Heterostructure design for high-quality, high-density, GaAs two-dimensional electron systems at large hydrostatic pressures
GaAs two-dimensional electron systems (2DESs) have a Lande $g$-factor close to zero under a sufficiently large hydrostatic pressure. Although this presents an intriguing platform to investigate electron-electron interaction in a system with $g=0$, studies are quite limited because the GaAs 2DES density decreases significantly with increasing hydrostatic pressure. Here we show that a simple model, based on pressure-dependent changes in the conduction band alignment, quantitatively explains this commonly observed trend. Furthermore, we demonstrate that the decrease in the 2DES density can be suppressed by more than a factor of 3 through an innovative heterostructure design.