Function reference

The following symbols are exported by AutoBZCore.jl

Brillouin-zone kinds

AutoBZCore.load_bz — Function
load_bz(bz::AbstractBZ, [T::Type=Float64])
load_bz(bz::AbstractBZ, A::AbstractMatrix, [B::AbstractMatrix])

Interface to loading Brillouin zones.

Arguments

  • bz::AbstractBZ: a kind of Brillouin zone to construct, e.g. FBZ or IBZ
  • T::Type: a numeric type to set the precision of the domain (default: Float64)
  • A::AbstractMatrix: a $d \times d$ matrix whose columns are the real-space lattice vectors of a $d$-dimensional crystal
  • B::AbstractMatrix: a $d \times d$ matrix whose columns are the reciprocal-space lattice vectors of a $d$-dimensional Brillouin zone (default: A' \ 2πI)
Assumptions

AutoBZCore assumes that all calculations occur in the reciprocal lattice basis, since that is the basis in which Wannier interpolants are most efficiently described. See SymmetricBZ for details. We also assume that the integrands are cheap to evaluate, which is why we provide adaptive methods in the first place, so that return types can be determined at runtime (and mechanisms are in place for compile time as well)

AutoBZCore.load_bz — Method
load_bz(::IBZ, A, B, species::AbstractVector, positions::AbstractMatrix; kws...)

species must have distinct labels for each atom type (e.g. can be any string or integer) and positions must be a matrix whose columns give the coordinates of the atom of the corresponding species.

AutoBZCore.AbstractBZ — Type
AbstractBZ{d}

Abstract supertype for all Brillouin zone data types parametrized by dimension.

AutoBZCore.FBZ — Type
FBZ{N} <: AbstractBZ

Singleton type representing first/full Brillouin zones of N dimensions. By default, N is nothing and the dimension is obtained from input files.

AutoBZCore.InversionSymIBZ — Type
InversionSymIBZ{N} <: AbstractBZ

Singleton type representing Brillouin zones with full inversion symmetry

Assumptions

Only expect this to work for systems with orthogonal lattice vectors

AutoBZCore.CubicSymIBZ — Type
CubicSymIBZ{N} <: AbstractBZ

Singleton type representing Brillouin zones with full cubic symmetry

Assumptions

Only expect this to work for systems with orthogonal lattice vectors

Symmetry representations

AutoBZCore.TrivialRep — Type
TrivialRep()

Symmetry representation of objects with trivial transformation under the group.

AutoBZCore.UnknownRep — Type
UnknownRep()

Fallback symmetry representation for array types without a user-defined SymRep. Will perform FBZ integration regardless of available BZ symmetries.

AutoBZCore.symmetrize — Function
symmetrize(rep::AbstractSymRep, ::SymmetricBZ, x)

Transform x by the representation of the symmetries of the point group used to reduce the domain, thus mapping the value of x on to the full Brillouin zone.

Internal

The following docstrings belong to internal types and functions that may change between versions of AutoBZCore.

AutoBZCore.PuncturedInterval — Type
PuncturedInterval(s)

Represent an interval (a, b) with interior points deleted by s = (a, c1, ..., cN, b), so that the integration algorithm can avoid the points c1, ..., cN for e.g. discontinuities. s must be a tuple or vector.

AutoBZCore.HyperCube — Type
HyperCube(a, b)

Represents a hypercube spanned by the vertices a, b, which must be iterables of the same length.

AutoBZCore.SymmetricBZ — Type
SymmetricBZ(A, B, lims::AbstractIteratedLimits, syms; atol=sqrt(eps()))

Data type representing a Brillouin zone reduced by a set of symmetries, syms with iterated integration limits lims, both of which are assumed to be in the lattice basis (since the Fourier series is). A and B should be identically-sized square matrices containing the real and reciprocal basis vectors in their columns.

Convention

This type assumes all integration limit data is in the reciprocal lattice basis with fractional coordinates, where the FBZ is just the hypercube spanned by the vertices (0,…,0) & (1,…,1). If necessary, use A or B to rotate these quantities into the convention.

lims should be limits compatible with IteratedIntegration.jl. syms should be an iterable collection of point group symmetries compatible with AutoSymPTR.jl.

AutoBZCore.cube_automorphisms — Function
cube_automorphisms(::Val{d}) where d

return a generator of the symmetries of the cube in d dimensions including the identity.