Quantum Electron Quasicrystal
Abstract
The strongly correlated phases of the homogeneous electron gas constitute the vocabulary of many-body condensed matter physics and find a natural realization in semiconductors. In this setting, recent neural-network variational Monte Carlo calculations discovered an unexpected quantum phase of matter in wide quantum wells: an electronic quasicrystal formed by a bilayer Wigner crystals with a 30-degrees twist. This state defies classical expectations and emerges in a regime dominated by quantum fluctuations. Here, we develop an analytical framework to reveal its origin. By computing zero-point energy corrections to bilayer Wigner crystal configurations, we show that quantum fluctuations qualitatively reshape the energetic landscape, destabilizing the classical honeycomb state and selecting the 30-degrees quasicrystalline ground state over a broad parameter range. Our results identify zero-point motion as the mechanism stabilizing the electronic quasicrystal and establish a route to spontaneous moir\'e physics driven by many-body quantum effects.
Cite
@article{arxiv.2605.06302,
title = {Quantum Electron Quasicrystal},
author = {Pierre-Antoine Graham and Filippo Gaggioli and Liang Fu},
journal= {arXiv preprint arXiv:2605.06302},
year = {2026}
}