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Redundant k-point in space group 216 #32

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thchr opened this issue Oct 3, 2024 · 0 comments
Open

Redundant k-point in space group 216 #32

thchr opened this issue Oct 3, 2024 · 0 comments

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@thchr
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thchr commented Oct 3, 2024

It seems there is a redundant k-point included in the data for space group 216. In particular, the K point is equivalent to the U point (related by a reciprocal lattice vector and a rotation of the space group):

julia> sgnum = 216
julia> Rs′ = directbasis(sgnum, Val(3))
julia> cntr = centering(sgnum, D)
julia> Rs = primitivize(Rs′, cntr)
julia> kp  = irrfbz_path(sgnum, Rs′)
KPath{3} (6 points, 2 paths, 8 points in paths):
 points: :U => [0.625, 0.25, 0.625]
         :W => [0.5, 0.25, 0.75]
         :K => [0.375, 0.375, 0.75]
          => [0.0, 0.0, 0.0]
         :L => [0.5, 0.5, 0.5]
         :X => [0.5, 0.0, 0.5]
  paths: [, :X, :U]
         [:K, , :L, :W, :X]
  basis: [-6.283185, 6.283185, 6.283185]
         [6.283185, -6.283185, 6.283185]
         [6.283185, 6.283185, -6.283185]

julia>  Ref(kp.points[:U]) .- orbit(primitivize(spacegroup(216)), ReciprocalPoint(kp.points[:K]))
12-element Vector{SVector{3, Float64}}:
 [0.25, -0.125, -0.125]
 [1.0, 0.625, 1.375]
 [0.25, 0.625, 0.625]
 [1.0, -0.125, 0.625]
 [-0.125, -0.125, 0.25]
 [1.375, 0.625, 1.0]
 [0.625, -0.125, 1.0]
 [0.625, 0.625, 0.25]
 [0.25, -0.5, 0.25]
 [1.0, 1.0, 1.0]     <------------ differ by a reciprocal lattice vector
 [1.0, 0.25, 0.25]
 [0.25, 0.25, 1.0]

Additionally, the "K point" is not included in the path listed on Bilbao

Bilbao Brillouin: plot(c, kp)
image image image

According to the legend on Bilbao (below), the "K-point" is likely an "auxiliary point"; i.e., just something that was included elsewhere, but not special.
The same is actually true for U - also not special. But there's no point in including both U and K when they are related by a reciprocal lattice vector. If they are included simply because it is two different directions to approach Gamma from, that might be okay - but in that case, they should get similar-looking names, like U and U-prime.

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