Origin and stability of generalized Wigner crystallinity in triangular moir\'e systems

TL;DR

This paper investigates the origins and stability of generalized Wigner crystals in triangular moiré systems, analyzing classical and quantum effects, and clarifies the limitations of different interaction models in explaining experimental observations.

Contribution

It provides a detailed microscopic analysis of GWC formation at specific fillings, highlighting the roles of interaction range and quantum effects, and predicts experimental realizations.

Findings

Finite-range interactions have limitations in describing GWC.

An effective nearest-neighbor model captures some properties.

Identification of a 'pinball' phase with quantum melting characteristics.

Abstract

Generalized Wigner crystals (GWC) on triangular moir\'e superlattices, formed from stacking two layers of transition metal chalcogenides, have been observed at multiple fractional fillings [Nature 587, 214 - 218 (2020), Nat. Phys. 17, 715 - 719 (2021), Nature 597, 650 - 654 (2021)]. Motivated by these experiments, tied with the need for accurate microscopic descriptions of these materials, we explore the origins of GWC at $n=1/3$ and $2/3$ filling. We demonstrate the general limitations of theoretical descriptions relying on finite-range, versus long-range interactions, however, we clarify why some properties are captured by an effective nearest-neighbor model. We study both classical and quantum effects at zero and finite temperatures, discussing the role of charge frustration, identifying a ``pinball" phase, a partially quantum melted GWC, with no classical analog. Our work addresses several experimental observations and makes predictions for how many of the theoretical findings can be potentially realized in future experiments.