1. Physical properties of an Aperiodic monotile: Graphene-like features, chirality and zero-modes
- Author
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Schirmann, Justin, Franca, Selma, Flicker, Felix, and Grushin, Adolfo G.
- Subjects
Condensed Matter - Mesoscale and Nanoscale Physics - Abstract
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 ($\phi$) is half of the flux quantum, zero-modes are found localized around the reflected `anti-hats'; and (v) its Hofstadter spectrum is periodic in $\phi$, 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., Comment: 8 + 4 pages; 3 + 5 figures
- Published
- 2023
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