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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| Accès en ligne: | https://arxiv.org/abs/2308.07701 |
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| _version_ | 1866909663436472320 |
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| author | Jagannathan, Anuradha Duneau, Michel |
| author_facet | Jagannathan, Anuradha Duneau, Michel |
| contents | Our understanding of physical properties of quasicrystals owes a great deal to studies of tight-binding models constructed on quasiperiodic tilings. Among the large number of possible quasiperiodic structures, two dimensional tilings are of particular importance -- in their own right, but also for information regarding properties of three dimensional systems. We provide here a users manual for those wishing to construct and study physical properties of the 8-fold Ammann-Beenker quasicrystal, a good starting point for investigations of two dimensional quasiperiodic systems. This tiling has a relatively straightforward construction. Thus, geometrical properties such as the type and number of local environments can be readily found by simple analytical computations. Transformations of sites under discrete scale changes -- called inflations and deflations -- are easier to establish compared to the celebrated Penrose tiling, for example. We have aimed to describe the methodology with a minimum of technicalities but in sufficient detail so as to enable non-specialists to generate quasiperiodic tilings and periodic approximants, with or without disorder. The discussion of properties includes some relations not previously published, and examples with figures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_07701 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Properties of the Ammann-Beenker tiling and its square approximants Jagannathan, Anuradha Duneau, Michel Strongly Correlated Electrons Our understanding of physical properties of quasicrystals owes a great deal to studies of tight-binding models constructed on quasiperiodic tilings. Among the large number of possible quasiperiodic structures, two dimensional tilings are of particular importance -- in their own right, but also for information regarding properties of three dimensional systems. We provide here a users manual for those wishing to construct and study physical properties of the 8-fold Ammann-Beenker quasicrystal, a good starting point for investigations of two dimensional quasiperiodic systems. This tiling has a relatively straightforward construction. Thus, geometrical properties such as the type and number of local environments can be readily found by simple analytical computations. Transformations of sites under discrete scale changes -- called inflations and deflations -- are easier to establish compared to the celebrated Penrose tiling, for example. We have aimed to describe the methodology with a minimum of technicalities but in sufficient detail so as to enable non-specialists to generate quasiperiodic tilings and periodic approximants, with or without disorder. The discussion of properties includes some relations not previously published, and examples with figures. |
| title | Properties of the Ammann-Beenker tiling and its square approximants |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2308.07701 |