ Kohn anomaly suggested a coincidence between $2Δ(0)$ and $\hbarω_{\bf q_{KA}}$ in Pb and Nb. Here we carry out a standard BCS calculation of the phonon linewidth to examine its temperature evolution and explore how close $2Δ(0)/\hbarω_{\bf q_{KA}}$ must be to unity in order to be consistent with the neutron data.