Effects of electron interaction on the change in sound velocity under de Haas-van Alphen conditions

Based on a temperature propagator technique in the grand ensemble of an interacting electron gas, the oscillatory sound velocity is examined under the de Haas-van Alphen conditions. In consideration of the oscillation of the Fermi energy (chemical potential) and the first order exchange effects, the dHvA oscillations of the sound velocity are shown to have the same one phase as in the case of an ideal electron gas, in agreement with experimental results. For large electron density, that is, for very small r_s, and by a proper renormalization of the Fermi energy, we have succeeded in eliminating one of the two oscillatory functions which have a phase difference of $\text{π}\text{2}$.