On the origin of energy gaps in quasicrystalline potentials

Emmanuel Gottlob; David Gröters; Ulrich Schneider

doi:10.1103/tpqy-pdmz

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arXiv · 2512.18328

On the origin of energy gaps in quasicrystalline potentials

Emmanuel Gottlob·David Gröters·Ulrich Schneider

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Abstract

Quasicrystals, structures that are ordered yet aperiodic, defy conventional band theory, confining most studies to finite-size real-space numerics. We overcome this limitation with a configuration-space framework that predicts and explains the positions and origins of energy gaps in quasicrystalline potentials. We find that a hierarchy of gaps stems from resonant hybridization between increasingly distant neighboring sites, pinning the integrated density of states below these gaps to specific irrational areas in configuration space. Large-scale simulations of a lowest-band tight-binding model built from localized Wannier functions show excellent agreement with these predictions. By moving beyond finite-size numerics, this study advances the understanding of quasicrystalline potentials, paving the way for new explorations of their quantum properties in the infinite-size limit.

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Emmanuel Gottlob, David Gröters, Ulrich Schneider. 2025-12-20. On the origin of energy gaps in quasicrystalline potentials. https://doi.org/10.1103/tpqy-pdmz

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