The continuously infinite group ∞1 is omitted.
Coordinates | Seitz symbol |
---|---|
a, b, c | x, y, z | { 1 ‖ 1 | 0 } |
a, -b+1/2, -c+1/2 | x, y, z | { 1 ‖ 2100 | 0 1/2 1/2 } |
-a, -b, -c | x, y, z | { 1 ‖ -1 | 0 } |
-a, b+1/2, c+1/2 | x, y, z | { 1 ‖ m100 | 0 1/2 1/2 } |
-a+1/2, b+1/2, -c+1/2 | -x, -y, -z | { -1 ‖ 2010 | 1/2 1/2 1/2 } |
-a+1/2, -b, c | -x, -y, -z | { -1 ‖ 2001 | 1/2 0 0 } |
a+1/2, -b+1/2, c+1/2 | -x, -y, -z | { -1 ‖ m010 | 1/2 1/2 1/2 } |
a+1/2, b, -c | -x, -y, -z | { -1 ‖ m001 | 1/2 0 0 } |
a, b, c | -x, y, z | { m ‖ 1 | 0 } |
a, -b+1/2, -c+1/2 | -x, y, z | { m ‖ 2100 | 0 1/2 1/2 } |
-a, -b, -c | -x, y, z | { m ‖ -1 | 0 } |
-a, b+1/2, c+1/2 | -x, y, z | { m ‖ m100 | 0 1/2 1/2 } |
-a+1/2, b+1/2, -c+1/2 | x, -y, -z | { 2 ‖ 2010 | 1/2 1/2 1/2 } |
-a+1/2, -b, c | x, -y, -z | { 2 ‖ 2001 | 1/2 0 0 } |
a+1/2, -b+1/2, c+1/2 | x, -y, -z | { 2 ‖ m010 | 1/2 1/2 1/2 } |
a+1/2, b, -c | x, -y, -z | { 2 ‖ m001 | 1/2 0 0 } |
WP | Site symmetry | Representative |
---|---|---|
4a | $\ce{^{1}{-1}}\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,z) |
4b | $\ce{^{1}{-1}}\ce{^{\infty m}{1}} $ | (0,0,1/2 | 0,0,z) |
4c | $..\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (1/4,0,c | 0,0,0) |
4d | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (a,1/4,1/4 | 0,0,z) |
8e | $\ce{^{1}{1}}\ce{^{\infty m}{1}} $ | (a,b,c | 0,0,z) |
Wavevector-k | Little co-group |
---|---|
Γ:(0,0,0) | $ \ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
R:(1/2,1/2,1/2) | $ \ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
S:(1/2,1/2,0) | $ \ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
T:(0,1/2,1/2) | $ \ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
U:(1/2,0,1/2) | $ \ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
X:(1/2,0,0) | $ \ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
Y:(0,1/2,0) | $ \ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
Z:(0,0,1/2) | $ \ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
A:(u,0,1/2) | $ \ce{^{m}{m}}\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
B:(0,v,1/2) | $ \ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
C:(u,1/2,0) | $ \ce{^{m}{m}}\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
D:(1/2,v,0) | $ \ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
Δ:(0,v,0) | $ \ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
E:(u,1/2,1/2) | $ \ce{^{m}{m}}\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
G:(1/2,0,w) | $ \ce{^{1}{m}}\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{\infty}{1}} $ |
H:(0,1/2,w) | $ \ce{^{1}{m}}\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{\infty}{1}} $ |
Λ:(0,0,w) | $ \ce{^{1}{m}}\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{\infty}{1}} $ |
P:(1/2,v,1/2) | $ \ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
Q:(1/2,1/2,w) | $ \ce{^{1}{m}}\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{\infty}{1}} $ |
Σ:(u,0,0) | $ \ce{^{m}{m}}\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
K:(0,v,w) | $ \ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
L:(1/2,v,w) | $ \ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
M:(u,0,w) | $ \ce{^{-1}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
N:(u,1/2,w) | $ \ce{^{-1}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
V:(u,v,0) | $ \ce{^{-1}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
W:(u,v,1/2) | $ \ce{^{-1}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
GP:(u,v,w) | $ \ce{^{m}{-1}}\ce{^{\infty}{1}} $ |
Spin Brillouin Zone
k-vector | k-vector-G↑ | Ag↑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) | C:(1/2,1/2,0) | $(R)C_{1}^{S,+}(2)⊕(R)C_{2}^{S,+}(2) $ | |
S:(1/2,-1/2,0) | D:(0,1/2,1/2) | $(S)D_{1}^{S}(4) $ | |
T:(0,-1/2,-1/2) | Y:(1/2,0,0) | $(T)Y_{1}^{S,+}(2)⊕(T)Y_{2}^{S,+}(2) $ | |
U:(1/2,-1,-1/2) | E:(1/2,1/2,1/2) | $(U)E_{1}^{S}(4) $ | |
X:(1/2,0,0) | Z:(0,1/2,0) | $(X)Z_{1}^{S,+}(2)⊕(X)Z_{2}^{S,+}(2) $ | |
Y:(0,-1/2,0) | B:(0,0,1/2) | $(Y)B_{1}^{S}(4) $ | |
Z:(0,-1,-1/2) | A:(1/2,0,1/2) | $(Z)A_{1}^{S}(4) $ | |
A:(u,-1,-1/2) | U:(1/2,u,1/2) | $(A)U_{1}^{S}U_{2}^{S}(4) $ | |
B:(0,v,1/2) | F:(-1/2,0,1/2-v) | $(B)F_{1}^{S}(2)⊕(B)F_{2}^{S}(2) $ | |
C:(u,-1/2,0) | V:(0,u,1/2) | $(C)V_{1}^{S}V_{2}^{S}(4) $ | |
D:(1/2,v,0) | G:(0,1/2,-v) | $(D)G_{1}^{S}(2)⊕(D)G_{2}^{S}(2) $ | |
Δ:(0,v,0) | F:(0,0,-v) | $(Δ)F_{1}^{S}(2)⊕(Δ)F_{2}^{S}(2) $ | |
E:(u,-1/2,-1/2) | W:(1/2,u,0) | $(E)W_{1}^{S}(2)⊕(E)W_{2}^{S}(2) $ | |
G:(1/2,0,w) | G:(-w,1/2,w) | $G_{1}^{S}(2)⊕G_{2}^{S}(2) $ | |
H:(0,1/2,w) | F:(-w,0,-1/2+w) | $(H)F_{1}^{S}(2)⊕(H)F_{2}^{S}(2) $ | |
Λ:(0,0,w) | F:(-w,0,w) | $(Λ)F_{1}^{S}(2)⊕(Λ)F_{2}^{S}(2) $ | |
P:(1/2,v,1/2) | G:(-1/2,1/2,1/2-v) | $(P)G_{1}^{S}(2)⊕(P)G_{2}^{S}(2) $ | |
Q:(1/2,1/2,w) | G:(-w,1/2,-1/2+w) | $(Q)G_{1}^{S}(2)⊕(Q)G_{2}^{S}(2) $ | |
Σ:(u,0,0) | Λ:(0,u,0) | $(Σ)Λ_{1}^{S}(2)⊕(Σ)Λ_{2}^{S}(2) $ | |
K:(0,v,w) | F:(-w,0,-v+w) | $2(K)F_{1}^{S}(1)⊕2(K)F_{2}^{S}(1)$ | Spin Splitting |
L:(1/2,v,w) | G:(-w,1/2,-v+w) | $2(L)G_{1}^{S}(1)⊕2(L)G_{2}^{S}(1)$ | Spin Splitting |
M:(u,0,w) | GP:(-w,u,w) | $2(M)GP_{1}^{S}(2) $ | |
N:(u,1/2,w) | GP:(-w,u,-1/2+w) | $2(N)GP_{1}^{S}(2) $ | |
V:(u,v,0) | GP:(0,u,-v) | $2(V)GP_{1}^{S}(2) $ | |
W:(u,v,1/2) | GP:(-1/2,u,1/2-v) | $2(W)GP_{1}^{S}(2) $ | |
GP:(u,v,w) | GP:(-w,u,-v+w) | $4GP_{1}^{S}(1)$ | Spin Splitting |
k-vector | k-vector-G↑ | Ag↑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) | C:(1/2,1/2,0) | $(R)C_{1}^{S,-}(2)⊕(R)C_{2}^{S,-}(2) $ | |
S:(1/2,-1/2,0) | D:(0,1/2,1/2) | $(S)D_{1}^{S}(4) $ | |
T:(0,-1/2,-1/2) | Y:(1/2,0,0) | $(T)Y_{1}^{S,-}(2)⊕(T)Y_{2}^{S,-}(2) $ | |
U:(1/2,-1,-1/2) | E:(1/2,1/2,1/2) | $(U)E_{1}^{S}(4) $ | |
X:(1/2,0,0) | Z:(0,1/2,0) | $(X)Z_{1}^{S,+}(2)⊕(X)Z_{2}^{S,+}(2) $ | |
Y:(0,-1/2,0) | B:(0,0,1/2) | $(Y)B_{1}^{S}(4) $ | |
Z:(0,-1,-1/2) | A:(1/2,0,1/2) | $(Z)A_{1}^{S}(4) $ | |
A:(u,-1,-1/2) | U:(1/2,u,1/2) | $(A)U_{1}^{S}U_{2}^{S}(4) $ | |
B:(0,v,1/2) | F:(-1/2,0,1/2-v) | $(B)F_{1}^{S}(2)⊕(B)F_{2}^{S}(2) $ | |
C:(u,-1/2,0) | V:(0,u,1/2) | $(C)V_{1}^{S}V_{2}^{S}(4) $ | |
D:(1/2,v,0) | G:(0,1/2,-v) | $(D)G_{1}^{S}(2)⊕(D)G_{2}^{S}(2) $ | |
Δ:(0,v,0) | F:(0,0,-v) | $(Δ)F_{1}^{S}(2)⊕(Δ)F_{2}^{S}(2) $ | |
E:(u,-1/2,-1/2) | W:(1/2,u,0) | $(E)W_{1}^{S}(2)⊕(E)W_{2}^{S}(2) $ | |
G:(1/2,0,w) | G:(-w,1/2,w) | $G_{1}^{S}(2)⊕G_{2}^{S}(2) $ | |
H:(0,1/2,w) | F:(-w,0,-1/2+w) | $(H)F_{1}^{S}(2)⊕(H)F_{2}^{S}(2) $ | |
Λ:(0,0,w) | F:(-w,0,w) | $(Λ)F_{1}^{S}(2)⊕(Λ)F_{2}^{S}(2) $ | |
P:(1/2,v,1/2) | G:(-1/2,1/2,1/2-v) | $(P)G_{1}^{S}(2)⊕(P)G_{2}^{S}(2) $ | |
Q:(1/2,1/2,w) | G:(-w,1/2,-1/2+w) | $(Q)G_{1}^{S}(2)⊕(Q)G_{2}^{S}(2) $ | |
Σ:(u,0,0) | Λ:(0,u,0) | $(Σ)Λ_{1}^{S}(2)⊕(Σ)Λ_{2}^{S}(2) $ | |
K:(0,v,w) | F:(-w,0,-v+w) | $2(K)F_{1}^{S}(1)⊕2(K)F_{2}^{S}(1)$ | Spin Splitting |
L:(1/2,v,w) | G:(-w,1/2,-v+w) | $2(L)G_{1}^{S}(1)⊕2(L)G_{2}^{S}(1)$ | Spin Splitting |
M:(u,0,w) | GP:(-w,u,w) | $2(M)GP_{1}^{S}(2) $ | |
N:(u,1/2,w) | GP:(-w,u,-1/2+w) | $2(N)GP_{1}^{S}(2) $ | |
V:(u,v,0) | GP:(0,u,-v) | $2(V)GP_{1}^{S}(2) $ | |
W:(u,v,1/2) | GP:(-1/2,u,1/2-v) | $2(W)GP_{1}^{S}(2) $ | |
GP:(u,v,w) | GP:(-w,u,-v+w) | $4GP_{1}^{S}(1)$ | Spin Splitting |
k-vector | k-vector-G↑ | A↑G(4) | |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{1}^{S,-}(2) $ | |
R:(1/2,-1/2,-1/2) | C:(1/2,1/2,0) | $(R)C_{1}^{S,+}(2)⊕(R)C_{1}^{S,-}(2) $ | |
S:(1/2,-1/2,0) | D:(0,1/2,1/2) | $(S)D_{1}^{S}(4) $ | |
T:(0,-1/2,-1/2) | Y:(1/2,0,0) | $(T)Y_{1}^{S,+}(2)⊕(T)Y_{1}^{S,-}(2) $ | |
U:(1/2,-1,-1/2) | E:(1/2,1/2,1/2) | $(U)E_{1}^{S}(4) $ | |
X:(1/2,0,0) | Z:(0,1/2,0) | $(X)Z_{1}^{S,+}(2)⊕(X)Z_{1}^{S,-}(2) $ | |
Y:(0,-1/2,0) | B:(0,0,1/2) | $(Y)B_{1}^{S}(4) $ | |
Z:(0,-1,-1/2) | A:(1/2,0,1/2) | $(Z)A_{1}^{S}(4) $ | |
A:(u,-1,-1/2) | U:(1/2,u,1/2) | $(A)U_{1}^{S}U_{2}^{S}(4) $ | |
B:(0,v,1/2) | F:(-1/2,0,1/2-v) | $(B)F_{1}^{S}(2)⊕(B)F_{2}^{S}(2) $ | |
C:(u,-1/2,0) | V:(0,u,1/2) | $(C)V_{1}^{S}V_{2}^{S}(4) $ | |
D:(1/2,v,0) | G:(0,1/2,-v) | $(D)G_{1}^{S}(2)⊕(D)G_{2}^{S}(2) $ | |
Δ:(0,v,0) | F:(0,0,-v) | $(Δ)F_{1}^{S}(2)⊕(Δ)F_{2}^{S}(2) $ | |
E:(u,-1/2,-1/2) | W:(1/2,u,0) | $2 (E)W_{1}^{S}(2) $ | |
G:(1/2,0,w) | G:(-w,1/2,w) | $G_{1}^{S}(2)⊕G_{2}^{S}(2) $ | |
H:(0,1/2,w) | F:(-w,0,-1/2+w) | $(H)F_{1}^{S}(2)⊕(H)F_{2}^{S}(2) $ | |
Λ:(0,0,w) | F:(-w,0,w) | $(Λ)F_{1}^{S}(2)⊕(Λ)F_{2}^{S}(2) $ | |
P:(1/2,v,1/2) | G:(-1/2,1/2,1/2-v) | $(P)G_{1}^{S}(2)⊕(P)G_{2}^{S}(2) $ | |
Q:(1/2,1/2,w) | G:(-w,1/2,-1/2+w) | $(Q)G_{1}^{S}(2)⊕(Q)G_{2}^{S}(2) $ | |
Σ:(u,0,0) | Λ:(0,u,0) | $2 (Σ)Λ_{1}^{S}(2) $ | |
K:(0,v,w) | F:(-w,0,-v+w) | $2(K)F_{1}^{S}(1)⊕2(K)F_{2}^{S}(1)$ | Spin Splitting |
L:(1/2,v,w) | G:(-w,1/2,-v+w) | $2(L)G_{1}^{S}(1)⊕2(L)G_{2}^{S}(1)$ | Spin Splitting |
M:(u,0,w) | GP:(-w,u,w) | $2(M)GP_{1}^{S}(2) $ | |
N:(u,1/2,w) | GP:(-w,u,-1/2+w) | $2(N)GP_{1}^{S}(2) $ | |
V:(u,v,0) | GP:(0,u,-v) | $2(V)GP_{1}^{S}(2) $ | |
W:(u,v,1/2) | GP:(-1/2,u,1/2-v) | $2(W)GP_{1}^{S}(2) $ | |
GP:(u,v,w) | GP:(-w,u,-v+w) | $4GP_{1}^{S}(1)$ | Spin Splitting |
k-vector | k-vector-G↑ | A↑G(8) | |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{1}^{S,-}(2)⊕Γ_{2}^{S,+}(2)⊕Γ_{2}^{S,-}(2) $ | |
R:(1/2,-1/2,-1/2) | C:(1/2,1/2,0) | $(R)C_{1}^{S,+}(2)⊕(R)C_{1}^{S,-}(2)⊕(R)C_{2}^{S,+}(2)⊕(R)C_{2}^{S,-}(2) $ | |
S:(1/2,-1/2,0) | D:(0,1/2,1/2) | $2(S)D_{1}^{S}(4) $ | |
T:(0,-1/2,-1/2) | Y:(1/2,0,0) | $(T)Y_{1}^{S,+}(2)⊕(T)Y_{1}^{S,-}(2)⊕(T)Y_{2}^{S,+}(2)⊕(T)Y_{2}^{S,-}(2) $ | |
U:(1/2,-1,-1/2) | E:(1/2,1/2,1/2) | $2(U)E_{1}^{S}(4) $ | |
X:(1/2,0,0) | Z:(0,1/2,0) | $(X)Z_{1}^{S,+}(2)⊕(X)Z_{1}^{S,-}(2)⊕(X)Z_{2}^{S,+}(2)⊕(X)Z_{2}^{S,-}(2) $ | |
Y:(0,-1/2,0) | B:(0,0,1/2) | $2(Y)B_{1}^{S}(4) $ | |
Z:(0,-1,-1/2) | A:(1/2,0,1/2) | $2(Z)A_{1}^{S}(4) $ | |
A:(u,-1,-1/2) | U:(1/2,u,1/2) | $2(A)U_{1}^{S}U_{2}^{S}(4) $ | |
B:(0,v,1/2) | F:(-1/2,0,1/2-v) | $2(B)F_{1}^{S}(2)⊕2(B)F_{2}^{S}(2) $ | |
C:(u,-1/2,0) | V:(0,u,1/2) | $2(C)V_{1}^{S}V_{2}^{S}(4) $ | |
D:(1/2,v,0) | G:(0,1/2,-v) | $2(D)G_{1}^{S}(2)⊕2(D)G_{2}^{S}(2) $ | |
Δ:(0,v,0) | F:(0,0,-v) | $2(Δ)F_{1}^{S}(2)⊕2(Δ)F_{2}^{S}(2) $ | |
E:(u,-1/2,-1/2) | W:(1/2,u,0) | $2(E)W_{1}^{S}(2)⊕2(E)W_{2}^{S}(2) $ | |
G:(1/2,0,w) | G:(-w,1/2,w) | $2G_{1}^{S}(2)⊕2G_{2}^{S}(2) $ | |
H:(0,1/2,w) | F:(-w,0,-1/2+w) | $2(H)F_{1}^{S}(2)⊕2(H)F_{2}^{S}(2) $ | |
Λ:(0,0,w) | F:(-w,0,w) | $2(Λ)F_{1}^{S}(2)⊕2(Λ)F_{2}^{S}(2) $ | |
P:(1/2,v,1/2) | G:(-1/2,1/2,1/2-v) | $2(P)G_{1}^{S}(2)⊕2(P)G_{2}^{S}(2) $ | |
Q:(1/2,1/2,w) | G:(-w,1/2,-1/2+w) | $2(Q)G_{1}^{S}(2)⊕2(Q)G_{2}^{S}(2) $ | |
Σ:(u,0,0) | Λ:(0,u,0) | $2(Σ)Λ_{1}^{S}(2)⊕2(Σ)Λ_{2}^{S}(2) $ | |
K:(0,v,w) | F:(-w,0,-v+w) | $4(K)F_{1}^{S}(1)⊕4(K)F_{2}^{S}(1)$ | Spin Splitting |
L:(1/2,v,w) | G:(-w,1/2,-v+w) | $4(L)G_{1}^{S}(1)⊕4(L)G_{2}^{S}(1)$ | Spin Splitting |
M:(u,0,w) | GP:(-w,u,w) | $4(M)GP_{1}^{S}(2) $ | |
N:(u,1/2,w) | GP:(-w,u,-1/2+w) | $4(N)GP_{1}^{S}(2) $ | |
V:(u,v,0) | GP:(0,u,-v) | $4(V)GP_{1}^{S}(2) $ | |
W:(u,v,1/2) | GP:(-1/2,u,1/2-v) | $4(W)GP_{1}^{S}(2) $ | |
GP:(u,v,w) | GP:(-w,u,-v+w) | $8GP_{1}^{S}(1)$ | Spin Splitting |