Symmetry Irrep Components
IrrepComponent
LatticeTools.IrrepComponent — TypeIrrepComponent{SymmetryType}Represent an irrep component. Consider a symmetry S, and the i'th irrep Γᵢ, which has D dimensions. The d-dimensional component (1 ≤ d ≤ D) is represented by Irrep(S, i, D). This type serves as a subscript for iterating over all components of all irreps.
Parameters
SymmetryType<:SymmetryOrEmbedding
Fields
symmetry::SymmetryTypeirrep_index::Intirrep_component::Int
GroupTools.group_order — Methodgroup_order(sic::IrrepComponent)Get order of the symmetry group of sic.
LatticeTools.get_irrep_components — Methodget_irrep_components(sym::SymmetryOrEmbedding)Return a generator which gives IrrepComponent(sym, irrep_index, irrep_component).
LatticeTools.get_irrep_iterator — Methodget_irrep_iterator(sic::IrrepComponent)Return a generator which gives (element, amplitude), where amplitude is the irrep component of element.
Little Group
LatticeTools.little_group_elements — Methodlittle_group_elements(tsic, psym)Return little group elements (i.e. indices) of psym corresponding to the irrep of translation symmetry specified by tsic. tsic and psym are either
IrrepComponent{FiniteTranslationSymmetry}andPointSymmetry, orIrrepComponent{SymmetryEmbedding{FiniteTranslationSymmetry}}andSymmetryEmbedding{PointSymmetry}
LatticeTools.little_group — Methodlittle_group(tsic, psym)Return the FiniteGroup object that corresponds to the little group of psym at tsic.
LatticeTools.little_group — Methodlittle_group(tsic, psymbed)Return the FiniteGroup object that corresponds to the little group of psymbed at tsic.
LatticeTools.little_symmetry — Methodlittle_symmetry(tsic, psym)Return the PointSymmetry object that corresponds to the little group of psym at tsic.
LatticeTools.iscompatible — Methodiscompatible(tsic, psym)Test whether the point symmetry psym is compatible with the irrep component tsic (i.e. momentum) of the translation symmetry.
SymmorphicIrrepComponent
LatticeTools.SymmorphicIrrepComponent — TypeSymmorphicIrrepComponent{S1<:SymmetryOrEmbedding, S2<:SymmetryOrEmbedding}Irrep component of a symmorphic symmetry (embedding).
Fields
normal::IrrepComponent{S1}rest::IrrepComponent{S2}
GroupTools.group_order — Methodgroup_order(arg::SymmorphicIrrepComponent)Group order of the underlying symmorphic group of arg.
LatticeTools.get_irrep_components — Methodget_irrep_components(sym::SymmorphicSymmetry)Return an iterator which iterates over the irrep component of the symmorphic symmetry sym.
LatticeTools.get_irrep_components — Methodget_irrep_components(sym::SymmorphicSymmetryEmbedding)Return an iterator which iterates over the irrep component of the symmorphic symmetry embedding sym.
LatticeTools.get_irrep_iterator — Methodget_irrep_iterator(ssic::SymmorphicIrrepComponent)Return an iterator which iterates over the elements, together with their corresponding irrep coefficient of the given irrep component.
Return
- [(r⋅n, cᵣ⋅cₙ) for all r for all n]