Stability of Wigner crystals and Mott insulators in twisted moir\'e structures

TL;DR

This study investigates the stability of charge-ordered states like Wigner crystals and Mott insulators in TMD monolayers and heterostructures, revealing how moiré potentials and dielectric environment influence their melting temperatures and stability.

Contribution

It introduces a combined phonon mode expansion and Lindemann criterion approach to analyze the stability of these phases in TMD structures, highlighting the effects of moiré potential and stacking configurations.

Findings

Moiré potential in heterobilayers significantly increases melting temperatures.

Reduced dielectric screening enhances stability of charge-ordered states.

Stacking type influences the robustness of generalized Wigner crystals.

Abstract

Transition metal dichalcogenides (TMDs) constitute an intriguing platform for studying charge-ordered states including conventional and generalized Wigner crystals as well as Mott insulating states. In this work, we combine a phonon mode expansion of the electronic crystal vibrations with the Lindemann criterion to investigate the quantum and thermal stability of these strongly correlated phases in the exemplary materials of MoSe$_2$ monolayers and twisted MoSe$_2$-WSe$_2$ heterostructures. We find that the moir\'e potential in heterobilayers acts as a harmonic trap, flattening the energy dispersion of phonon excitations and resulting in an order of magnitude larger melting temperatures compared to monolayer Wigner crystals. Furthermore, we explore the tunability of the correlated states with respect to dielectric environment and bilayer stacking. In particular, we show that the reduced screening in free-standing TMDs results in a tenfold increase in the melting temperature compared to hBN-encapsulated TMDs. Moreover, the deeper moir\'e potential in R-type stacked heterostructures makes generalized Wigner crystals more stable than in H-type stacking. Overall, our study provides important microscopic insights on the stability and tunability of charge-ordered states in TMD-based structures.