https://github.com/brainandforce/crystalline.jl

Utilities for space, little, and crystallographic point group symmetries and irreps

https://github.com/brainandforce/crystalline.jl

Repository

Utilities for space, little, and crystallographic point group symmetries and irreps

https://github.com/brainandforce/Crystalline.jl/blob/master/

# Crystalline.jl

[![Documentation (stable)][docs-stable-img]][docs-stable-url] [![Documentation (dev)][docs-dev-img]][docs-dev-url] [![Build status][ci-status-img]][ci-status-url] [![Coverage][coverage-img]][coverage-url]

Tools for crystalline symmetry analysis implemented in the Julia language.

This package provides access e.g. to the symmetry operations of crystalline point groups, space groups, Wyckoff positions, their irreducible representations and band representations, as well as tools for their associated manipulation.

## Installation

The package can be installed via Julia's package manager from the `pkg>` prompt (accessed by typing `]` at the Julia REPL):
```julia
pkg> add Crystalline
```
whereafter Crystalline.jl can be loaded via
```julia
julia> using Crystalline
```

## Functionality

Crystalline.jl currently provides several functionalities for line groups, plane groups, and space groups, as well as crystallographic point groups.

Example usage includes:
```julia
# construct a 3D `SymOperation` from its triplet form
julia> S"x,-y,-z"
2  (x,-y,-z)
  1  0  0  0 
  0 -1  0  0 
  0  0 -1  0 

# load the `SymOperation`s of the 3D space group 16 in a conventional setting
julia> sg = spacegroup(16, Val(3))
SpaceGroup{3} 16 (P222) with 4 operations:
 1
 2
 2
 2

# load a dictionary of small irreps and their little groups for space group 16,
# indexed by their k-point labels; then inspect the small irreps at the A point
julia> lgirs = lgirreps(16, Val(3))
julia> lgirs["A"]
LGIrrep{3}: 16 (P222) at A = [, 0, 1/2]
A 
     1:  (x,y,z)
         1.0
         
     2:  (x,-y,-z)
         1.0
    
A 
     1:  (x,y,z)
         1.0
         
     2:  (x,-y,-z)
         -1.0
    

# construct the character table for the small irreps at the  point
julia> characters(lgirs[""])
CharacterTable{3}: 16 (P222) at  = [0, 0, 0]

              

    1   1   1   1   1 
 2   1  -1   1  -1
 2   1  -1  -1   1
 2   1   1  -1  -1

```

Additional functionality includes e.g. point group operations (`pointgroup`) and irreps (`pgirreps`), elementary band representations (`bandreps`), Wyckoff positions (`wyckoffs`), conjugacy classes (`classes`), class-specific characters (`classcharacters`), group generators (`generators`), physically real irreps (`realify`), and Bravais lattice utilities and conventions (accessible via the lightweight stand-alone sub-package [Bravais.jl](https://github.com/thchr/Crystalline.jl/tree/master/Bravais)).
For a full description of the public API, see the [documentation][docs-dev-url].

### Current limitations
At present, the package's emphasis is on spinless systems (i.e., double groups and spinful irreps are not implemented).

## API stability
Crystalline.jl is a research package in active development: breaking changes are likely (but will respect semantic versioning).

## Citation

If you find this package useful in your reseach, please cite our arXiv paper:

- T. Christensen, H.C. Po, J.D. Joannopoulos, & M. Soljai, *Location and Topology of the Fundamental Gap in Photonic Crystals*, [Phys. Rev. X **12**, 021066 (2022)](https://doi.org/10.1103/PhysRevX.12.021066).

In addition, please consider citing any earlier works explicitly referenced in the documentation of individual functions.


[ci-status-img]:   https://github.com/thchr/Crystalline.jl/workflows/CI/badge.svg
[ci-status-url]:   https://github.com/thchr/Crystalline.jl/actions
[docs-dev-img]:    https://img.shields.io/badge/docs-dev-blue.svg
[docs-dev-url]:    https://thchr.github.io/Crystalline.jl/dev
[docs-stable-img]: https://img.shields.io/badge/docs-stable-blue.svg
[docs-stable-url]: https://thchr.github.io/Crystalline.jl/stable
[coverage-img]:    https://codecov.io/gh/thchr/Crystalline.jl/branch/master/graph/badge.svg
[coverage-url]:    https://codecov.io/gh/thchr/Crystalline.jl

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