Ballistic heating of a two-dimensional electron system by phonon excitation of the magnetoroton minimum at v=1/3

A two-dimensional electron system (2DES) is excited with ballistic phonons. Using the 2DES as a thermometer we directly measure the specific heat of t he electron system. At a Landau level filling factor nu = 1/3 we deduce a s trongly reduced specific heat compared to nu = 1/2 which we can assign to a small but finite density of states in the fractional quantum Hall gap. Fur thermore, at nu = 1/3 the phonons are shown to excite finite wave vector ma gnetorotons across a gap, in excellent agreement with theoretical predictio ns.