On the Question of Coincidence Between Energy Gaps and Kohn Anomalies

Abstract

Recently, neutron scattering spin echo measurements have provided high resolution data on the temperature dependence of the linewidth $\hat{I}“(\mathbf{q},T)$ of acoustic phonons in conventional superconductors Pb and Nb. [P. Aynajian, et al, Science 319, 1509 (2008)]. At low temperatures the merging of the $2\hat{I}”(T)$ structure in the linewidth with a peak associated with a low lying $\hslash \ddot{I}{‰}_{{\mathbf{q}}_{\mathbf{KA}}}$ Kohn anomaly suggested a coincidence between $2\hat{I}”(0)$ and $\hslash \ddot{I}{‰}_{{\mathbf{q}}_{\mathbf{KA}}}$ 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 $2\hat{I}”(0)/\hslash \ddot{I}{‰}_{{\mathbf{q}}_{\mathbf{KA}}}$ must be to unity in order to be consistent with the neutron data.

6 pages, 5 figures