Ultra-high quality two-dimensional electron systems

Two-dimensional electrons confined to GaAs quantum wells are hallmark platforms for probing electron-electron interaction. Many key observations have been made in these systems as sample quality improved over the years. Here, we present a breakthrough in sample quality via source-material purification and innovation in GaAs molecular beam epitaxy vacuum chamber design. Our samples display an ultra-high mobility of $44\times10^6$ cm$^2$/Vs at an electron density of $2.0\times10^{11}$ /cm$^2$. These results imply only 1 residual impurity for every $10^{10}$ Ga/As atoms. The impact of such low impurity concentration is manifold. Robust stripe/bubble phases are observed, and several new fractional quantum Hall states emerge. Furthermore, the activation gap of the $\nu=5/2$ state, which is widely believed to be non-Abelian and of potential use for topological quantum computing, reaches $\Delta\simeq820$ mK. We expect that our results will stimulate further research on interaction-driven physics in a two-dimensional setting and significantly advance the field.