The continuously infinite group ∞1 is omitted.
Coordinates | Seitz symbol |
---|---|
a, b, c | x, y, z | { 1 ‖ 1 | 0 } |
-a+1/2, -b+1/2, c | x, y, z | { 1 ‖ 2001 | 1/2 1/2 0 } |
-a, -b, -c | x, y, z | { 1 ‖ -1 | 0 } |
a+1/2, b+1/2, -c | x, y, z | { 1 ‖ m001 | 1/2 1/2 0 } |
a+1/2, -b, -c | -x, -y, -z | { -1 ‖ 2100 | 1/2 0 0 } |
-a, b+1/2, -c | -x, -y, -z | { -1 ‖ 2010 | 0 1/2 0 } |
-a+1/2, b, c | -x, -y, -z | { -1 ‖ m100 | 1/2 0 0 } |
a, -b+1/2, c | -x, -y, -z | { -1 ‖ m010 | 0 1/2 0 } |
a, b, c | -x, y, z | { m ‖ 1 | 0 } |
-a+1/2, -b+1/2, c | -x, y, z | { m ‖ 2001 | 1/2 1/2 0 } |
-a, -b, -c | -x, y, z | { m ‖ -1 | 0 } |
a+1/2, b+1/2, -c | -x, y, z | { m ‖ m001 | 1/2 1/2 0 } |
a+1/2, -b, -c | x, -y, -z | { 2 ‖ 2100 | 1/2 0 0 } |
-a, b+1/2, -c | x, -y, -z | { 2 ‖ 2010 | 0 1/2 0 } |
-a+1/2, b, c | x, -y, -z | { 2 ‖ m100 | 1/2 0 0 } |
a, -b+1/2, c | x, -y, -z | { 2 ‖ m010 | 0 1/2 0 } |
WP | Site symmetry | Representative |
---|---|---|
2a | $\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/4,1/4,c | 0,0,0) |
2b | $\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/4,3/4,c | 0,0,0) |
4c | $\ce{^{1}{-1}}\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,z) |
4d | $\ce{^{1}{-1}}\ce{^{\infty m}{1}} $ | (0,0,1/2 | 0,0,z) |
4e | $\ce{^{-1}{m}}..\ce{^{\infty m}{1}} $ | (1/4,b,c | 0,0,0) |
4f | $.\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (a,1/4,c | 0,0,0) |
8g | $\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{^{-1}{m}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
B:(0,v,1/2) | $ \ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
C:(u,1/2,0) | $ \ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
D:(1/2,v,0) | $ \ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
Δ:(0,v,0) | $ \ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
E:(u,1/2,1/2) | $ \ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
G:(1/2,0,w) | $ \ce{^{2}{m}}\ce{^{2}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
H:(0,1/2,w) | $ \ce{^{2}{m}}\ce{^{2}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
Λ:(0,0,w) | $ \ce{^{2}{m}}\ce{^{2}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
P:(1/2,v,1/2) | $ \ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
Q:(1/2,1/2,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}} $ |
K:(0,v,w) | $ \ce{^{-1}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
L:(1/2,v,w) | $ \ce{^{-1}{2/}}\ce{^{2}{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{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
W:(u,v,1/2) | $ \ce{^{m}{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,-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) | Y:(1/2,0,0) | $(S)Y_{1}^{S,+}(2)⊕(S)Y_{2}^{S,+}(2) $ | |
T:(0,1/2,-1/2) | D:(0,1/2,1/2) | $(T)D_{1}^{S}(4) $ | |
U:(1/2,0,-1/2) | E:(1/2,1/2,1/2) | $(U)E_{1}^{S}(4) $ | |
X:(1/2,0,0) | A:(1/2,0,1/2) | $(X)A_{1}^{S}(4) $ | |
Y:(0,1/2,0) | B:(0,0,1/2) | $(Y)B_{1}^{S}(4) $ | |
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,u) | $(A)G_{1}^{S}(2)⊕(A)G_{2}^{S}(2) $ | |
B:(0,v,-1/2) | G:(0,1/2,v) | $(B)G_{1}^{S}(2)⊕(B)G_{2}^{S}(2) $ | |
C:(u,1/2,0) | F:(u,0,1/2+u) | $(C)F_{1}^{S}(2)⊕(C)F_{2}^{S}(2) $ | |
D:(1/2,v,0) | F:(1/2,0,1/2+v) | $(D)F_{1}^{S}(2)⊕(D)F_{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) | G:(u,1/2,1/2+u) | $(E)G_{1}^{S}(2)⊕(E)G_{2}^{S}(2) $ | |
G:(1/2,0,w) | U:(1/2,-w,1/2) | $(G)U_{1}^{S}U_{2}^{S}(4) $ | |
H:(0,1/2,w) | V:(0,-w,1/2) | $(H)V_{1}^{S}V_{2}^{S}(4) $ | |
Λ:(0,0,w) | Λ:(0,-w,0) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2) $ | |
P:(1/2,v,-1/2) | G:(1/2,1/2,1/2+v) | $(P)G_{1}^{S}(2)⊕(P)G_{2}^{S}(2) $ | |
Q:(1/2,-1/2,w) | W:(1/2,-w,0) | $(Q)W_{1}^{S}(2)⊕(Q)W_{2}^{S}(2) $ | |
Σ:(u,0,0) | F:(u,0,u) | $(Σ)F_{1}^{S}(2)⊕(Σ)F_{2}^{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,1/2+v) | $2(L)GP_{1}^{S}(2) $ | |
M:(u,0,w) | GP:(u,-w,u) | $2(M)GP_{1}^{S}(2) $ | |
N:(u,1/2,w) | GP:(u,-w,1/2+u) | $2(N)GP_{1}^{S}(2) $ | |
V:(u,v,0) | F:(u,0,u+v) | $2(V)F_{1}^{S}(1)⊕2(V)F_{2}^{S}(1)$ | Spin Splitting |
W:(u,v,-1/2) | G:(u,1/2,u+v) | $2(W)G_{1}^{S}(1)⊕2(W)G_{2}^{S}(1)$ | Spin Splitting |
GP:(u,v,w) | GP:(u,-w,u+v) | $4GP_{1}^{S}(1)$ | 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) | Y:(1/2,0,0) | $(S)Y_{1}^{S,+}(2)⊕(S)Y_{2}^{S,+}(2) $ | |
T:(0,1/2,-1/2) | D:(0,1/2,1/2) | $(T)D_{1}^{S}(4) $ | |
U:(1/2,0,-1/2) | E:(1/2,1/2,1/2) | $(U)E_{1}^{S}(4) $ | |
X:(1/2,0,0) | A:(1/2,0,1/2) | $(X)A_{1}^{S}(4) $ | |
Y:(0,1/2,0) | B:(0,0,1/2) | $(Y)B_{1}^{S}(4) $ | |
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,u) | $(A)G_{1}^{S}(2)⊕(A)G_{2}^{S}(2) $ | |
B:(0,v,-1/2) | G:(0,1/2,v) | $(B)G_{1}^{S}(2)⊕(B)G_{2}^{S}(2) $ | |
C:(u,1/2,0) | F:(u,0,1/2+u) | $(C)F_{1}^{S}(2)⊕(C)F_{2}^{S}(2) $ | |
D:(1/2,v,0) | F:(1/2,0,1/2+v) | $(D)F_{1}^{S}(2)⊕(D)F_{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) | G:(u,1/2,1/2+u) | $(E)G_{1}^{S}(2)⊕(E)G_{2}^{S}(2) $ | |
G:(1/2,0,w) | U:(1/2,-w,1/2) | $(G)U_{1}^{S}U_{2}^{S}(4) $ | |
H:(0,1/2,w) | V:(0,-w,1/2) | $(H)V_{1}^{S}V_{2}^{S}(4) $ | |
Λ:(0,0,w) | Λ:(0,-w,0) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2) $ | |
P:(1/2,v,-1/2) | G:(1/2,1/2,1/2+v) | $(P)G_{1}^{S}(2)⊕(P)G_{2}^{S}(2) $ | |
Q:(1/2,-1/2,w) | W:(1/2,-w,0) | $(Q)W_{1}^{S}(2)⊕(Q)W_{2}^{S}(2) $ | |
Σ:(u,0,0) | F:(u,0,u) | $(Σ)F_{1}^{S}(2)⊕(Σ)F_{2}^{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,1/2+v) | $2(L)GP_{1}^{S}(2) $ | |
M:(u,0,w) | GP:(u,-w,u) | $2(M)GP_{1}^{S}(2) $ | |
N:(u,1/2,w) | GP:(u,-w,1/2+u) | $2(N)GP_{1}^{S}(2) $ | |
V:(u,v,0) | F:(u,0,u+v) | $2(V)F_{1}^{S}(1)⊕2(V)F_{2}^{S}(1)$ | Spin Splitting |
W:(u,v,-1/2) | G:(u,1/2,u+v) | $2(W)G_{1}^{S}(1)⊕2(W)G_{2}^{S}(1)$ | Spin Splitting |
GP:(u,v,w) | GP:(u,-w,u+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,-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) | Y:(1/2,0,0) | $(S)Y_{1}^{S,+}(2)⊕(S)Y_{1}^{S,-}(2)⊕(S)Y_{2}^{S,+}(2)⊕ (S)Y_{2}^{S,-}(2) $ | |
T:(0,1/2,-1/2) | D:(0,1/2,1/2) | $2(T)D_{1}^{S}(4) $ | |
U:(1/2,0,-1/2) | E:(1/2,1/2,1/2) | $2(U)E_{1}^{S}(4) $ | |
X:(1/2,0,0) | A:(1/2,0,1/2) | $2(X)A_{1}^{S}(4) $ | |
Y:(0,1/2,0) | B:(0,0,1/2) | $2(Y)B_{1}^{S}(4) $ | |
Z:(0,0,-1/2) | Z:(0,1/2,0) | $Z_{1}^{S,+}(2)⊕Z_{1}^{S,-}(2)⊕Z_{2}^{S,+}(2)⊕Z_{2}^{S,-}(2) $ | |
A:(u,0,-1/2) | G:(u,1/2,u) | $2(A)G_{1}^{S}(2)⊕2(A)G_{2}^{S}(2) $ | |
B:(0,v,-1/2) | G:(0,1/2,v) | $2(B)G_{1}^{S}(2)⊕2(B)G_{2}^{S}(2) $ | |
C:(u,1/2,0) | F:(u,0,1/2+u) | $2(C)F_{1}^{S}(2)⊕2(C)F_{2}^{S}(2) $ | |
D:(1/2,v,0) | F:(1/2,0,1/2+v) | $2(D)F_{1}^{S}(2)⊕2(D)F_{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) | G:(u,1/2,1/2+u) | $2(E)G_{1}^{S}(2)⊕2(E)G_{2}^{S}(2) $ | |
G:(1/2,0,w) | U:(1/2,-w,1/2) | $2(G)U_{1}^{S}U_{2}^{S}(4) $ | |
H:(0,1/2,w) | V:(0,-w,1/2) | $2(H)V_{1}^{S}V_{2}^{S}(4) $ | |
Λ:(0,0,w) | Λ:(0,-w,0) | $2Λ_{1}^{S}(2)⊕2Λ_{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) | W:(1/2,-w,0) | $2(Q)W_{1}^{S}(2)⊕2(Q)W_{2}^{S}(2) $ | |
Σ:(u,0,0) | F:(u,0,u) | $2(Σ)F_{1}^{S}(2)⊕2(Σ)F_{2}^{S}(2) $ | |
K:(0,v,w) | GP:(0,-w,v) | $4(K)GP_{1}^{S}(2) $ | |
L:(1/2,v,w) | GP:(1/2,-w,1/2+v) | $4(L)GP_{1}^{S}(2) $ | |
M:(u,0,w) | GP:(u,-w,u) | $4(M)GP_{1}^{S}(2) $ | |
N:(u,1/2,w) | GP:(u,-w,1/2+u) | $4(N)GP_{1}^{S}(2) $ | |
V:(u,v,0) | F:(u,0,u+v) | $4(V)F_{1}^{S}(1)⊕4(V)F_{2}^{S}(1)$ | Spin Splitting |
W:(u,v,-1/2) | G:(u,1/2,u+v) | $4(W)G_{1}^{S}(1)⊕4(W)G_{2}^{S}(1)$ | Spin Splitting |
GP:(u,v,w) | GP:(u,-w,u+v) | $8GP_{1}^{S}(1)$ | Spin Splitting |