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arXiv · 2605.06302

Quantum Electron Quasicrystal

Pierre-Antoine Graham·Filippo Gaggioli·Liang Fu
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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.

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Pierre-Antoine Graham, Filippo Gaggioli, Liang Fu. 2026-05-07. Quantum Electron Quasicrystal. https://arxiv.org/abs/2605.06302

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