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Neutron-scattering profile of Q ≠ 0 phonons in BCS superconductors

1997; American Physical Society; Volume: 56; Issue: 9 Linguagem: Inglês

10.1103/physrevb.56.5552

1095-3795

Philip B. Allen, Vladimir N. Kostur, Naohisa Takesue, G. Shirane,

Physics of Superconductivity and Magnetism

Phonons in a metal interact with conduction electrons. In the normal state, this gives rise to a linewidth ${\ensuremath{\gamma}}_{Q}$ which is small compared with the frequency ${\ensuremath{\omega}}_{Q}.$ In the superconducting state, the line shape can be altered if $\ensuremath{\Elzxh}{\ensuremath{\omega}}_{Q}\ensuremath{\lesssim}(1+2r)2\ensuremath{\Delta}$ where $\ensuremath{\Delta}$ is the superconducting gap, and $r$ is the ratio ${\ensuremath{\gamma}}_{Q}/{\ensuremath{\omega}}_{Q},$ which scales with the strength of the electron-phonon coupling $\ensuremath{\lambda}$. As long as ${\ensuremath{\omega}}_{Q}\ensuremath{\ll}{\mathrm{Qv}}_{F}$ where ${v}_{F}$ is the Fermi velocity, BCS theory predicts a line shape which is a universal function of the dimensionless parameters $r$, ${\ensuremath{\omega}}_{Q}/2\ensuremath{\Delta}$, $\ensuremath{\omega}/2\ensuremath{\Delta}$, and ${T/T}_{c}$ where ${T}_{c}$ is the superconducting transition temperature. Formulas and curves are given for the full range of these parameters. The BCS predictions correspond well to key features seen in recent experiments on YNi${}_{2}$B${}_{2}$C and LuNi${}_{2}$B${}_{2}$C.