The Terahertz Frequency Hall Conductivity of a High-Mobility Two-Dimensional Electron Gas

We have performed the first measurement of the \emph{terahertz-frequency} complex conductivity tensor of a Landau-quantized high mobility ($10^{6}$ cm$^{2}$ V$^{-1}$ s$^{-1}$) GaAs two-dimensional electron gas. We use polarization-sensitive ultrafast terahertz magnetospectroscopy to resolve the on-axis and off-diagonal Hall conductivity elements. We focus our measurements near cyclotron resonance to determine the line width from 0.4 K to 100 K at $\pm$1.25 T. This line width decreases monotonically with temperature and does not saturate at the lowest temperatures measured. In this talk, we will develop a model of these data to discuss the relative influence of electron-electron, electron-phonon, and impurity scattering on the temperature dependent sample mobility.