Phonon emission and absorption in the fractional quantum Hall effect

We investigate the time dependent thermal relaxation of a two-dimensional electron system (2DES) in the fractional quantum Hall regime, where ballistic phonons are used to heat up the system to a non-equilibrium temperature. The thermal relaxation of a 2DES at ν = 1/2 can be described in terms of a broad band emission of phonons, with a temperature dependence proportional to T⁴. In contrast, the relaxation at fractional filling ν = 2/3 is characterized by phonon emission around a single energy, the magneto-roton gap. This leads to a strongly reduced energy relaxation rate compared to ν = 1/2 with only a weak temperature dependence for temperatures 150 mK < T < 400 mK.