Subtract the reciprocal lattice vector , leaving a reduced wave vector along . A linear-acoustic estimate givesInterpret the quoted intrinsic width as the full width at half maximum in energy, meV. The corresponding energy-relaxation mean lifetime is s, giving mean free path nm. If the given width instead denotes a half width, the inferred mean lifetime differs by a factor of two; the convention must be specified.
Approximating the thermal average by this velocity and mean lifetime, and using the isotropic angular factor , kinetic theory givesUsing a single purely -directed effective channel without angular averaging gives W m K, still far below the observed total W m K. The isotropic estimate is roughly times smaller than the measured total.
The calculation is not a complete thermal-transport average. Electrons in this metallic compound can carry substantial heat, the supplied total heat capacity need not be entirely phononic, and one meV phonon need not represent all thermally active branches and mean lifetimes. At K, meV, so that measured mode is relatively high in the thermal distribution; lower-energy modes can have much longer mean lifetimes. A measured phase velocity is also only an estimate of the group velocity if the branch is nonlinear.
electron-phonon interaction is a plausible damping mechanism in a phonon-mediated superconductor, but the measurement is above its K transition and probes the normal state. It cannot be attributed directly to decay into an already established superconducting condensate. Below the transition an energy gap can modify electron-hole damping. The weak-coupling scale meV is below the meV phonon energy, so even superconductivity need not prohibit all pair-breaking damping of this mode. Temperature-dependent spectra would distinguish that mechanism from defects or anharmonic phonon decay.
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