Related papers: Tile Hamiltonian for Decagonal AlCoCu
The recently discovered chiral monotile Tile(1,1) is tiling the plane in a quasiperiodic fashion by taking twelve different orientations when applying $2\pi/12$ rotation. An homochiral inflation construction of such a quasiperiodic tiling…
Quasicrystals possess long-range order but lack the translational symmetry of crystalline solids. In solid state physics, periodicity is one of the fundamental properties that prescribes the electronic band structure in crystals. In the…
In the Al-Co-Cu alloy system, both the decagonal quasicrystal with the space group of $P\overline{10}m2$ and its approximant Al$_{13}$Co$_4$ phase with monoclinic $Cm$ symmetry are present around 20 at.% Co-10 at.% Cu. In this study, we…
Dodecagonal oxide quasicrystals (OQCs) have so far been limited to a few elemental systems, with no general formation mechanism established. Here, we demonstrate a versatile approach to OQC formation via a host-atom-induced transformation…
The occurrence of stable decagonal quasicrystalline phase in Al-Co-Ni and Al-Cu-Co alloys through conventional solidification is well established. Earlier, we have studied the effect of Cu substitution in place of Co in the Al70 Co15Ni15…
Tiling models can reveal unexpected ways in which local constraints give rise to exotic long-range spatial structure. The recently discovered Hat monotile (and its mirror image) has been shown to be aperiodic~[Smith et al., arXiv:2303.10798…
Aperiodic tiling --- a form of complex global geometric structure arising through locally checkable, constant-time matching rules --- has long been closely tied to a wide range of physical, information-theoretic, and foundational…
We propose a new example of discrete holography that provides a new step towards establishing the AdS/CFT duality for discrete spaces. A class of boundary Hamiltonians is obtained in a natural way from regular tilings of the hyperbolic…
The Penrose tiling is a perfectly ordered two dimensional structure with fivefold symmetry and scale invariance under site decimation. Quantum spin models on such a system can be expected to differ significantly from more conventional…
Quasicrystals exhibit superconductivity under the unique interplay of long-range order and strong inhomogeneity, distinguishing them from both crystalline and amorphous systems. Understanding how this structural complexity affects…
We present a novel variant of a planar quasiperiodic tiling with tenfold symmetry, employing the same thick and thin rhombuses as the celebrated rhombic Penrose tiling. Despite its distinct visual appearance, this new tiling shares several…
This paper is about the tiling dynamical systems approach to the study of aperiodic order. We compare and contrast four related types of systems: ordinary (one-dimensional) symbolic systems, one-dimensional tiling systems, multidimensional…
We show how we found substitution rules for a quasiperiodic tiling with local rotational symmetry and inflation factor 1 + sqrt(3). The base tiles are a square, a rhomb with an acute angle of 30 degrees, and equilateral triangles that are…
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…
Symmetry sharing facilitates coherent interfaces which can transition from periodic to aperiodic structures. Motivated by the design and construction of such systems, we present hexagonal aperiodic tilings with a single edge-length which…
Single cluster covering approach provides a plausible mechanism for the formation and stability of octagonal and decagonal quasiperiodic structures. For dodecagonal quasiperiodic pattern such a single cluster covering scheme is still…
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…
Metasurface, a kind of two-dimensional structured medium, represents a novel platform to manipulate the propagation of light at subwavelength scale. In linear optical regime, many interesting topics such as planar metalens, metasurface…
FeF$_3$, with its half-filled Fe$^{3+}$ $3d$ orbital, hence zero orbital angular momentum and $S=5/2$, is often put forward as a prototypical highly-frustrated classical Heisenberg pyrochlore antiferromagnet. By employing {\it ab initio}…
The magnetic phase diagram and the thermodynamic properties of a square lattice containing antiferromagnetically coupled spin-1/2 triangles are studied. A Heisenberg Hamiltonian with three strong intra-triangle exchange coupling constants…