Lattice vibrations in thin-film carbon: Electron–Rayleigh-wave interaction

Sound-wave propagation in thin-film carbon is investigated in the long-wavelength approximation. The Rayleigh wave, with a small damping constant and with polarization along the c axis, has a small sound velocity vR{~}10⁴ cm/sec if C₄₄ is small. Since the Rayleigh-wave phonons interacting with carriers have small energies ({}{ω}/kB{}1 K), these phonons are highly excited even at helium temperature and they scatter carriers. Of particular interest for transport properties is the carrier relaxation time τR{~}10^-12 sec for film thickness d{}100 A{} at T{}1 K. If the sample is assumed to be composed of an aggregate of many thin films, and each film weakly couples elastically with the others, the present theory is applicable to a sample with bulk thickness. The electron--Rayleigh-wave interaction is responsible for the unusual temperature dependence of the resistivity observed for a polyacrylonitrile-based fiber heat-treated to {~}1300 ^∘{}C. A comment is given about one possible mechanism for the anomalous linear temperature-dependent specific heat observed in some kinds of carbons and in polycrystalline graphite.