The continuously infinite group ∞1 is omitted.
Coordinates | Seitz symbol |
---|---|
a, b, c | x, y, z | { 1 ‖ 1 | 0 } |
-a, -b, c | x, y, z | { 1 ‖ 2001 | 0 } |
a, -b, -c | -x, -y, -z | { -1 ‖ 2100 | 0 } |
-a, b, -c | -x, -y, -z | { -1 ‖ 2010 | 0 } |
a, b, c | -x, y, z | { m ‖ 1 | 0 } |
-a, -b, c | -x, y, z | { m ‖ 2001 | 0 } |
a, -b, -c | x, -y, -z | { 2 ‖ 2100 | 0 } |
-a, b, -c | x, -y, -z | { 2 ‖ 2010 | 0 } |
WP | Site symmetry | Representative |
---|---|---|
1a | $\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,0) |
1b | $\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/2,0,0 | 0,0,0) |
1c | $\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,1/2,0 | 0,0,0) |
1d | $\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,0,1/2 | 0,0,0) |
1e | $\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/2,1/2,0 | 0,0,0) |
1f | $\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/2,0,1/2 | 0,0,0) |
1g | $\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,1/2,1/2 | 0,0,0) |
1h | $\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/2,1/2,1/2 | 0,0,0) |
2i | $\ce{^{-1}{2}}..\ce{^{\infty m}{1}} $ | (a,0,0 | 0,0,0) |
2j | $\ce{^{-1}{2}}..\ce{^{\infty m}{1}} $ | (a,0,1/2 | 0,0,0) |
2k | $\ce{^{-1}{2}}..\ce{^{\infty m}{1}} $ | (a,1/2,0 | 0,0,0) |
2l | $\ce{^{-1}{2}}..\ce{^{\infty m}{1}} $ | (a,1/2,1/2 | 0,0,0) |
2m | $.\ce{^{-1}{2}}.\ce{^{\infty m}{1}} $ | (0,b,0 | 0,0,0) |
2n | $.\ce{^{-1}{2}}.\ce{^{\infty m}{1}} $ | (0,b,1/2 | 0,0,0) |
2o | $.\ce{^{-1}{2}}.\ce{^{\infty m}{1}} $ | (1/2,b,0 | 0,0,0) |
2p | $.\ce{^{-1}{2}}.\ce{^{\infty m}{1}} $ | (1/2,b,1/2 | 0,0,0) |
2q | $..\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,0,c | 0,0,z) |
2r | $..\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/2,0,c | 0,0,z) |
2s | $..\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,1/2,c | 0,0,z) |
2t | $..\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/2,1/2,c | 0,0,z) |
4u | $\ce{^{1}{1}}\ce{^{\infty m}{1}} $ | (a,b,c | 0,0,z) |
Wavevector-k | Little co-group |
---|---|
Γ:(0,0,0) | $ \ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
R:(1/2,1/2,1/2) | $ \ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
S:(1/2,1/2,0) | $ \ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
T:(0,1/2,1/2) | $ \ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
U:(1/2,0,1/2) | $ \ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
X:(1/2,0,0) | $ \ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
Y:(0,1/2,0) | $ \ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
Z:(0,0,1/2) | $ \ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
A:(u,0,1/2) | $ \ce{^{2}{2}}\ce{^{-1}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
B:(0,v,1/2) | $ \ce{^{-1}{2}}\ce{^{2}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
C:(u,1/2,0) | $ \ce{^{2}{2}}\ce{^{-1}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
D:(1/2,v,0) | $ \ce{^{-1}{2}}\ce{^{2}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
Δ:(0,v,0) | $ \ce{^{-1}{2}}\ce{^{2}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
E:(u,1/2,1/2) | $ \ce{^{2}{2}}\ce{^{-1}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
G:(1/2,0,w) | $ \ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty}{1}} $ |
H:(0,1/2,w) | $ \ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty}{1}} $ |
Λ:(0,0,w) | $ \ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty}{1}} $ |
P:(1/2,v,1/2) | $ \ce{^{-1}{2}}\ce{^{2}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
Q:(1/2,1/2,w) | $ \ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty}{1}} $ |
Σ:(u,0,0) | $ \ce{^{2}{2}}\ce{^{-1}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
K:(0,v,w) | $ \ce{^{-1}{2}}\ce{^{\infty}{1}} $ |
L:(1/2,v,w) | $ \ce{^{-1}{2}}\ce{^{\infty}{1}} $ |
M:(u,0,w) | $ \ce{^{-1}{2}}\ce{^{\infty}{1}} $ |
N:(u,1/2,w) | $ \ce{^{-1}{2}}\ce{^{\infty}{1}} $ |
V:(u,v,0) | $ \ce{^{m}{2}}\ce{^{\infty}{1}} $ |
W:(u,v,1/2) | $ \ce{^{m}{2}}\ce{^{\infty}{1}} $ |
GP:(u,v,w) | $ \ce{^{1}{1}}\ce{^{\infty}{1}} $ |
Spin Brillouin Zone
k-vector | k-vector-G↑ | A↑G(2) | |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2) $ | |
R:(1/2,1/2,-1/2) | E:(1/2,1/2,1/2) | $(R)E_{1}^{S}(2) $ | |
S:(1/2,1/2,0) | A:(1/2,0,1/2) | $(S)A_{1}^{S}(2) $ | |
T:(0,1/2,-1/2) | D:(0,1/2,1/2) | $(T)D_{1}^{S}(2) $ | |
U:(1/2,0,-1/2) | C:(1/2,1/2,0) | $(U)C_{1}^{S}(2) $ | |
X:(1/2,0,0) | Y:(1/2,0,0) | $(X)Y_{1}^{S}(2) $ | |
Y:(0,1/2,0) | B:(0,0,1/2) | $(Y)B_{1}^{S}(2) $ | |
Z:(0,0,-1/2) | Z:(0,1/2,0) | $Z_{1}^{S}(2) $ | |
A:(u,0,-1/2) | G:(u,1/2,0) | $(A)G_{1}^{S}(2) $ | |
B:(0,v,-1/2) | G:(0,1/2,v) | $(B)G_{1}^{S}(2) $ | |
C:(u,1/2,0) | F:(u,0,1/2) | $(C)F_{1}^{S}(2) $ | |
D:(1/2,v,0) | F:(1/2,0,v) | $(D)F_{1}^{S}(2) $ | |
Δ:(0,v,0) | F:(0,0,v) | $(Δ)F_{1}^{S}(2) $ | |
E:(u,1/2,-1/2) | G:(u,1/2,1/2) | $(E)G_{1}^{S}(2) $ | |
G:(1/2,0,w) | W:(1/2,-w,0) | $(G)W_{1}^{S}(2) $ | |
H:(0,1/2,w) | V:(0,-w,1/2) | $(H)V_{1}^{S}(2) $ | |
Λ:(0,0,w) | Λ:(0,-w,0) | $Λ_{1}^{S}(2) $ | |
P:(1/2,v,-1/2) | G:(1/2,1/2,v) | $(P)G_{1}^{S}(2) $ | |
Q:(1/2,1/2,w) | U:(1/2,-w,1/2) | $(Q)U_{1}^{S}(2) $ | |
Σ:(u,0,0) | F:(u,0,0) | $(Σ)F_{1}^{S}(2) $ | |
K:(0,v,w) | GP:(0,-w,v) | $(K)GP_{1}^{S}(2) $ | |
L:(1/2,v,w) | GP:(1/2,-w,v) | $(L)GP_{1}^{S}(2) $ | |
M:(u,0,w) | GP:(u,-w,0) | $(M)GP_{1}^{S}(2) $ | |
N:(u,1/2,w) | GP:(u,-w,1/2) | $(N)GP_{1}^{S}(2) $ | |
V:(u,v,0) | F:(u,0,v) | $2(V)F_{1}^{S}(1)$ | Spin Splitting |
W:(u,v,-1/2) | G:(u,1/2,v) | $2(W)G_{1}^{S}(1)$ | Spin Splitting |
GP:(u,v,w) | GP:(u,-w,v) | $2GP_{1}^{S}(1)$ | Spin Splitting |
k-vector | k-vector-G↑ | A↑G(2) | |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2) $ | |
R:(1/2,1/2,-1/2) | E:(1/2,1/2,1/2) | $(R)E_{2}^{S}(2) $ | |
S:(1/2,1/2,0) | A:(1/2,0,1/2) | $(S)A_{2}^{S}(2) $ | |
T:(0,1/2,-1/2) | D:(0,1/2,1/2) | $(T)D_{1}^{S}(2) $ | |
U:(1/2,0,-1/2) | C:(1/2,1/2,0) | $(U)C_{1}^{S}(2) $ | |
X:(1/2,0,0) | Y:(1/2,0,0) | $(X)Y_{1}^{S}(2) $ | |
Y:(0,1/2,0) | B:(0,0,1/2) | $(Y)B_{2}^{S}(2) $ | |
Z:(0,0,-1/2) | Z:(0,1/2,0) | $Z_{1}^{S}(2) $ | |
A:(u,0,-1/2) | G:(u,1/2,0) | $(A)G_{1}^{S}(2) $ | |
B:(0,v,-1/2) | G:(0,1/2,v) | $(B)G_{1}^{S}(2) $ | |
C:(u,1/2,0) | F:(u,0,1/2) | $(C)F_{1}^{S}(2) $ | |
D:(1/2,v,0) | F:(1/2,0,v) | $(D)F_{1}^{S}(2) $ | |
Δ:(0,v,0) | F:(0,0,v) | $(Δ)F_{1}^{S}(2) $ | |
E:(u,1/2,-1/2) | G:(u,1/2,1/2) | $(E)G_{1}^{S}(2) $ | |
G:(1/2,0,w) | W:(1/2,-w,0) | $(G)W_{1}^{S}(2) $ | |
H:(0,1/2,w) | V:(0,-w,1/2) | $(H)V_{2}^{S}(2) $ | |
Λ:(0,0,w) | Λ:(0,-w,0) | $Λ_{1}^{S}(2) $ | |
P:(1/2,v,-1/2) | G:(1/2,1/2,v) | $(P)G_{1}^{S}(2) $ | |
Q:(1/2,1/2,w) | U:(1/2,-w,1/2) | $(Q)U_{2}^{S}(2) $ | |
Σ:(u,0,0) | F:(u,0,0) | $(Σ)F_{1}^{S}(2) $ | |
K:(0,v,w) | GP:(0,-w,v) | $(K)GP_{1}^{S}(2) $ | |
L:(1/2,v,w) | GP:(1/2,-w,v) | $(L)GP_{1}^{S}(2) $ | |
M:(u,0,w) | GP:(u,-w,0) | $(M)GP_{1}^{S}(2) $ | |
N:(u,1/2,w) | GP:(u,-w,1/2) | $(N)GP_{1}^{S}(2) $ | |
V:(u,v,0) | F:(u,0,v) | $2(V)F_{1}^{S}(1)$ | Spin Splitting |
W:(u,v,-1/2) | G:(u,1/2,v) | $2(W)G_{1}^{S}(1)$ | Spin Splitting |
GP:(u,v,w) | GP:(u,-w,v) | $2GP_{1}^{S}(1)$ | Spin Splitting |
k-vector | k-vector-G↑ | A↑G(2) | |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2) $ | |
R:(1/2,1/2,-1/2) | E:(1/2,1/2,1/2) | $(R)E_{2}^{S}(2) $ | |
S:(1/2,1/2,0) | A:(1/2,0,1/2) | $(S)A_{2}^{S}(2) $ | |
T:(0,1/2,-1/2) | D:(0,1/2,1/2) | $(T)D_{1}^{S}(2) $ | |
U:(1/2,0,-1/2) | C:(1/2,1/2,0) | $(U)C_{2}^{S}(2) $ | |
X:(1/2,0,0) | Y:(1/2,0,0) | $(X)Y_{2}^{S}(2) $ | |
Y:(0,1/2,0) | B:(0,0,1/2) | $(Y)B_{1}^{S}(2) $ | |
Z:(0,0,-1/2) | Z:(0,1/2,0) | $Z_{1}^{S}(2) $ | |
A:(u,0,-1/2) | G:(u,1/2,0) | $(A)G_{1}^{S}(2) $ | |
B:(0,v,-1/2) | G:(0,1/2,v) | $(B)G_{1}^{S}(2) $ | |
C:(u,1/2,0) | F:(u,0,1/2) | $(C)F_{1}^{S}(2) $ | |
D:(1/2,v,0) | F:(1/2,0,v) | $(D)F_{1}^{S}(2) $ | |
Δ:(0,v,0) | F:(0,0,v) | $(Δ)F_{1}^{S}(2) $ | |
E:(u,1/2,-1/2) | G:(u,1/2,1/2) | $(E)G_{1}^{S}(2) $ | |
G:(1/2,0,w) | W:(1/2,-w,0) | $(G)W_{2}^{S}(2) $ | |
H:(0,1/2,w) | V:(0,-w,1/2) | $(H)V_{1}^{S}(2) $ | |
Λ:(0,0,w) | Λ:(0,-w,0) | $Λ_{1}^{S}(2) $ | |
P:(1/2,v,-1/2) | G:(1/2,1/2,v) | $(P)G_{1}^{S}(2) $ | |
Q:(1/2,1/2,w) | U:(1/2,-w,1/2) | $(Q)U_{2}^{S}(2) $ | |
Σ:(u,0,0) | F:(u,0,0) | $(Σ)F_{1}^{S}(2) $ | |
K:(0,v,w) | GP:(0,-w,v) | $(K)GP_{1}^{S}(2) $ | |
L:(1/2,v,w) | GP:(1/2,-w,v) | $(L)GP_{1}^{S}(2) $ | |
M:(u,0,w) | GP:(u,-w,0) | $(M)GP_{1}^{S}(2) $ | |
N:(u,1/2,w) | GP:(u,-w,1/2) | $(N)GP_{1}^{S}(2) $ | |
V:(u,v,0) | F:(u,0,v) | $2(V)F_{1}^{S}(1)$ | Spin Splitting |
W:(u,v,-1/2) | G:(u,1/2,v) | $2(W)G_{1}^{S}(1)$ | Spin Splitting |
GP:(u,v,w) | GP:(u,-w,v) | $2GP_{1}^{S}(1)$ | Spin Splitting |
k-vector | k-vector-G↑ | A↑G(2) | |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2) $ | |
R:(1/2,1/2,-1/2) | E:(1/2,1/2,1/2) | $(R)E_{1}^{S}(2) $ | |
S:(1/2,1/2,0) | A:(1/2,0,1/2) | $(S)A_{1}^{S}(2) $ | |
T:(0,1/2,-1/2) | D:(0,1/2,1/2) | $(T)D_{2}^{S}(2) $ | |
U:(1/2,0,-1/2) | C:(1/2,1/2,0) | $(U)C_{2}^{S}(2) $ | |
X:(1/2,0,0) | Y:(1/2,0,0) | $(X)Y_{2}^{S}(2) $ | |
Y:(0,1/2,0) | B:(0,0,1/2) | $(Y)B_{2}^{S}(2) $ | |
Z:(0,0,-1/2) | Z:(0,1/2,0) | $Z_{1}^{S}(2) $ | |
A:(u,0,-1/2) | G:(u,1/2,0) | $(A)G_{1}^{S}(2) $ | |
B:(0,v,-1/2) | G:(0,1/2,v) | $(B)G_{1}^{S}(2) $ | |
C:(u,1/2,0) | F:(u,0,1/2) | $(C)F_{1}^{S}(2) $ | |
D:(1/2,v,0) | F:(1/2,0,v) | $(D)F_{1}^{S}(2) $ | |
Δ:(0,v,0) | F:(0,0,v) | $(Δ)F_{1}^{S}(2) $ | |
E:(u,1/2,-1/2) | G:(u,1/2,1/2) | $(E)G_{1}^{S}(2) $ | |
G:(1/2,0,w) | W:(1/2,-w,0) | $(G)W_{2}^{S}(2) $ | |
H:(0,1/2,w) | V:(0,-w,1/2) | $(H)V_{2}^{S}(2) $ | |
Λ:(0,0,w) | Λ:(0,-w,0) | $Λ_{1}^{S}(2) $ | |
P:(1/2,v,-1/2) | G:(1/2,1/2,v) | $(P)G_{1}^{S}(2) $ | |
Q:(1/2,1/2,w) | U:(1/2,-w,1/2) | $(Q)U_{1}^{S}(2) $ | |
Σ:(u,0,0) | F:(u,0,0) | $(Σ)F_{1}^{S}(2) $ | |
K:(0,v,w) | GP:(0,-w,v) | $(K)GP_{1}^{S}(2) $ | |
L:(1/2,v,w) | GP:(1/2,-w,v) | $(L)GP_{1}^{S}(2) $ | |
M:(u,0,w) | GP:(u,-w,0) | $(M)GP_{1}^{S}(2) $ | |
N:(u,1/2,w) | GP:(u,-w,1/2) | $(N)GP_{1}^{S}(2) $ | |
V:(u,v,0) | F:(u,0,v) | $2(V)F_{1}^{S}(1)$ | Spin Splitting |
W:(u,v,-1/2) | G:(u,1/2,v) | $2(W)G_{1}^{S}(1)$ | Spin Splitting |
GP:(u,v,w) | GP:(u,-w,v) | $2GP_{1}^{S}(1)$ | Spin Splitting |
k-vector | k-vector-G↑ | A↑G(4) | |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}(2) $ | |
R:(1/2,1/2,-1/2) | E:(1/2,1/2,1/2) | $(R)E_{1}^{S}(2)⊕(R)E_{2}^{S}(2) $ | |
S:(1/2,1/2,0) | A:(1/2,0,1/2) | $(S)A_{1}^{S}(2)⊕(S)A_{2}^{S}(2) $ | |
T:(0,1/2,-1/2) | D:(0,1/2,1/2) | $(T)D_{1}^{S}(2)⊕(T)D_{2}^{S}(2) $ | |
U:(1/2,0,-1/2) | C:(1/2,1/2,0) | $(U)C_{1}^{S}(2)⊕(U)C_{2}^{S}(2) $ | |
X:(1/2,0,0) | Y:(1/2,0,0) | $(X)Y_{1}^{S}(2)⊕(X)Y_{2}^{S}(2) $ | |
Y:(0,1/2,0) | B:(0,0,1/2) | $(Y)B_{1}^{S}(2)⊕(Y)B_{2}^{S}(2) $ | |
Z:(0,0,-1/2) | Z:(0,1/2,0) | $Z_{1}^{S}(2)⊕Z_{2}^{S}(2) $ | |
A:(u,0,-1/2) | G:(u,1/2,0) | $2(A)G_{1}^{S}(2) $ | |
B:(0,v,-1/2) | G:(0,1/2,v) | $2(B)G_{1}^{S}(2) $ | |
C:(u,1/2,0) | F:(u,0,1/2) | $2(C)F_{1}^{S}(2) $ | |
D:(1/2,v,0) | F:(1/2,0,v) | $2(D)F_{1}^{S}(2) $ | |
Δ:(0,v,0) | F:(0,0,v) | $2(Δ)F_{1}^{S}(2) $ | |
E:(u,1/2,-1/2) | G:(u,1/2,1/2) | $2(E)G_{1}^{S}(2) $ | |
G:(1/2,0,w) | W:(1/2,-w,0) | $(G)W_{1}^{S}(2)⊕(G)W_{2}^{S}(2) $ | |
H:(0,1/2,w) | V:(0,-w,1/2) | $(H)V_{1}^{S}(2)⊕(H)V_{2}^{S}(2) $ | |
Λ:(0,0,w) | Λ:(0,-w,0) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2) $ | |
P:(1/2,v,-1/2) | G:(1/2,1/2,v) | $2(P)G_{1}^{S}(2) $ | |
Q:(1/2,1/2,w) | U:(1/2,-w,1/2) | $(Q)U_{1}^{S}(2)⊕(Q)U_{2}^{S}(2) $ | |
Σ:(u,0,0) | F:(u,0,0) | $2(Σ)F_{1}^{S}(2) $ | |
K:(0,v,w) | GP:(0,-w,v) | $2(K)GP_{1}^{S}(2) $ | |
L:(1/2,v,w) | GP:(1/2,-w,v) | $2(L)GP_{1}^{S}(2) $ | |
M:(u,0,w) | GP:(u,-w,0) | $2(M)GP_{1}^{S}(2) $ | |
N:(u,1/2,w) | GP:(u,-w,1/2) | $2(N)GP_{1}^{S}(2) $ | |
V:(u,v,0) | F:(u,0,v) | $4(V)F_{1}^{S}(1)$ | Spin Splitting |
W:(u,v,-1/2) | G:(u,1/2,v) | $4(W)G_{1}^{S}(1)$ | Spin Splitting |
GP:(u,v,w) | GP:(u,-w,v) | $4GP_{1}^{S}(1)$ | Spin Splitting |