Momentum-Resolved Electronic Structure for Quasicrystals: Full-Band Spectra and Chern Number
Abstract
Quasicrystals lack the translational symmetry that underlies Bloch decomposition and Brillouin-zone integration, making full-band momentum-resolved electronic structure difficult to formulate and compute. We develop a systematically convergent reciprocal-space tight-binding framework for a broad class of quasicrystals. The method combines two systematically refinable components: a Fourier-module scattering-channel Hamiltonian that yields local spectral and current-current correlation quantities at each physical momentum, and an expanding hierarchy of pseudo-Brillouin zones that converts the resulting local quantities into bulk thermodynamic observables through an exact local-to-global relation. Applied to the Penrose and Ammann-Beenker models, the framework uncovers full-band momentum-resolved quasibands and a multichannel mechanism for pseudogap formation, both beyond the scope of low-energy effective models. It further resolves Zeeman-driven gap closings and reopenings, quantized Chern plateaus, and the phason invariance of bulk spectral and topological observables. This framework provides a unified reciprocal-space route to full-band spectral and topological properties of quasicrystals.
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BibTeX
@misc{yang2026momentumresolved,
title = {{Momentum-Resolved Electronic Structure for Quasicrystals: Full-Band Spectra and Chern Number}},
author = {Donglin Yang and Huajie Chen and Dexuan Zhou and Xiaoxu Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06043},
eprint = {2609.06043},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06043},
}
RIS
TY - UNPB
TI - Momentum-Resolved Electronic Structure for Quasicrystals: Full-Band Spectra and Chern Number
AU - Donglin Yang
AU - Huajie Chen
AU - Dexuan Zhou
AU - Xiaoxu Li
PY - 2026
DA - 2026/09/05
PB - arXiv
DO - 10.48550/arxiv.2609.06043
UR - https://arxiv.org/abs/2609.06043
AB - Quasicrystals lack the translational symmetry that underlies Bloch decomposition and Brillouin-zone integration, making full-band momentum-resolved electronic structure difficult to formulate and compute. We develop a systematically convergent reciprocal-space tight-binding framework for a broad class of quasicrystals. The method combines two systematically refinable components: a Fourier-module scattering-channel Hamiltonian that yields local spectral and current-current correlation quantities at each physical momentum, and an expanding hierarchy of pseudo-Brillouin zones that converts the resulting local quantities into bulk thermodynamic observables through an exact local-to-global relation. Applied to the Penrose and Ammann-Beenker models, the framework uncovers full-band momentum-resolved quasibands and a multichannel mechanism for pseudogap formation, both beyond the scope of low-energy effective models. It further resolves Zeeman-driven gap closings and reopenings, quantized Chern plateaus, and the phason invariance of bulk spectral and topological observables. This framework provides a unified reciprocal-space route to full-band spectral and topological properties of quasicrystals.
ER -