Related papers: Layer group classification of two-dimensional mate…
The structure of the coincidence symmetry group of an arbitrary $n$-dimensional lattice in the $n$-dimensional Euclidean space is considered by describing a set of generators. Particular attention is given to the coincidence isometry…
The phase diagram of binary mixtures of particles interacting via a pair potential of parallel dipoles is computed at zero temperature as a function of composition and the ratio of their magnetic susceptibilities. Using lattice sums, a rich…
A general theory of topological classification of defects is introduced. We illustrate the application of tools from algebraic topology, including homotopy and cohomology groups, to classify defects including several explicit calculations…
Crystals are the foundation of numerous scientific and industrial applications. While various learning-based approaches have been proposed for crystal generation, existing methods seldom consider the space group constraint which is crucial…
We introduce the Computational 2D Materials Database (C2DB), which organises a variety of structural, thermodynamic, elastic, electronic, magnetic, and optical properties of around 1500 two-dimensional materials distributed over more than…
The past decade has seen rapid growth in the number of experimentally realized two-dimensional (2D) materials with diverse chemical and physical properties. However, information on their crystal structure, synthesis routes, and measured or…
Two-dimensional materials are a class of atomically thin materials with assorted electronic and quantum properties. Accurate identification of layer thickness, especially for a single monolayer, is crucial for their characterization. This…
Two-dimensional (2D) materials are categorized into van der Waals (vdW) and non-vdW types. However, no relevant descriptors have been proposed for identifying the latter. Here, we identify the non-vdW 2D materials by calculating the…
As is well known, crystals have discrete space translational symmetry. It was recently noticed that one-dimensional crystals possibly have discrete Poincar\'{e} symmetry, which contains discrete Lorentz and discrete time translational…
The last decade has seen intense research in materials with reduced dimensionality. The low dimensionality leads to interesting electronic behavior due to electronic confinement and reduced screening. The investigations have to a large…
A computer algorithm to search symmetries of crystal structures as implemented in the \texttt{spglib} code is described. An iterative algorithm is employed to robustly identify space group types tolerating a certain amount of distortion in…
Two-dimensional (2D) materials have been a hot research topic in the last decade, due to novel fundamental physics in the reduced dimension and appealing applications. Systematic discovery of functional 2D materials has been the focus of…
The structure of the densest crystal packings is determined for a variety of concave shapes in 2D constructed by the overlap of two or three disks. The maximum contact number per particle pair is defined and proposed as a useful means of…
We present a scheme to explicitly construct and classify general topological states jointly protected by an onsite symmetry group and a spatial symmetry group. We show that all these symmetry protected topological states can be…
Two-dimensional (2D) materials have received extensive research attentions over the past two decades due to their intriguing physical properties (such as the ultrahigh mobility and strong light-matter interaction at atomic thickness) and a…
We introduce the problem of material-aware part grouping in untextured meshes. Many real-world shapes, such as scales of pinecones or windows of buildings, contain repeated structures that share the same material but exhibit geometric…
The continuous 1D defects of an isotropic homogeneous material in a flat 3D space are classified by the Volterra process construction method. We employ the same method to classify the continuous 2D defects of a vacuum in a 4D maximally…
A vertical 2-sum of a two-coatom lattice $L$ and a two-atom lattice $U$ is obtained by removing the top of $L$ and the bottom of $U$, and identifying the coatoms of $L$ with the atoms of $U$. This operation creates one or two nonisomorphic…
The classifications approaches for the crystallographic symmetries of patterns that are more or less periodic in two dimensions are critically reviewed and their relative performance qualitatively evaluated. The information theory based…
The discovery of two-dimensional (2D) materials with tailored properties is critical to meet the increasing demands of high-performance applications across flexible electronics, optoelectronics, catalysis, and energy storage. However,…