# Honeycomb Crystal in a Mass-Asymmetric Electron-Hole Bilayer

arXiv: https://arxiv.org/abs/2610.17030 · HTML: https://mlsanity.com/paper/2610.17030/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 97 references that are in the map.
- First posted on arXiv 12 Oct 2026.

## Builds on (most cited first, 10 of 10)

- [Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networks](https://mlsanity.com/paper/1909.02487/) (2019)
- [Deep neural network solution of the electronic Schr"odinger equation](https://mlsanity.com/paper/1909.08423/) (2019)
- [A Self-Attention Ansatz for Ab-initio Quantum Chemistry](https://mlsanity.com/paper/2211.13672/) (2022)
- [Discovering Quantum Phase Transitions with Fermionic Neural Networks](https://mlsanity.com/paper/2202.05183/) (2022)
- [Accurate Computation of Quantum Excited States with Neural Networks](https://mlsanity.com/paper/2308.16848/) (2023)
- [An ab initio foundation model of wavefunctions that accurately describes chemical bond breaking](https://mlsanity.com/paper/2506.19960/) (2025)
- [Neural Wave Functions for Superfluids](https://mlsanity.com/paper/2305.06989/) (2023)
- [Pairing-based graph neural network for simulating quantum materials](https://mlsanity.com/paper/2311.02143/) (2023)
- [Deep Variational Free Energy Approach to Dense Hydrogen](https://mlsanity.com/paper/2209.06095/) (2022)
- [Revisiting the Broken Symmetry Phase of Solid Hydrogen: A Neural Network Variational Monte Carlo Study](https://mlsanity.com/paper/2512.17703/) (2025)

## Abstract (arXiv)

A two-dimensional electron gas in a uniform neutralizing background forms a triangular Wigner crystal at low density. In a strongly mass-asymmetric electron-hole bilayer, localized heavy holes instead provide a nonuniform positive background that supports an electron crystal at densities two orders of magnitude higher than for a homogeneous electron gas in the same material. Here we show that correlated mobile electrons can overturn the preference for triangular order, stabilizing a honeycomb electron-hole crystal. Using the powerful real-space neural-network variational Monte Carlo in the Born-Oppenheimer limit with fixed holes, we find that increasing the density drives a transition from a triangular electron-hole crystal to a honeycomb crystal, which eventually melts into itinerant electrons coexisting with the honeycomb or the triangular hole lattice at fixed interlayer separation. Relative to triangular order, honeycomb order emerges when gains in electronic kinetic energy and electron-hole attraction outweigh its higher intralayer Coulomb repulsion, a threshold never reached in the rigid point-dipole model. Moreover, the honeycomb hole lattice supports paramagnetic, antiferromagnetic, and stripe-ordered spin states. Complex polarization indicates a metal-insulator transition, while the states on the honeycomb hole lattice are consistent with a stripe-ordered Dirac semimetal and paramagnetic or antiferromagnetic Mott insulators via mapping to the half-filled Hubbard model. We further propose a BLG/hBN/WS2-WSe2 heterostructure as a platform for the predicted honeycomb crystal, at an experimentally feasible density n~1011~cm-2.