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 ‖ -1 | 0 } |
a, b, -c | x, y, z | { 1 ‖ m001 | 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 | { -1 ‖ m100 | 0 } |
a, -b, c | -x, -y, -z | { -1 ‖ m010 | 0 } |
a+1/2, b+1/2, c+1/2 | x, y, z | { 1 ‖ 1 | 1/2 1/2 1/2 } |
-a+1/2, -b+1/2, c+1/2 | x, y, z | { 1 ‖ 2001 | 1/2 1/2 1/2 } |
-a+1/2, -b+1/2, -c+1/2 | x, y, z | { 1 ‖ -1 | 1/2 1/2 1/2 } |
a+1/2, b+1/2, -c+1/2 | x, y, z | { 1 ‖ m001 | 1/2 1/2 1/2 } |
a+1/2, -b+1/2, -c+1/2 | -x, -y, -z | { -1 ‖ 2100 | 1/2 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+1/2, c+1/2 | -x, -y, -z | { -1 ‖ m100 | 1/2 1/2 1/2 } |
a+1/2, -b+1/2, c+1/2 | -x, -y, -z | { -1 ‖ m010 | 1/2 1/2 1/2 } |
a, b, c | -x, y, z | { m ‖ 1 | 0 } |
-a, -b, c | -x, y, z | { m ‖ 2001 | 0 } |
-a, -b, -c | -x, y, z | { m ‖ -1 | 0 } |
a, b, -c | -x, y, z | { m ‖ m001 | 0 } |
a, -b, -c | x, -y, -z | { 2 ‖ 2100 | 0 } |
-a, b, -c | x, -y, -z | { 2 ‖ 2010 | 0 } |
-a, b, c | x, -y, -z | { 2 ‖ m100 | 0 } |
a, -b, c | x, -y, -z | { 2 ‖ m010 | 0 } |
a+1/2, b+1/2, c+1/2 | -x, y, z | { m ‖ 1 | 1/2 1/2 1/2 } |
-a+1/2, -b+1/2, c+1/2 | -x, y, z | { m ‖ 2001 | 1/2 1/2 1/2 } |
-a+1/2, -b+1/2, -c+1/2 | -x, y, z | { m ‖ -1 | 1/2 1/2 1/2 } |
a+1/2, b+1/2, -c+1/2 | -x, y, z | { m ‖ m001 | 1/2 1/2 1/2 } |
a+1/2, -b+1/2, -c+1/2 | x, -y, -z | { 2 ‖ 2100 | 1/2 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+1/2, c+1/2 | x, -y, -z | { 2 ‖ m100 | 1/2 1/2 1/2 } |
a+1/2, -b+1/2, c+1/2 | x, -y, -z | { 2 ‖ m010 | 1/2 1/2 1/2 } |
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}} $ | (0,1/2,1/2 | 0,0,0) |
2c | $\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ | (1/2,1/2,0 | 0,0,0) |
2d | $\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ | (1/2,0,1/2 | 0,0,0) |
4e | $\ce{^{-1}{2}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ | (a,0,0 | 0,0,0) |
4f | $\ce{^{-1}{2}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ | (a,1/2,0 | 0,0,0) |
4g | $\ce{^{-1}{m}}\ce{^{-1}{2}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ | (0,b,0 | 0,0,0) |
4h | $\ce{^{-1}{m}}\ce{^{-1}{2}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ | (0,b,1/2 | 0,0,0) |
4i | $\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,0,c | 0,0,0) |
4j | $\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/2,0,c | 0,0,0) |
8k | $\ce{^{1}{-1}}\ce{^{\infty m}{1}} $ | (1/4,1/4,1/4 | 0,0,z) |
8l | $\ce{^{-1}{m}}..\ce{^{\infty m}{1}} $ | (0,b,c | 0,0,0) |
8m | $.\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (a,0,c | 0,0,0) |
8n | $..\ce{^{1}{m}}\ce{^{\infty m}{1}} $ | (a,b,0 | 0,0,z) |
16o | $\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}} $ |
X:(1,1,1) | $\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
R:(1/2,0,1/2) | $\ce{^{2}{2/}}\ce{^{2}{m}}\ce{^{\infty m}{1}} $ |
S:(0,1/2,1/2) | $\ce{^{2}{2/}}\ce{^{2}{m}}\ce{^{\infty m}{1}} $ |
T:(1/2,1/2,0) | $\ce{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
W:(1/2,1/2,1/2) | $\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
Δ:(0,v,0) | $ \ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
Λ:(0,0,w) | $\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
Σ:(u,0,0) | $\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
A:(0,v,w) | $\ce{^{-1}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
B:(u,0,w) | $\ce{^{-1}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
C:(u,v,0) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
D:(u,1/2,1/2) | $\ce{^{2}{2/}}\ce{^{-1}{m}}\ce{^{\infty}{1}} $ |
P:(1/2,1/2,w) | $\ce{^{1}{2/}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
Q:(1/2,v,1/2) | $\ce{^{2}{2/}}\ce{^{-1}{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:(1/2,0,1/2) | V:(1/2,1/2,0) | $(R)V_{1}^{S,+}(2)⊕(R)V_{1}^{S,-}(2) $ | |
S:(1,-1/2,1/2) | L:(1/2,1/2,1/2) | $(S)L_{1}^{S,+}(2)⊕(S)L_{1}^{S,-}(2) $ | |
T:(1/2,-1/2,1) | M:(0,1,1/2) | $2 (T)M_{1}^{S,-}(1)⊕2 (T)M_{2}^{S,-}(1)$ | Spin Splitting |
W:(1/2,-1/2,3/2) | U:(0,3/2,1/2) | $(W)U_{1}^{S}(2)⊕(W)U_{2}^{S}(2) $ | |
X:(0,0,1) | Y:(0,1,0) | $(X)Y_{1}^{S,-}(2)⊕(X)Y_{2}^{S,-}(2) $ | |
D:(u,1/2,1/2) | GP:(1/2+u,1/2,-1/2) | $2(D)GP_{1}^{S}(2) $ | |
Δ:(0,v,0) | B:(v,0,-v) | $(Δ)B_{1}^{S}(2)⊕(Δ)B_{2}^{S}(2) $ | |
Λ:(0,0,w) | Λ:(0,w,0) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2) $ | |
P:(1/2,-1/2,1+w) | U:(0,1+w,1/2) | $2(P)U_{1}^{S}(1)⊕2(P)U_{2}^{S}(1)$ | Spin Splitting |
Q:(1/2,v,1/2) | GP:(1/2+v,1/2,-v) | $2(Q)GP_{1}^{S}(2) $ | |
Σ:(u,0,0) | B:(u,0,0) | $(Σ)B_{1}^{S}(2)⊕(Σ)B_{2}^{S}(2) $ | |
A:(0,v,w) | GP:(v,w,-v) | $2(A)GP_{1}^{S}(2) $ | |
B:(u,0,w) | GP:(u,w,0) | $2(B)GP_{1}^{S}(2) $ | |
C:(u,v,0) | B:(u+v,0,-v) | $2(C)B_{1}^{S}(1)⊕2(C)B_{2}^{S}(1)$ | Spin Splitting |
GP:(u,v,w) | GP:(u+v,w,-v) | $4GP_{1}^{S}(1)$ | Spin Splitting |
k-vector | k-vector-G↑ | A'↑G(4) | |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{2}^{S,-}(2) $ | |
R:(1/2,0,1/2) | V:(1/2,1/2,0) | $(R)V_{1}^{S,+}(2)⊕(R)V_{1}^{S,-}(2) $ | |
S:(1,-1/2,1/2) | L:(1/2,1/2,1/2) | $(S)L_{1}^{S,+}(2)⊕(S)L_{1}^{S,-}(2) $ | |
T:(1/2,-1/2,1) | M:(0,1,1/2) | $2 (T)M_{1}^{S,+}(1)⊕2 (T)M_{2}^{S,-}(1)$ | Spin Splitting |
W:(1/2,-1/2,3/2) | U:(0,3/2,1/2) | $(W)U_{1}^{S}(2)⊕(W)U_{2}^{S}(2) $ | |
X:(0,0,1) | Y:(0,1,0) | $(X)Y_{1}^{S,+}(2)⊕(X)Y_{2}^{S,-}(2) $ | |
D:(u,1/2,1/2) | GP:(1/2+u,1/2,-1/2) | $2(D)GP_{1}^{S}(2) $ | |
Δ:(0,v,0) | B:(v,0,-v) | $2 (Δ)B_{1}^{S}(2) $ | |
Λ:(0,0,w) | Λ:(0,w,0) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2) $ | |
P:(1/2,-1/2,1+w) | U:(0,1+w,1/2) | $2(P)U_{1}^{S}(1)⊕2(P)U_{2}^{S}(1)$ | Spin Splitting |
Q:(1/2,v,1/2) | GP:(1/2+v,1/2,-v) | $2(Q)GP_{1}^{S}(2) $ | |
Σ:(u,0,0) | B:(u,0,0) | $2 (Σ)B_{1}^{S}(2) $ | |
A:(0,v,w) | GP:(v,w,-v) | $2(A)GP_{1}^{S}(2) $ | |
B:(u,0,w) | GP:(u,w,0) | $2(B)GP_{1}^{S}(2) $ | |
C:(u,v,0) | B:(u+v,0,-v) | $2(C)B_{1}^{S}(1)⊕2(C)B_{2}^{S}(1)$ | Spin Splitting |
GP:(u,v,w) | GP:(u+v,w,-v) | $4GP_{1}^{S}(1)$ | 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:(1/2,0,1/2) | V:(1/2,1/2,0) | $2(R)V_{1}^{S,+}(2)⊕2(R)V_{1}^{S,-}(2) $ | |
S:(1,-1/2,1/2) | L:(1/2,1/2,1/2) | $2(S)L_{1}^{S,+}(2)⊕2(S)L_{1}^{S,-}(2) $ | |
T:(1/2,-1/2,1) | M:(0,1,1/2) | $2 (T)M_{1}^{S,+}(1)⊕2 (T)M_{1}^{S,-}(1)⊕2 (T)M_{2}^{S,+}(1)⊕2 (T)M_{2}^{S,-}(1)$ | Spin Splitting |
W:(1/2,-1/2,3/2) | U:(0,3/2,1/2) | $2(W)U_{1}^{S}(2)⊕2(W)U_{2}^{S}(2) $ | |
X:(0,0,1) | Y:(0,1,0) | $(X)Y_{1}^{S,+}(2)⊕(X)Y_{1}^{S,-}(2)⊕(X)Y_{2}^{S,+}(2)⊕(X)Y_{2}^{S,-}(2) $ | |
D:(u,1/2,1/2) | GP:(1/2+u,1/2,-1/2) | $4(D)GP_{1}^{S}(2) $ | |
Δ:(0,v,0) | B:(v,0,-v) | $2(Δ)B_{1}^{S}(2)⊕2(Δ)B_{2}^{S}(2) $ | |
Λ:(0,0,w) | Λ:(0,w,0) | $2Λ_{1}^{S}(2)⊕2Λ_{2}^{S}(2) $ | |
P:(1/2,-1/2,1+w) | U:(0,1+w,1/2) | $4(P)U_{1}^{S}(1)⊕4(P)U_{2}^{S}(1)$ | Spin Splitting |
Q:(1/2,v,1/2) | GP:(1/2+v,1/2,-v) | $4(Q)GP_{1}^{S}(2) $ | |
Σ:(u,0,0) | B:(u,0,0) | $2(Σ)B_{1}^{S}(2)⊕2(Σ)B_{2}^{S}(2) $ | |
A:(0,v,w) | GP:(v,w,-v) | $4(A)GP_{1}^{S}(2) $ | |
B:(u,0,w) | GP:(u,w,0) | $4(B)GP_{1}^{S}(2) $ | |
C:(u,v,0) | B:(u+v,0,-v) | $4(C)B_{1}^{S}(1)⊕4(C)B_{2}^{S}(1)$ | Spin Splitting |
GP:(u,v,w) | GP:(u+v,w,-v) | $8GP_{1}^{S}(1)$ | Spin Splitting |