Wigner crystallization in transition metal dichalcogenides: A new approach to correlation energy

TL;DR

This paper presents a novel method for calculating correlation energy in 2D electron systems, accurately predicting Wigner crystallization in monolayer TMDs and showing valley degeneracy has minimal impact on the transition point.

Contribution

It introduces a combined high-density and low-density approach for correlation energy and applies it to predict Wigner crystallization in monolayer TMDs, challenging previous assumptions.

Findings

Correlation energy approach agrees with Quantum Monte Carlo results.

Wigner crystallization occurs at similar $r_s$ values for one- and two-valley systems.

Valley degeneracy has little effect on the critical $r_s$ for crystallization.

Abstract

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 a random phase approximation at high densities and a classical approach at low densities, with interpolation between the two limits. This approach gives excellent agreement with available Quantum Monte Carlo (QMC) calculations. We employ the two-valley 2DEG model to describe the electron correlations in monolayer transition metal dichalcogenides (TMDs). The zero-temperature transition from a Fermi liquid to a quantum Wigner crystal phase in monolayer TMDs is obtained using density-functional theory within the local-density approximation. Consistent with QMC, we find that electrons crystallize at $r_s=30.5$ in one-valley 2DEG. For two-valleys, we predict Wigner crystallization at $r_s= 29.5$, indicating that valley degeneracy has little effect on the critical $r_s$, in contrast to an earlier claim.