Among very-low-disorder systems of condensed matter, the high-mobility two-dimensional electron gas (2DEG) confined in aluminum gallium arsenide (AlGaAs)–gallium arsenide (GaAs) heterostructures holds a privileged position as a platform for the discovery of new electronic states driven by strong Coulomb interactions. Molecular beam epitaxy (MBE), an ultra-high vacuum (UHV), 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 the evolution of our understanding of disorder that result in improved material quality and facilitate discovery of new phenomena at ever finer energy scales.


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