Brillouin zone labelling for quasicrystals
We propose a scheme to determine the energy-band dispersion of quasicrystals that does not require any periodic approximation and directly provides the correct structure of the extended Brillouin zones. From the gap labelling viewpoint, this allows us to transpose the measurement of the integrated d...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2014-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/16/4/043013 |
| _version_ | 1797751549688020992 |
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| author | Jean-Marc Gambaudo Patrizia Vignolo |
| author_facet | Jean-Marc Gambaudo Patrizia Vignolo |
| author_sort | Jean-Marc Gambaudo |
| collection | DOAJ |
| description | We propose a scheme to determine the energy-band dispersion of quasicrystals that does not require any periodic approximation and directly provides the correct structure of the extended Brillouin zones. From the gap labelling viewpoint, this allows us to transpose the measurement of the integrated density of states with that of the effective Brillouin zone areas, which are uniquely determined by the position of the Bragg peaks. Moreover, we show that the Bragg vectors can be determined by stability analysis of the law of recurrence used to generate the quasicrystal. Our analysis of gap labelling in the quasi-momentum space opens the way to experimental proof of gap labelling itself within the framework of optics experiments, polaritons, or with ultracold atoms. |
| first_indexed | 2024-03-12T16:51:10Z |
| format | Article |
| id | doaj.art-f646a530b14f4306b603faf6c687fafd |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:51:10Z |
| publishDate | 2014-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-f646a530b14f4306b603faf6c687fafd2023-08-08T11:21:24ZengIOP PublishingNew Journal of Physics1367-26302014-01-0116404301310.1088/1367-2630/16/4/043013Brillouin zone labelling for quasicrystalsJean-Marc Gambaudo0Patrizia Vignolo1Université de Nice - Sophia Antipolis , Institut non Linéaire de Nice, CNRS, 1361 route des Lucioles, F-06560 Valbonne, FranceUniversité de Nice - Sophia Antipolis , Institut non Linéaire de Nice, CNRS, 1361 route des Lucioles, F-06560 Valbonne, FranceWe propose a scheme to determine the energy-band dispersion of quasicrystals that does not require any periodic approximation and directly provides the correct structure of the extended Brillouin zones. From the gap labelling viewpoint, this allows us to transpose the measurement of the integrated density of states with that of the effective Brillouin zone areas, which are uniquely determined by the position of the Bragg peaks. Moreover, we show that the Bragg vectors can be determined by stability analysis of the law of recurrence used to generate the quasicrystal. Our analysis of gap labelling in the quasi-momentum space opens the way to experimental proof of gap labelling itself within the framework of optics experiments, polaritons, or with ultracold atoms.https://doi.org/10.1088/1367-2630/16/4/043013quasicrystalsband structureBrillouin zones71.23.Ft71.20.-b61.50.Ah |
| spellingShingle | Jean-Marc Gambaudo Patrizia Vignolo Brillouin zone labelling for quasicrystals New Journal of Physics quasicrystals band structure Brillouin zones 71.23.Ft 71.20.-b 61.50.Ah |
| title | Brillouin zone labelling for quasicrystals |
| title_full | Brillouin zone labelling for quasicrystals |
| title_fullStr | Brillouin zone labelling for quasicrystals |
| title_full_unstemmed | Brillouin zone labelling for quasicrystals |
| title_short | Brillouin zone labelling for quasicrystals |
| title_sort | brillouin zone labelling for quasicrystals |
| topic | quasicrystals band structure Brillouin zones 71.23.Ft 71.20.-b 61.50.Ah |
| url | https://doi.org/10.1088/1367-2630/16/4/043013 |
| work_keys_str_mv | AT jeanmarcgambaudo brillouinzonelabellingforquasicrystals AT patriziavignolo brillouinzonelabellingforquasicrystals |