Velocity of Sound in a Many-Valley Conductor

The effect on the velocity of sound corresponding to the “Keyes effect,” for nonzero frequency and finite wavelength, is calculated by means of the electron Boltzmann equation. The result may be expressed as an effective electronic contribution to the elastic constant; the deviation,
χ
dK
0
of δK from the Keyes electronic contribution to the elastic constant, δK
0
, is examined as a function of frequency and other parameters. When the Fermi velocity v is much larger than the sound velocity s and the mean free path is of the same order or larger than the acoustic wavelength, we find that χ ≈ (s/v)
²
. When the mean free path is small compared to wavelength, χ = ω
²
/[ω
²
+ (ν + 1/τ
d
)
²
], where ν is the intervalley scattering rate and τ
d
is an average diffusion relaxation time.