相关论文: Tile Hamiltonians for Decagonal Phases

The AlPdMn quasicrystal approximants xi, xi', and xi'_n of the 1.6 nm decagonal phase and R, T, and T_n of the 1.2 nm decagonal phase can be viewed as arrangements of cluster columns on two-dimensional tilings. We substitute the tiles by…

Higher-order topological insulators (HOTIs) are a newly discovered class of topological insulators which exhibit unconventional bulk-boundary correspondence. Very recently, the concept of HOTIs has been extended to aperiodic…

We study magnetic properties of the half-filled Hubbard model on the two-dimensional $H_{00}$ hexagonal golden-mean quasiperiodic tiling. The tiling is composed of large and small hexagons, and parallelograms, and its vertex model is…

Aperiodic crystals constitute a fascinating class of materials that includes incommensurate (IC) modulated structures and quasicrystals (QCs). Although these two categories share a common foundation in the concept of superspace, the…

We propose a family of modulated honeycomb lattices, a class of quasiperiodic tilings characterized by the metallic mean. These lattices consist of six distinct hexagonal prototiles with two edge lengths, $\ell$ and $s$, and can be regarded…

A set of tiles for covering a surface is composed of two types of tiles. The base shape of each one of them is a diamond or rhombus, both with angles 60 and 120 degrees. They are distinguished by labeling one as an acute diamond with a base…

Quasicrystals are intriguing ordered structures characterized by the lack of translational symmetry and the existence of rotational symmetry. The tiling of different geometric units such as triangles and squares in two-dimensional space can…

Hubbard-like Hamiltonians are widely used to describe on-site Coulomb interactions in magnetic and strongly-correlated solids, but there is much confusion in the literature about the form these Hamiltonians should take for shells of p and d…

We discover the detailed atomic structure of $d$-MgZnY, a stable decagonal quasicrystal alloy of the layered Frank-Kasper type, and related phases, using the "tiling and decoration" approach. The atoms have invariable sites in the rectangle…

Surfaces in i-Al68Pd23Mn9 as observed with STM and LEED experiments show atomic terraces in a Fibonacci spacing. We analyze them in a bulk tiling model due to Elser which incorporates many experimental data. The model has dodecahedral…

A new family of decagonal quasiperiodic tilings are constructed by the use of generalized point substitution processes, which is a new substitution formalism developed by the author [N. Fujita, Acta Cryst. A 65, 342 (2009)]. These tilings…

Two-dimensional colloidal suspensions subject to laser interference patterns with decagonal symmetry can form an Archimedean-like tiling phase where rows of squares and triangles order aperiodically along one direction [J. Mikhael et al.,…

We apply systematic methods previously used by Mihalkovic et al. to predict the structure of the `basic' Co-rich modification of the decagonal Al70 Co20 Ni10 layered quasicrystal, based on known lattice constants and previously calculated…

Quasiperiodic patterns described by polyhedral "atomic surfaces" and admitting matching rules are considered. It is shown that the cohomology ring of the continuous hull of such patterns is isomorphic to that of the complement of a torus…

Topological phases supported by quasi-periodic spin-chain models and their bulk-boundary principles are investigated by numerical and K-theoretic methods. We show that, for both the un-correlated and correlated phases, the operator algebras…

We show that a single prototile can fill space uniformly but not admit a periodic tiling. A two-dimensional, hexagonal prototile with markings that enforce local matching rules is proven to be aperiodic by two independent methods. The…

Recently Taylor and Socolar introduced an aperiodic mono-tile. The associated tiling can be viewed as a substitution tiling. We use the substitution rule for this tiling and apply the algorithm of \cite{AL} to check overlap coincidence. It…

The eigenstates of d-dimensional quasicrystalline models with a separable Hamiltonian are studied within the tight-binding model. The approach is based on mathematical sequences, constructed by an inflation rule P = {w -> s, s -> sws^(b-1)}…

It is shown that tiling in icosahedral quasicrystals can also be properly described by cyclic twinning at the unit cell level. The twinning operation is applied on the primitive prolate golden rhombohedra, which can be considered a result…

Motivated by the rich phase diagram of the high temperature superconductors, we introduce a toy model with three state variables which can be interpreted as two state particles and holes. The Hamiltonian has a term which favors…