We introduce a new approach for the correlation energy of one- and two-valley two-dimensional electron gas (2DEG) systems. Our approach is based on an interpolation between two limits, a random phase approximation at high densities and a classical approach at low densities which gives excellent agreement with available Quantum Monte Carlo (QMC) calculations. The two-valley 2DEG model is introduced to describe the electron correlations in monolayer transition metal dichalcogenides (TMDs). We study the zero-temperature transition from a Fermi liquid to a quantum Wigner crystal phase in monolayer TMDs. Consistent with QMC, we find that electrons crystallize at $r_s=31$ in one-valley 2DEG. For two valleys, we predict Wigner crystallization at $r_s=30$, implying that valley degeneracy has little effect on the critical $r_s$, in contrast to an earlier claim.

• Received 15 November 2016
• Revised 20 February 2017

DOI:https://doi.org/10.1103/PhysRevB.95.115438