The homogeneous electron gas is a cornerstone of quantum condensed matter physics, providing the foundation for developing density functional theory and understanding electronic phases in semiconductors. However, theoretical understanding of strongly-correlated electrons in realistic semiconductor systems remains limited. In this work, we develop a neural network based variational approach to study quantum wells in three dimensional geometry for a variety of electron densities and well thicknesses. Starting from first principles, our unbiased AI-powered method reveals metallic and crystalline phases with both monolayer and bilayer charge distributions. In the emergent bilayer, we discover a new quantum phase of matter: the electronic quasicrystal.
@article{arxiv.2512.10909,
title = {Electronic crystals and quasicrystals in semiconductor quantum wells: an AI-powered discovery},
author = {Filippo Gaggioli and Pierre-Antoine Graham and Liang Fu},
journal= {arXiv preprint arXiv:2512.10909},
year = {2025}
}