Non-uniform quantum geometry stabilizes generalized Wigner crystals
Abstract
Moiré materials host fractional Chern insulators and electron crystals in close proximity, but the mechanism selecting between them remains an open question. We address this competition in Chern bands with ideal but momentum-dependent quantum geometry -- Aharonov-Casher bands. We present an ansatz wave function for generalized Wigner crystals and, by comparing its energy to that of the competing Laughlin-like state, map out the phase diagram at filling fraction ν=1/m as a function of the degree of geometric non-uniformity. Our work identifies quantum geometry-controlled zero point fluctuations of the charge density of the generalized Wigner crystal as the mechanism controlling its relative stability, implying a kind of quantum Lindemann criterion for the crystal-liquid phase boundary.
Related
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BibTeX
@misc{moralesduran2026nonuniform,
title = {{Non-uniform quantum geometry stabilizes generalized Wigner crystals}},
author = {Nicolás Morales-Durán and Tobias M. R. Wolf and Jingtian Shi and Tomohiro Soejima and Andrew J. Millis and Jennifer Cano},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04149},
eprint = {2609.04149},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04149},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Non-uniform quantum geometry stabilizes generalized Wigner crystals
AU - Nicolás Morales-Durán
AU - Tobias M. R. Wolf
AU - Jingtian Shi
AU - Tomohiro Soejima
AU - Andrew J. Millis
AU - Jennifer Cano
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.04149
UR - https://arxiv.org/abs/2609.04149
AB - Moiré materials host fractional Chern insulators and electron crystals in close proximity, but the mechanism selecting between them remains an open question. We address this competition in Chern bands with ideal but momentum-dependent quantum geometry -- Aharonov-Casher bands. We present an ansatz wave function for generalized Wigner crystals and, by comparing its energy to that of the competing Laughlin-like state, map out the phase diagram at filling fraction ν=1/m as a function of the degree of geometric non-uniformity. Our work identifies quantum geometry-controlled zero point fluctuations of the charge density of the generalized Wigner crystal as the mechanism controlling its relative stability, implying a kind of quantum Lindemann criterion for the crystal-liquid phase boundary.
ER -