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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2307.11054 |
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| _version_ | 1866914715134853120 |
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| author | Schirmann, Justin Franca, Selma Flicker, Felix Grushin, Adolfo G. |
| author_facet | Schirmann, Justin Franca, Selma Flicker, Felix Grushin, Adolfo G. |
| contents | The discovery of the Hat, an aperiodic monotile, has revealed novel mathematical aspects of aperiodic tilings. However, the physics of particles propagating in such a setting remains unexplored. In this work we study spectral and transport properties of a tight-binding model defined on the Hat. We find that (i) the spectral function displays striking similarities to that of graphene, including six-fold symmetry and Dirac-like features; (ii) unlike graphene, the monotile spectral function is chiral, differing for its two enantiomers; (iii) the spectrum has a macroscopic number of degenerate states at zero energy; (iv) when the magnetic flux per plaquette ($ϕ$) is half of the flux quantum, zero-modes are found localized around the reflected `anti-hats'; and (v) its Hofstadter spectrum is periodic in $ϕ$, unlike for other quasicrystals. Our work serves as a basis to study wave and electron propagation in possible experimental realizations of the Hat, which we suggest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_11054 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Physical properties of an Aperiodic monotile: Graphene-like features, chirality and zero-modes Schirmann, Justin Franca, Selma Flicker, Felix Grushin, Adolfo G. Mesoscale and Nanoscale Physics The discovery of the Hat, an aperiodic monotile, has revealed novel mathematical aspects of aperiodic tilings. However, the physics of particles propagating in such a setting remains unexplored. In this work we study spectral and transport properties of a tight-binding model defined on the Hat. We find that (i) the spectral function displays striking similarities to that of graphene, including six-fold symmetry and Dirac-like features; (ii) unlike graphene, the monotile spectral function is chiral, differing for its two enantiomers; (iii) the spectrum has a macroscopic number of degenerate states at zero energy; (iv) when the magnetic flux per plaquette ($ϕ$) is half of the flux quantum, zero-modes are found localized around the reflected `anti-hats'; and (v) its Hofstadter spectrum is periodic in $ϕ$, unlike for other quasicrystals. Our work serves as a basis to study wave and electron propagation in possible experimental realizations of the Hat, which we suggest. |
| title | Physical properties of an Aperiodic monotile: Graphene-like features, chirality and zero-modes |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2307.11054 |