Moiré engineering in atomically thin van der Waals heterostructures creates artificial quantum materials with designer properties. We solve the many-body problem of interacting electrons confined to a moiré superlattice potential minimum (the moiré atom) using a 2D fermionic neural network. We show that strong Coulomb interactions in combination with the anisotropic moiré potential lead to striking ``Wigner molecule" charge density distributions observable with scanning tunneling microscopy.
Moiré engineering in atomically thin van der Waals heterostructures creates artificial quantum materials with designer properties. We solve the many-body problem of interacting electrons confined to a moiré superlattice potential minimum (the moiré atom) using a 2D fermionic neural network. We show that strong Coulomb interactions in combination with the anisotropic moiré potential lead to striking ``Wigner molecule" charge density distributions observable with scanning tunneling microscopy.
Moiré 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 νm=1/4 (one electron every four moiré minima). In this state, two opposite-spin electrons pair to form a singlet-like valence bond state which restores local C6 symmetry in hexagonal molecules each spanning 6 moiré minima. These molecules of pairs then form a molecular Wigner crystal, leaving one quarter of the moiré 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.
Abstract 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 neural-network-based quantum Monte Carlo approach, we discover a new ground state of the two-dimensional electron gas in a honeycomb moiré potential at a filling factor of ν m = 1/4 (one electron every four moiré minima). In this state, two opposite-spin electrons pair to form singlet-like valence bond states which restore local C 6 symmetry in hexagonal molecules each spanning 6 moiré minima. These molecules of pairs then form a molecular Wigner crystal, leaving one quarter of the moiré 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 in a system within current experimental setups. This discovery signals a new level of predictive power in quantum many-body computations enabled by neural networks and machine learning.
Abstract Moiré superlattice designed in stacked van der Waals material provides a dynamic platform for hosting exotic and emergent condensed matter phenomena. However, the relevance of strong correlation effects and the large size of moiré unit cells pose significant challenges for traditional computational techniques. To overcome these challenges, we develop an unsupervised deep learning approach to uncover electronic phases emerging from moiré systems based on variational optimization of neural network many-body wavefunction. Our approach has identified diverse quantum states, including novel phases such as generalized Wigner crystals, Wigner molecular crystals, and previously unreported Wigner covalent crystals. These discoveries provide insights into recent experimental studies and suggest new phases for future exploration. They also highlight the crucial role of spin polarization in determining Wigner phases. More importantly, our proposed deep learning approach is proven general and efficient, offering a powerful framework for studying moiré physics.
Moiré materials provide an ideal platform for exploring quantum phases of matter. However, solving the many-electron problem in moiré systems is challenging due to strong correlation effects. We introduce a powerful variational representation of quantum states, many-body neural Bloch wavefunction, to solve many-electron problems in moiré materials accurately and efficiently. Applying our method to the semiconductor heterobilayer WSe2/WS2 , we obtain a generalized Wigner crystal at filling factor n = 1/3, a Mott insulator n = 1, and a correlated insulator with local magnetic moments and antiferromagnetic spin correlation at n = 2. Our neural network approach improves the simulation accuracy of strongly interacting moiré materials and paves the way for discovery of new quantum phases with variational learning principle in a unified framework.
Quantum Wigner molecules (WMs) in strongly interacting few-body fermionic moir\'e quantum dots in twisted bilayers of transition metal dichalcogenide (TMD) materials are uncovered via full configuration interaction calculations, going beyond the Aufbau principle of natural atoms and Hubbard modeling. Nested polygonal sliding rings of localized fermions, hidden in the exact particle densities, are revealed through wavefunction correlation analysis [see (3,9) and (1,6,10) electron WMs in 2D semiconductors], broadening the WM portfolio to include the TMD trilobal symmetry as an added resource in twistronics, and providing benchmarks for AI-based many-body computations.
Solid-state platforms are particularly attractive for quantum optics because they facilitate on-chip integration and are compatible with established semiconductor and photonic technologies. However, a major challenge in solid-state quantum optics is the fabrication of arrays of identical emitters, such as quantum dots. In this work, we propose moire superlattices as a novel solid-state platform for manipulating light at the single-photon level. Moire superlattices form arrays of artificial-atom states characterized by nearly identical optical transition energies, tunable spacing, and highly adjustable electronic structures. They naturally operate as atomically thin, scalable, periodic emitters, making them ideal for quantum applications. Additionally, the extensive materials database of moire superlattices offers spectral coverage spanning a broad range of optical wavelengths.