Related papers: Layer group classification of two-dimensional mate…
As "2D" materials (i.e. materials just a few atoms thick) continue to gain prominence, understanding their symmetries is critical for unlocking their full potential. In this work, we present comprehensive tables that tabulate the rod group…
Computational methods that automatically extract knowledge from data are critical for enabling data-driven materials science. A reliable identification of lattice symmetry is a crucial first step for materials characterization and…
The Materials Project crystal structure database has been searched for materials possessing layered motifs in their crystal structures using a topology-scaling algorithm. The algorithm identifies and measures the sizes of bonded atomic…
The concept of space group has long served as the fundamental framework to describe the physical properties of crystalline materials, from electronic bands to photonic dispersions. The recent progress of spatiotemporal control, such as…
We analyze the occurrence of in-plane anisotropy in the electronic, magnetic, elastic and transport properties of more than one thousand 2D materials from the C2DB database. We identify hundreds of anisotropic materials and classify them…
A procedure for the construction and the classification of multilattices in arbitrary dimension is proposed. The algorithm allows to determine explicitly the location of the points of a multilattice given its space group, and to determine…
Spin layer groups are the crystallographic symmetry groups with a periodic plane, and their symmetry operations are inherited from three-dimensional (3D) spin space groups. However, the direct application of 3D symmetry groups to…
Crystals which have a uniform distribution of defects are endowed with a Lie group description which allows one to construct an associated discrete structure. These structures are in fact the discrete subgroups of the ambient Lie group. The…
By high-throughput calculations based on the density functional theory, we construct a structure map for AB$_2$ type monolayers of 3844 compounds which are all the combinations of 62 elements selected from the periodic table. The structure…
We compute the mod-2 cohomology ring for three-dimensional (3D) space groups and establish a connection between them and the lattice structure of crystals with space group symmetry. This connection allows us to obtain a complete set of…
Crystal generative models have shown rapid progress for accelerating the discovery of bulk, periodic materials. However, many material systems such as 2D superconductors, thin film semiconductors, and catalytic surfaces are diperiodic,…
Solid materials possess both long-range order and some degree of disorder are critical for understanding the nature of crystal and glassy state, but how to controllable introduce specific type of disorder into a crystalline material is a…
Crystal phase is well studied and presents a periodical atom arrangement in three dimensions lattice, but the "amorphous phase" is poorly understood. Here, by starting from cage-like bicyclocalix[2]arene[2]triazines building block, a…
Two-dimensional (2D) layered materials offer intriguing possibilities for novel physics and applications. Before any attempt at exploring the materials space in a systematic fashion, or combining insights from theory, computation and…
The robust and automated determination of crystal symmetry is of utmost importance in material characterization and analysis. Recent studies have shown that deep learning (DL) methods can effectively reveal the correlations between X-ray or…
Crystallographic symmetry classifications from real-world images with periodicities in two dimensions (2D) are of interest to crystallographers and practitioners of computer vision studies alike. Currently, these classifications are…
Raman spectroscopy is frequently used to identify composition, structure and layer thickness of 2D materials. Here, we describe an efficient first-principles workflow for calculating resonant first-order Raman spectra of solids within…
Lattices in three dimensions are oft studied from the ``reciprocal space'' perspective of diffraction. Today, the full lattice of a crystal can often be inferred from direct-space information about three sets of non-parallel lattice planes.…
We perform extensive density functional theory (DFT) calculations to determine the stability and elementary properties of 4249 previously unexplored monolayer crystals. The monolayers comprise the most stable subset (energy within 0.1…
This paper develops geographic-style maps containing 2D lattices in all known crystals parameterised by recent complete invariants. Motivated by rigid crystal structures, lattices are considered up to rigid motion and uniform scaling. The…