Anomalous behavior of giant quantum attenuation in bismuth

Abstract

Giant quantum attenuation in Bi has been measured as function of temperature and ultrasonic frequency. We found many anomalous behaviors which cannot be explained by existing theories of the giant quantum attenuation in metals; the measured attenuation coefficient at the peak position ${\ensuremath{\alpha}}_{p}$ is expressed by ${\ensuremath{\alpha}}_{p}\ensuremath{\propto}{\ensuremath{\omega}}^{\ensuremath{\nu}}{T}^{\ensuremath{-}\ensuremath{\mu}}$ with $\ensuremath{\nu}\ensuremath{\simeq}1$ and $0.34\ensuremath{\leqq}\ensuremath{\mu}\ensuremath{\leqq}1.25$. The measured value $\ensuremath{\nu}\ensuremath{\simeq}1$ deviates from the theoretical value $\ensuremath{\nu}=2$ which is estimated from the approved value of the relaxation time in Bi. The coefficient ${\ensuremath{\alpha}}_{p}$ of nearly independent peaks shows $\ensuremath{\mu}=0.34$, while a strong temperature depedence $\ensuremath{\mu}\ensuremath{\gtrsim}1$ was observed only when the attenuations due to both electrons and holes take place simultaneously at a certain magnetic field strength. Both results anomalously deviate from the theoretical values $0.5\ensuremath{\leqq}\ensuremath{\mu}(\mathrm{theory})\ensuremath{\leqq}1.0$. We suggest that some effect due to the combined system of electrons and holes in Bi has a contribution to these anomalies.