Theory of phonon spectroscopy in the fractional quantum Hall regime

We describe a theoretical framework for the interpretation of time-resolved phonon absorption experiments carried out in the fractional quantum Hall regime of a magnetically quantized two-dimensional electron system. The only phonons which can be absorbed at low temperature are those whose energies exceed the magnetoroton gap predicted by Girvin, MacDonald and Platzman @Phys. Rev. B 33, 2481 \char1261986!#. The rate of energy transfer from the phonons to the electron liquid is entirely controlled by the creation of these collective excitations. Using simple isotropic approximations for the phonon propagation and electron-phonon coupling, we obtain analytic results for the regime in which the electron temperature and the characteristic temperature of the phonons are much less than the gap, and identify the way in which the dispersion curve of the magnetorotons could be extracted from time- and angle-resolved experiments.