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 ‖ 2100 | 0 } |
-a, -b, -c | x, y, z | { 1 ‖ -1 | 0 } |
-a, b, c | x, y, z | { 1 ‖ m100 | 0 } |
-a, b, -c | -x, -y, -z | { -1 ‖ 2010 | 0 } |
-a, -b, c | -x, -y, -z | { -1 ‖ 2001 | 0 } |
a, -b, c | -x, -y, -z | { -1 ‖ m010 | 0 } |
a, b, -c | -x, -y, -z | { -1 ‖ m001 | 0 } |
a+1/2, b+1/2, c | x, y, z | { 1 ‖ 1 | 1/2 1/2 0 } |
a+1/2, -b+1/2, -c | x, y, z | { 1 ‖ 2100 | 1/2 1/2 0 } |
-a+1/2, -b+1/2, -c | x, y, z | { 1 ‖ -1 | 1/2 1/2 0 } |
-a+1/2, b+1/2, c | x, y, z | { 1 ‖ m100 | 1/2 1/2 0 } |
-a+1/2, b+1/2, -c | -x, -y, -z | { -1 ‖ 2010 | 1/2 1/2 0 } |
-a+1/2, -b+1/2, c | -x, -y, -z | { -1 ‖ 2001 | 1/2 1/2 0 } |
a+1/2, -b+1/2, c | -x, -y, -z | { -1 ‖ m010 | 1/2 1/2 0 } |
a+1/2, b+1/2, -c | -x, -y, -z | { -1 ‖ m001 | 1/2 1/2 0 } |
a, b, c | -x, y, z | { m ‖ 1 | 0 } |
a, -b, -c | -x, y, z | { m ‖ 2100 | 0 } |
-a, -b, -c | -x, y, z | { m ‖ -1 | 0 } |
-a, b, c | -x, y, z | { m ‖ m100 | 0 } |
-a, b, -c | x, -y, -z | { 2 ‖ 2010 | 0 } |
-a, -b, c | x, -y, -z | { 2 ‖ 2001 | 0 } |
a, -b, c | x, -y, -z | { 2 ‖ m010 | 0 } |
a, b, -c | x, -y, -z | { 2 ‖ m001 | 0 } |
a+1/2, b+1/2, c | -x, y, z | { m ‖ 1 | 1/2 1/2 0 } |
a+1/2, -b+1/2, -c | -x, y, z | { m ‖ 2100 | 1/2 1/2 0 } |
-a+1/2, -b+1/2, -c | -x, y, z | { m ‖ -1 | 1/2 1/2 0 } |
-a+1/2, b+1/2, c | -x, y, z | { m ‖ m100 | 1/2 1/2 0 } |
-a+1/2, b+1/2, -c | x, -y, -z | { 2 ‖ 2010 | 1/2 1/2 0 } |
-a+1/2, -b+1/2, c | x, -y, -z | { 2 ‖ 2001 | 1/2 1/2 0 } |
a+1/2, -b+1/2, c | x, -y, -z | { 2 ‖ m010 | 1/2 1/2 0 } |
a+1/2, b+1/2, -c | x, -y, -z | { 2 ‖ m001 | 1/2 1/2 0 } |
WP | Site symmetry | Representative |
---|---|---|
2a | $\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,0) |
2b | $\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (1/2,0,0 | 0,0,0) |
2c | $\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (1/2,0,1/2 | 0,0,0) |
2d | $\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (0,0,1/2 | 0,0,0) |
4e | $..\ce{^{-1}{2}}/\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (1/4,1/4,0 | 0,0,0) |
4f | $..\ce{^{-1}{2}}/\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (1/4,1/4,1/2 | 0,0,0) |
4g | $\ce{^{1}{2}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (a,0,0 | 0,0,0) |
4h | $\ce{^{1}{2}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (a,0,1/2 | 0,0,0) |
4i | $\ce{^{1}{m}}\ce{^{-1}{2}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (0,b,0 | 0,0,0) |
4j | $\ce{^{1}{m}}\ce{^{-1}{2}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (0,b,1/2 | 0,0,0) |
4k | $\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (0,0,c | 0,0,0) |
4l | $\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (0,1/2,c | 0,0,0) |
8m | $..\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (1/4,1/4,c | 0,0,0) |
8n | $\ce{^{1}{m}}..\ce{^{\infty m}{1}} $ | (0,b,c | 0,0,z) |
8o | $.\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (a,0,c | 0,0,0) |
8p | $..\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (a,b,0 | 0,0,0) |
8q | $..\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (a,b,1/2 | 0,0,0) |
16r | $\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}} $ |
T:(1,0,1/2) | $\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
Y:(1,0,0) | $\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}} $ |
R:(1/2,1/2,1/2) | $\ce{^{2}{2/}}\ce{^{2}{m}}\ce{^{\infty m}{1}} $ |
S:(1/2,1/2,0) | $\ce{^{2}{2/}}\ce{^{2}{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}} $ |
Δ:(0,v,0) | $\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
H:(1,0,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}} $ |
Σ:(u,0,0) | $\ce{^{m}{m}}\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
D:(1/2,1/2,w) | $\ce{^{2}{2/}}\ce{^{-1}{m}}\ce{^{\infty}{1}} $ |
K:(0,v,w) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
M:(u,0,w) | $\ce{^{-1}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
P:(u,v,0) | $\ce{^{-1}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
Q:(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↑ | 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) | L:(1/2,1/2,1/2) | $(R)L_{1}^{S,+}(2)⊕ (R)L_{1}^{S,-}(2) $ | |
S:(1/2,-1/2,0) | V:(1/2,1/2,0) | $(S)V_{1}^{S,+}(2)⊕(S)V_{1}^{S,-}(2) $ | |
T:(1,0,1/2) | M:(0,1,1/2) | $(T)M_{1}^{S,+}(2)⊕(T)M_{2}^{S,-}(2) $ | |
Y:(1,0,0) | Y:(0,1,0) | $Y_{1}^{S,+}(2)⊕Y_{2}^{S,-}(2) $ | |
Z:(0,0,1/2) | A:(0,0,1/2) | $(Z)A_{1}^{S,+}(2)⊕(Z)A_{2}^{S,-}(2) $ | |
A:(u,0,1/2) | U:(0,u,1/2) | $(A)U_{1}^{S}(2)⊕(A)U_{2}^{S}(2) $ | |
B:(0,v,1/2) | B:(-v,0,1/2) | $2 B_{1}^{S}(2) $ | |
D:(1/2,1/2,w) | GP:(-1/2,1/2,w) | $2(D)GP_{1}^{S}(2) $ | |
Δ:(0,v,0) | B:(-v,0,0) | $2 (Δ)B_{1}^{S}(2) $ | |
H:(0,-1,w) | B:(1,0,w) | $2 (H)B_{1}^{S}(2) $ | |
Λ:(0,0,w) | B:(0,0,w) | $2 (Λ)B_{1}^{S}(2) $ | |
Σ:(u,0,0) | Λ:(0,u,0) | $2 (Σ)Λ_{1}^{S}(2)⊕(Σ)Λ_{2}^{S}(2) $ | |
K:(0,v,w) | B:(-v,0,w) | $4(K)B_{1}^{S}(1)$ | Spin Splitting |
M:(u,0,w) | GP:(0,u,w) | $2(M)GP_{1}^{S}(2) $ | |
P:(u,v,0) | GP:(-v,u,0) | $2(P)GP_{1}^{S}(2) $ | |
Q:(u,v,1/2) | GP:(-v,u,1/2) | $2(Q)GP_{1}^{S}(2) $ | |
GP:(u,v,w) | GP:(-v,u,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) | L:(1/2,1/2,1/2) | $2(R)L_{1}^{S,-}(2)⊕(R)L_{1}^{S,+}(2) $ | |
S:(1/2,-1/2,0) | V:(1/2,1/2,0) | $2(S)V_{1}^{S,+}(2)⊕2(S)V_{1}^{S,-}(2) $ | |
T:(1,0,1/2) | M:(0,1,1/2) | $(T)M_{1}^{S,+}(2)⊕(T)M_{2}^{S,-}(2)⊕(T)M_{1}^{S,-}(2)⊕(T)M_{2}^{S,+}(2) $ | |
Y:(1,0,0) | Y:(0,1,0) | $Y_{1}^{S,+}(2)⊕Y_{1}^{S,-}(2)⊕Y_{2}^{S,+}(2)⊕Y_{2}^{S,-}(2) $ | |
Z:(0,0,1/2) | A:(0,0,1/2) | $(Z)A_{1}^{S,+}(2)⊕(Z)A_{2}^{S,-}(2)⊕(Z)A_{1}^{S,-}(2)⊕(Z)A_{2}^{S,+}(2) $ | |
A:(u,0,1/2) | U:(0,u,1/2) | $2(A)U_{1}^{S}(2)⊕2 (A)U_{2}^{S}(2) $ | |
B:(0,v,1/2) | B:(-v,0,1/2) | $2B_{1}^{S}(2)⊕2B_{2}^{S}(2) $ | |
D:(1/2,1/2,w) | GP:(-1/2,1/2,w) | $4(D)GP_{1}^{S}(2) $ | |
Δ:(0,v,0) | B:(-v,0,0) | $2(Δ)B_{1}^{S}(2)⊕2(Δ)B_{2}^{S}(2) $ | |
H:(0,-1,w) | B:(1,0,w) | $2(H)B_{1}^{S}(2)⊕2(H)B_{2}^{S}(2) $ | |
Λ:(0,0,w) | B:(0,0,w) | $2(Λ)B_{1}^{S}(2)⊕2(Λ)B_{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) | B:(-v,0,w) | $4(K)B_{1}^{S}(1)⊕4(K)B_{2}^{S}(1)$ | Spin Splitting |
M:(u,0,w) | GP:(0,u,w) | $4(M)GP_{1}^{S}(2) $ | |
P:(u,v,0) | GP:(-v,u,0) | $4(P)GP_{1}^{S}(2) $ | |
Q:(u,v,1/2) | GP:(-v,u,1/2) | $4(Q)GP_{1}^{S}(2) $ | |
GP:(u,v,w) | GP:(-v,u,w) | $8GP_{1}^{S}(1)$ | Spin Splitting |