On the origin of energy gaps in quasicrystalline potentials
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866918454278225920 |
|---|---|
| author | Gottlob, Emmanuel Gröters, David Schneider, Ulrich |
| author_facet | Gottlob, Emmanuel Gröters, David Schneider, Ulrich |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18328 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the origin of energy gaps in quasicrystalline potentials Gottlob, Emmanuel Gröters, David Schneider, Ulrich Materials Science Disordered Systems and Neural Networks Mesoscale and Nanoscale Physics Quantum Gases 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. |
| title | On the origin of energy gaps in quasicrystalline potentials |
| topic | Materials Science Disordered Systems and Neural Networks Mesoscale and Nanoscale Physics Quantum Gases |
| url | https://arxiv.org/abs/2512.18328 |