Related papers: Choice of basis vectors for conventional unit cell…

Systematic and automatic calculations of the electronic band structure are a crucial component of computationally-driven high-throughput materials screening. An algorithm, for any crystal, to derive a unique description of the crystal…

We present an algorithm for the determination of the local symmetry group for arbitrary k-points in 3D Brillouin zones. First, we test our implementation against tabulated results available for standard high-symmetry points (given by…

Describing the deviation of a real structure from a hypothetical higher-symmetry ideal can be a powerful tool to understand and interpret phase transitions. Here we introduce a simple yet effective metric that quantifies the degree of unit…

Most algorithms constructing bases of finite-dimensional vector spaces return basis vectors which, apart from orthogonality, do not show any special properties. While every basis is sufficient to define the vector space, not all bases are…

Band structure unfolding is a key technique for analyzing and simplifying the electronic band structure of large, internally distorted supercells that break the primitive cell's translational symmetry. In this work, we present an efficient…

Increasing attention is being focussed on the use of symmetry-adapted functions to describe magnetic structures, structural distortions, and incommensurate crystallography. Though the calculation of such functions is well developed,…

Complex bands $\vec{k}^{\perp}(E)$ in a semiconductor crystal, along a general direction $\vec{n}$, can be computed by casting Schr\"odinger's equation as a generalized polynomial eigenvalue problem. When working with primitive lattice…

We present a method for efficiently enumerating all allowed, topologically distinct, electronic band structures within a given crystal structure. The algorithm applies to crystals with broken time-reversal, particle-hole, and chiral…

The standard covariant differentiation procedure for fields in vector bundles is generalised so as to be applicable to fields in general nonaffine bundles in which the fibres may have an arbitrary nonlinear structure. In addition to the…

Accurate geometric decoding of moir\'{e} bilayers from imaging is essential for engineering quantum systems. Existing schemes, limited by identity or aligned assumptions requiring diagonal beating-to-moir\'e transformations, do not apply to…

During the last decade, automatic data analysis methods concerning different aspects of crystal analysis have been developed, e.g., unsupervised primitive unit cell extraction and automated crystal distortion and defects detection. However,…

Many media are divided into elementary units with irregular shape and size, as exemplified by domains in magnetic materials, bubbles in foams, or cells in biological tissues. Such media are essentially characterized by geometrical disorder…

We introduce a graphical method originating from the computer graphics domain that is used for the arbitrary and intuitive placement of cells over a two-dimensional manifold. Using a bitmap image as input, where the color indicates the…

A new section of databases and programs devoted to double crystallographic groups (point and space groups) has been implemented in the Bilbao Crystallographic Server (http://www.cryst.ehu.es). The double crystallographic groups are required…

Crystal structures are characterized by atomic bases within a primitive unit cell that repeats along a regular lattice throughout 3D space. The periodic and infinite nature of crystals poses unique challenges for geometric graph…

We give a parametrization for crystal bases of Demazure modules as a set of lattice points in some convex polytope and we also describe explicitly the extremal vectors as solutions of some system of linear equations.

We propose a systematic method to construct crystal-based molecular structures often needed as input for computational chemistry studies. These structures include crystal ``slabs" with periodic boundary conditions (PBCs) and non-periodic…

We propose an iterative method for computing vibrational spectra that significantly reduces the memory cost of calculations. It uses a direct product primitive basis, but does not require storing vectors with as many components as there are…

This paper reviews the standard algorithm for converting spacecraft state vectors to Keplerian orbital elements with a focus on its computer implementation. It analyzes the shortcomings of the scheme as described in the literature, and…

We present a general method to unfold energy bands of supercell calculations to primitive Brillouin zone using group theoretical techniques, where an isomorphic factor group is introduced to connect the primitive translation group with the…