On the Question of Coincidence Between Energy Gaps and Kohn Anomalies

TL;DR

This paper investigates whether the energy gap in superconductors coincides with Kohn anomalies by analyzing phonon linewidth data through BCS calculations, aiming to clarify the relationship between these phenomena.

Contribution

It provides a theoretical analysis of phonon linewidth temperature dependence to assess the coincidence between energy gaps and Kohn anomalies in superconductors.

Findings

Theoretical BCS calculations match experimental linewidth data.

Close proximity of 2Δ(0) and ω_KA is necessary for observed coincidences.

Quantifies the conditions for energy gap and Kohn anomaly coincidence.

Abstract

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