Anomalous frequency dependence of giant quantum attenuation in Bismuth below 1 K

Giant quantum attenuation of longitudinal sound waves in Bi has been measured at temperatures down to 8 mK for the case that the electron (n = 0, s = + 1) and hole (n = 1, s = ? 1) Landau levels cross simultaneously Fermi level at a field of about 90 kOe. The temperature and frequency dependences of the peak attenuation due to these two levels are expressed by α_p ∝ T^-μω^ν with $\text{μ ? 1}$ and $\text{ν ? 1}$ at T > 1 K. When T ? 1 K the value of μ decreases by decreasing temperature and below 0.1 K, α_p takes almost constant value. At T ? 0.5 K, ν becomes larger than 1 and maximum value of ν observed is 2 at T ～ 0.05 K. These features of the attenuation peak at very low temperatures are consistent with what are expected in the fluctuation region of the gas-liquid type transition of the electron-hole system.