Kohn Anomalies in Superconductors

TL;DR

This paper investigates Kohn anomalies in superconductors, revealing that they are stronger and persist at finite temperature compared to normal metals, with potential applications in high-temperature superconductor analysis.

Contribution

It demonstrates the existence and characteristics of Kohn anomalies in superconductors, highlighting their differences from metallic anomalies and their dependence on phonon frequency and temperature.

Findings

Anomalies exist when phonon frequency exceeds twice the superconducting gap.

Superconducting anomalies are stronger and survive at finite temperature.

Anomalies can help determine Fermi surface features in superconductors.

Abstract

I present the detailed behavior of phonon dispersion curves near momenta which span the electronic Fermi sea in a superconductor. I demonstrate that an anomaly, similar to the metallic Kohn anomaly, exists in a superconductor's dispersion curves when the frequency of the phonon spanning the Fermi sea exceeds twice the superconducting energy gap. This anomaly occurs at approximately the same momentum but is {\it stronger} than the normal-state Kohn anomaly. It also survives at finite temperature, unlike the metallic anomaly. Determination of Fermi surface diameters from the location of these anomalies, therefore, may be more successful in the superconducting phase than in the normal state. However, the superconductor's anomaly fades rapidly with increased phonon frequency and becomes unobservable when the phonon frequency greatly exceeds the gap. This constraint makes these anomalies useful only in high-temperature superconductors such as $\rm La_{1.85}Sr_{.15}CuO_4$.