Neural Network Discovery of Paired Wigner Crystals in Artificial Graphene

TL;DR

This paper uses neural network quantum Monte Carlo methods to discover a novel paired Wigner crystal state in a moiré honeycomb system at quarter filling, revealing complex collective phenomena in strongly interacting electrons.

Contribution

It introduces a neural-network-based approach to identify a new paired Wigner crystal state in a moiré system, highlighting a novel quantum many-body phenomenon.

Findings

Discovery of a paired Wigner crystal state at 1/4 filling.

Formation of singlet-like electron pairs restoring local symmetry.

Presence of a molecular Wigner crystal with depleted moiré minima.

Abstract

Moir\'e systems have emerged as an exciting tunable platform for engineering and probing quantum matter. A large number of exotic states have been observed, stimulating intense efforts in experiment, theory, and simulation. Utilizing a neural-network-based quantum Monte Carlo approach, we discover a new ground state of the two-dimensional electron gas in a honeycomb moire potential at a filling factor of $\nu_m =1/4$ (one electron every four moir\'e minima). In this state, two opposite-spin electrons pair to form a singlet-like valence bond state which restores local $C_6$ symmetry in hexagonal molecules each spanning $6$ moir\'e minima. These molecules of pairs then form a molecular Wigner crystal, leaving one quarter of the moir\'e minima mostly depleted. The formation of such a paired Wigner crystal, absent any confining potential or attractive interaction to facilitate "pre-assembling" the molecule, provides a fascinating case of collective phenomena in strongly interacting quantum many-body systems, and opportunities to engineer exotic properties.