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Two-dimensional electron gases (2DEGs) with high mobility, engineered insemiconductor heterostructures host a variety of ordered phases arising fromstrong correlations, which emerge at sufficiently low temperatures. The 2DEGcan be further controlled by surface gates to create quasi-one dimensionalsystems, with potential spintronic applications. Here we address thelong-standing challenge of cooling such electrons to below 1$\,$mK, potentiallyimportant for identification of topological phases and spin correlated states.The 2DEG device was immersed in liquid $^3$He, cooled by the nuclear adiabaticdemagnetization of copper. The temperature of the 2D electrons was inferredfrom the electronic noise in a gold wire, connected to the 2DEG by a metallicohmic contact. With effective screening and filtering, we demonstrate atemperature of 0.9$\,\pm\,$0.1$\,$mK, with scope for significant furtherimprovement. This platform is a key technological step, paving the way toobserving new quantum phenomena, and developing new generations ofnanoelectronic devices exploiting correlated electron states.

Cooling low-dimensional electron systems into the microkelvin regime