  Among very low disorder systems of condensed matter, the high mobility
two-dimensional electron gas confined in gallium arsenide/aluminum gallium
arsenide heterostructures holds a privileged position as platform for the
discovery of new electronic states driven by strong Coulomb interactions.
Molecular beam epitaxy (MBE), an ultra-high vacuum thin-film deposition
technique, produces the highest quality 2DEGs and has played a central role in
a number of discoveries that have at their root the interplay of reduced
dimensionality, strong electron-electron interactions, and disorder. This
review attempts to describe the latest developments in heterostructure design,
MBE technology, and our evolving understanding of disorder that result in
improved material quality and facilitate discovery of new phenomena at ever
finer energy scales.
