Physical properties of an Aperiodic monotile: Graphene-like features, chirality and zero-modes
arXiv:2307.11054 · doi:10.1103/PhysRevLett.132.086402
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 () is half of the flux quantum, zero-modes are found localized around the reflected `anti-hats'; and (v) its Hofstadter spectrum is periodic in , 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.
arXiv comment8 + 4 pages; 3 + 5 figures
References in corpus (60)
- The electronic properties of graphene
- Anderson Transitions
- Kwant: a software package for quantum transport
- Topological States and Adiabatic Pumping in Quasicrystals
- The Kernel Polynomial Method
- Majorana fermions in chains of magnetic atoms on a superconductor
- Dirac Electrons in a Dodecagonal Graphene Quasicrystal
- Mapping topological order in coordinate space
- Design and characterization of electronic fractals
- Gyrotropic magnetic effect and the magnetic moment on the Fermi surface
- Chiral Optical Response of Multifold Fermions
- Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport
- Fractal energy spectrum of a polariton gas in a Fibonacci quasi-periodic potential
- Three-dimensional Dirac fermions in quasicrystals as seen via optical conductivity
- Quantum Spin Hall Effect and Spin Bott Index in a Quasicrystal Lattice
- Chiral magnetic effect and natural optical activity in (Weyl) metals
- Emergence of criticality through a cascade of delocalization transitions in quasiperiodic chains
- Topological phases without crystalline counterparts
- Topological Hofstadter Insulators in a Two-Dimensional Quasicrystal
- Topological insulators and fractional quantum Hall effect on the ruby lattice
- Controlled length-dependent interaction of Majorana modes in Yu-Shiba-Rusinov chains
- Theory of spin Bott index for quantum spin Hall states in non-periodic systems
- Aperiodic Weak Topological Superconductors
- Topological Weaire-Thorpe models of amorphous matter
- Observation of spin-momentum locked surface states in amorphous BiSe
- Dodecagonal bilayer graphene quasicrystal and its approximants
- Chiral anomaly and giant magnetochiral anisotropy in noncentrosymmetric Weyl semimetals
- Higher-Order topological insulator in a dodecagonal quasicrystal
- Antiferromagnetic order in the Hubbard Model on the Penrose Lattice
- Critical eigenstates and their properties in one and two dimensional quasicrystals
- Topological models in rotationally symmetric quasicrystals
- Effective Model for Fractional Topological Corner Modes in Quasicrystals
- Topological states in quasicrystals
- Hofstadter butterfly of a quasicrystal
- Two-dimensional Shiba lattices as possible platform for crystalline topological superconductivity
- Topological Anderson insulator phase in a quasicrystal lattice
- Quasicrystalline Chern Insulators
- Multifractal analysis of the metal-insulator transition in anisotropic systems
- Band dispersion of graphene with structural defects
- Higher-order topological Anderson insulators in quasicrystals
- Energy landscape in two-dimensional Penrose-tiled quasicrystal
- Strictly localized states in the octagonal Ammann-Beenker quasicrystal
- Bulk Spectrum and K-theory for Infinite-Area Topological Quasicrystal
- Landau levels in quasicrystals
- Nature of Protected Zero Energy States in Penrose Quasicrystals
- Localization of Electronic Wave Functions on Quasiperiodic Lattices
- Length scale formation in the Landau levels of quasicrystals
- Obstructed insulators and flat bands in topological phase-change materials
- Classical Dimers on Penrose Tilings
- Energy level statistics of electrons in a 2D quasicrystal
- Topological Gaps in Quasi-Periodic Spin Chains: A Numerical and K-Theoretic Analysis
- Optical rotation in thin chiral/twisted materials and the gyrotropic magnetic effect
- Statistical mechanics of dimers on quasiperiodic Ammann-Beenker tilings
- Macroscopically degenerate localized zero-energy states of quasicrystalline bilayer systems in strong coupling limit
- Quasiperiodic tilings under magnetic field
- Quasicrystalline structure of the Smith monotile tilings
- Dulmage-Mendelsohn percolation: Geometry of maximally-packed dimer models and topologically-protected zero modes on site-diluted bipartite lattices
- Bulk Localised Transport States in Infinite and Finite Quasicrystals via Magnetic Aperiodicity
- Higher-dimensional Hofstadter butterfly on Penrose lattice
- Closing of gaps and gap labeling and passage from molecular states to critical states in a 2D quasicrystal
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- 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