Neural Quantum State Prediction of Paired Molecular Wigner Crystal in Honeycomb Moiré

Moiré systems have emerged as an exciting new 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 flexible and expressive neural quantum state ansatz based on the attention mechanism, we discover a new ground state in the two-dimensional electron gas in a honeycomb moiré potential at a filling factor of 1/4 (one electron for every four moiré minima). In this exotic state, opposite spin electrons pair to form a singlet-like valence bond state which restores local C6 symmetry. These pairs of electrons then maximize the distance between pairs by forming a molecular Wigner crystal, with one quarter of the moiré minima mostly depleted. This is remiscent to molecular Wigner crystals observed in twisted bilayer tungsten disulfide but is distinct in that, in this case, there are fewer electrons than minima. There is nothing forcing multiple electrons into a single minima nor is there any attractive interaction between electrons but in spite of this molecules form.