Physical properties of an Aperiodic monotile: Graphene-like features, chirality and zero-modes

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 ($\varphi$) is half of the flux quantum, zero-modes are found localized around the reflected `anti-hats'; and (v) its Hofstadter spectrum is periodic in $\varphi$, 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.

8 + 4 pages; 3 + 5 figures

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Cited by in corpus (10)

• Scaling of the Integrated Quantum Metric in Disordered Topological Phases
• Beating the aliasing limit with aperiodic monotile arrays
• Exact Solution to the Quantum and Classical Dimer Models on the Spectre Aperiodic Monotiling
• A tale of two localizations: coexistence of flat bands and Anderson localization in a photonics-inspired amorphous system
• Non-equilibrium dynamics of localization phase transition in the non-Hermitian Disorder-Aubry-André model
• Hamiltonian Cycles on Ammann-Beenker Tilings
• Family of Aperiodic Tilings with Tunable Quantum Geometric Tensor
• Proximity Effects Between the Graphene Quasicrystal and Magic-Angle Twisted Bilayer Graphene
• Chiral Diffraction from Aperiodic Monotile Lattice
• Superconducting order parameter in aperiodic binary systems