Giant Quantum Attenuation of Sound Waves in Bismuth. II. Line Shape of the Attenuation Coefficient

The line shape of the giant quantum attenuation of sound waves in bismuth is studied on the basis of current theories and compared with our measurements. By taking into account the energy and magnetic field dependences of the level broadening and the hot electron effect, we may understand the symmetry of the line shape with regard to each peak field and the tendency to saturation of the attenuation peaks observed in a high field region. The minimum value of the life time of the electron Landau level touching the Fermi level is 2.5×10 -10 sec; this is obtained for the magnetic field parallel to a bisectrix axis at liquid helium temperature and is about two orders of magnitude larger than the value derived from the de Hass-van Alphen effect by Bhargava. The remarkable change of the experimental line shape under conditions such that the electrons and holes simultaneously satisfy resonance can be qualitatively explained by taking into account the magnetic field dependence of the Fermi energy.