Phonon Anomalies Induced by Superconductivity

TL;DR

This paper investigates how superconductivity affects phonon behavior, revealing a sharp peak in lattice vibrations near certain wave vectors and discussing the likelihood of a charge density wave transition, supported by neutron scattering data.

Contribution

It provides a theoretical calculation of electronic polarizability in superconductors and predicts phonon anomalies near extremum vectors of the Fermi surface.

Findings

A pole in polarizability near the superconducting gap leads to a phonon peak below 2Δ.

A second order transition to a charge density wave state is unlikely.

Results align with recent neutron scattering experiments in nickel borocarbides.

Abstract

We calculate the electronic polarizability in the superconducting state near extremum vectors ${\vec Q}_0$ of the Fermi surface. A pole appears in the polarizability at frequencies $\omega$ near the superconducting gap $2\Delta$ which leads to a sharp peak at $\omega$ just below $2 \Delta$ in the lattice vibrations near ${\vec Q}_0$. A second order transition to a charge density wave state below the superconducting transition is shown to be unlikely. The results are compared with the recent inelastic neutron scattering measurements in compounds, $ANi_2B_2C$, $A=Y$ or $Lu$.