In devices based on two-dimensional electron gases (2DEGs), gate electrodes can be used to tune the electronic properties by controlling the electron density. Despite the prevalence of such gated systems, the properties of 2DEGs in these environments remain poorly understood quantitatively. To address this, we have studied the 2DEG in a dual-gate geometry using quantum Monte Carlo simulations alongside simpler approximate methods, and we have mapped out the phase diagram of the gated 2DEG as a function of electron density and gate distance. We find that the Wigner crystal is unstable at all densities when the gates are sufficiently close to the 2DEG, and we identify the critical gate distance at which the Wigner crystal phase appears. For larger gate separations, we determine the phase boundary for the reentrant crystal to liquid transition that occurs with decreasing density. Our Letter is particularly relevant to Wigner crystal phases recently observed in a variety of gated two-dimensional materials.

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• Liquid crystal phase transitions
• Quantum phase transitions
• Two-dimensional electron system
• Diffusion quantum Monte Carlo
• Variational approach