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 } |
| b, a, -c | x, y, z | { 1 ‖ 2110 | 0 } |
| -b, -a, -c | x, y, z | { 1 ‖ 21-10 | 0 } |
| -b+1/2, a+1/2, c | -x, -y, -z | { -1 ‖ 4+001 | 1/2 1/2 0 } |
| b+1/2, -a+1/2, c | -x, -y, -z | { -1 ‖ 4-001 | 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 ‖ 2010 | 1/2 1/2 0 } |
| a, b, c | -x, y, z | { m ‖ 1 | 0 } |
| -a, -b, c | -x, y, z | { m ‖ 2001 | 0 } |
| b, a, -c | -x, y, z | { m ‖ 2110 | 0 } |
| -b, -a, -c | -x, y, z | { m ‖ 21-10 | 0 } |
| -b+1/2, a+1/2, c | x, -y, -z | { 2 ‖ 4+001 | 1/2 1/2 0 } |
| b+1/2, -a+1/2, c | x, -y, -z | { 2 ‖ 4-001 | 1/2 1/2 0 } |
| a+1/2, -b+1/2, -c | x, -y, -z | { 2 ‖ 2100 | 1/2 1/2 0 } |
| -a+1/2, b+1/2, -c | x, -y, -z | { 2 ‖ 2010 | 1/2 1/2 0 } |
| WP | Site symmetry | Representative |
|---|---|---|
| 2a | $\ce{^{1}{2}}.\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,z) |
| 2b | $\ce{^{1}{2}}.\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,0,1/2 | 0,0,z) |
| 2c | $\ce{^{-1}{4}}..\ce{^{\infty m}{1}} $ | (0,1/2,c | 0,0,0) |
| 4d | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (0,0,c | 0,0,z) |
| 4e | $..\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (a,a,0 | 0,0,z) |
| 4f | $..\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (a,a,1/2 | 0,0,z) |
| 8g | $\ce{^{1}{1}}\ce{^{\infty m}{1}} $ | (a,b,c | 0,0,z) |
| Wavevector-k | Little co-group |
|---|---|
| A:(1/2,1/2,1/2) | $\ce{^{-1}{4}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| Γ:(0,0,0) | $\ce{^{-1}{4}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| M:(1/2,1/2,0) | $\ce{^{-1}{4}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| Z:(0,0,1/2) | $\ce{^{-1}{4}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| R:(0,1/2,1/2) | $\ce{^{2}{2}}\ce{^{2}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| X:(0,1/2,0) | $\ce{^{2}{2}}\ce{^{2}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| Λ:(0,0,w) | $\ce{^{2}{4}}\ce{^{-1}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| V:(1/2,1/2,w) | $\ce{^{2}{4}}\ce{^{-1}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| Δ:(0,v,0) | $\ce{^{-1}{2}}\ce{^{2}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| S:(u,u,1/2) | $\ce{^{m}{2}}\ce{^{1}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| Σ:(u,u,0) | $\ce{^{m}{2}}\ce{^{1}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| T:(u,1/2,1/2) | $\ce{^{2}{2}}\ce{^{-1}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| U:(0,v,1/2) | $\ce{^{-1}{2}}\ce{^{2}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| W:(0,1/2,w) | $\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty}{1}} $ |
| Y:(u,1/2,0) | $\ce{^{2}{2}}\ce{^{-1}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| B:(0,v,w) | $\ce{^{-1}{2}}\ce{^{\infty}{1}} $ |
| C:(u,u,w) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| D:(u,v,0) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| E:(u,v,1/2) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| F:(u,1/2,w) | $\ce{^{-1}{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) $ | |
| A:(1/2,1/2,1/2) | T:(1,0,1/2) | $(A)T_{1}^{S}(2) $ | |
| M:(1/2,1/2,0) | Y:(1,0,0) | $(M)Y_{1}^{S}(2) $ | |
| R:(0,1/2,1/2) | R:(1/2,1/2,1/2) | $R_{1}^{S}(2) $ | |
| X:(0,1/2,0) | S:(1/2,1/2,0) | $(X)S_{1}^{S}(2) $ | |
| Z:(0,0,1/2) | Z:(0,0,1/2) | $Z_{1}^{S}(2) $ | |
| Δ:(0,v,0) | P:(v,v,0) | $(Δ)P_{1}^{S}(2) $ | |
| Λ:(0,0,w) | Λ:(0,0,w) | $Λ_{1}^{S}(2) $ | |
| S:(u,u,1/2) | A:(2*u,0,1/2) | $2(S)A_{1}^{S}(1)$ | Spin Splitting |
| Σ:(u,u,0) | Σ:(2*u,0,0) | $2Σ_{1}^{S}(1)$ | Spin Splitting |
| T:(u,1/2,1/2) | Q:(1/2+u,1/2-u,1/2) | $2(T)Q_{1}^{S}(2) $ | |
| U:(0,v,1/2) | Q:(v,v,1/2) | $2(U)Q_{1}^{S}(2) $ | |
| V:(1/2,1/2,w) | H:(1,0,w) | $(V)H_{1}^{S}(2) $ | |
| W:(0,1/2,w) | D:(1/2,1/2,w) | $(W)D_{1}^{S}(2) $ | |
| Y:(u,1/2,0) | P:(1/2+u,1/2-u,0) | $(Y)P_{1}^{S}(2) $ | |
| B:(0,v,w) | GP:(v,v,w) | $(B)GP_{1}^{S}(2) $ | |
| C:(u,u,w) | M:(2*u,0,w) | $2(C)M_{1}^{S}(1)$ | Spin Splitting |
| D:(u,v,0) | P:(u+v,-u+v,0) | $2(D)P_{1}^{S}(1)$ | Spin Splitting |
| E:(u,v,1/2) | Q:(u+v,-u+v,1/2) | $2(E)Q_{1}^{S}(1)$ | Spin Splitting |
| F:(u,1/2,w) | GP:(1/2+u,1/2-u,w) | $(F)GP_{1}^{S}(2) $ | |
| GP:(u,v,w) | GP:(u+v,-u+v,w) | $2GP_{1}^{S}(1)$ | Spin Splitting |
| k-vector | k-vector-G↑ | A↑G(2) | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2) $ | |
| A:(1/2,1/2,1/2) | T:(1,0,1/2) | $(A)T_{2}^{S}(2) $ | |
| M:(1/2,1/2,0) | Y:(1,0,0) | $(M)Y_{1}^{S}(2) $ | |
| R:(0,1/2,1/2) | R:(1/2,1/2,1/2) | $R_{1}^{S}(2) $ | |
| X:(0,1/2,0) | S:(1/2,1/2,0) | $(X)S_{1}^{S}(2) $ | |
| Z:(0,0,1/2) | Z:(0,0,1/2) | $Z_{2}^{S}(2) $ | |
| Δ:(0,v,0) | P:(v,v,0) | $(Δ)P_{1}^{S}(2) $ | |
| Λ:(0,0,w) | Λ:(0,0,w) | $Λ_{1}^{S}(2) $ | |
| S:(u,u,1/2) | A:(2*u,0,1/2) | $2(S)A_{2}^{S}(1)$ | Spin Splitting |
| Σ:(u,u,0) | Σ:(2*u,0,0) | $2Σ_{1}^{S}(1)$ | Spin Splitting |
| T:(u,1/2,1/2) | Q:(1/2+u,1/2-u,1/2) | $2(T)Q_{1}^{S}(2) $ | |
| U:(0,v,1/2) | Q:(v,v,1/2) | $2(U)Q_{1}^{S}(2) $ | |
| V:(1/2,1/2,w) | H:(1,0,w) | $(V)H_{1}^{S}(2) $ | |
| W:(0,1/2,w) | D:(1/2,1/2,w) | $(W)D_{1}^{S}(2) $ | |
| Y:(u,1/2,0) | P:(1/2+u,1/2-u,0) | $(Y)P_{1}^{S}(2) $ | |
| B:(0,v,w) | GP:(v,v,w) | $(B)GP_{1}^{S}(2) $ | |
| C:(u,u,w) | M:(2*u,0,w) | $2(C)M_{1}^{S}(1)$ | Spin Splitting |
| D:(u,v,0) | P:(u+v,-u+v,0) | $2(D)P_{1}^{S}(1)$ | Spin Splitting |
| E:(u,v,1/2) | Q:(u+v,-u+v,1/2) | $2(E)Q_{1}^{S}(1)$ | Spin Splitting |
| F:(u,1/2,w) | GP:(1/2+u,1/2-u,w) | $(F)GP_{1}^{S}(2) $ | |
| GP:(u,v,w) | GP:(u+v,-u+v,w) | $2GP_{1}^{S}(1)$ | Spin Splitting |
| k-vector | k-vector-G↑ | A↑G(4) | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{4}^{S}(2) $ | |
| A:(1/2,1/2,1/2) | T:(1,0,1/2) | $(A)T_{1}^{S}(2)⊕(A)T_{4}^{S}(2) $ | |
| M:(1/2,1/2,0) | Y:(1,0,0) | $(M)Y_{1}^{S}(2)⊕(M)Y_{4}^{S}(2) $ | |
| R:(0,1/2,1/2) | R:(1/2,1/2,1/2) | $R_{1}^{S}(2)⊕R_{2}^{S}(2) $ | |
| X:(0,1/2,0) | S:(1/2,1/2,0) | $(X)S_{1}^{S}(2)⊕(X)S_{2}^{S}(2) $ | |
| Z:(0,0,1/2) | Z:(0,0,1/2) | $Z_{1}^{S}(2)⊕Z_{4}^{S}(2) $ | |
| Δ:(0,v,0) | P:(v,v,0) | $2(Δ)P_{1}^{S}(2) $ | |
| Λ:(0,0,w) | Λ:(0,0,w) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2) $ | |
| S:(u,u,1/2) | A:(2*u,0,1/2) | $2(S)A_{1}^{S}(1)⊕2(S)A_{2}^{S}(1)$ | Spin Splitting |
| Σ:(u,u,0) | Σ:(2*u,0,0) | $2Σ_{1}^{S}(1)⊕2Σ_{2}^{S}(1)$ | Spin Splitting |
| T:(u,1/2,1/2) | Q:(1/2+u,1/2-u,1/2) | $2(T)Q_{1}^{S}(2) $ | |
| U:(0,v,1/2) | Q:(v,v,1/2) | $2(U)Q_{1}^{S}(2) $ | |
| V:(1/2,1/2,w) | H:(1,0,w) | $(V)H_{1}^{S}(2)⊕(V)H_{2}^{S}(2) $ | |
| W:(0,1/2,w) | D:(1/2,1/2,w) | $(W)D_{1}^{S}(2)⊕(W)D_{2}^{S}(2) $ | |
| Y:(u,1/2,0) | P:(1/2+u,1/2-u,0) | $2(Y)P_{1}^{S}(2) $ | |
| B:(0,v,w) | GP:(v,v,w) | $2(B)GP_{1}^{S}(2) $ | |
| C:(u,u,w) | M:(2*u,0,w) | $4(C)M_{1}^{S}(1)$ | Spin Splitting |
| D:(u,v,0) | P:(u+v,-u+v,0) | $4(D)P_{1}^{S}(1)$ | Spin Splitting |
| E:(u,v,1/2) | Q:(u+v,-u+v,1/2) | $4(E)Q_{1}^{S}(1)$ | Spin Splitting |
| F:(u,1/2,w) | GP:(1/2+u,1/2-u,w) | $2(F)GP_{1}^{S}(2) $ | |
| GP:(u,v,w) | GP:(u+v,-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_{4}^{S}(2) $ | |
| A:(1/2,1/2,1/2) | T:(1,0,1/2) | $(A)T_{2}^{S}(2)⊕(A)T_{3}^{S}(2) $ | |
| M:(1/2,1/2,0) | Y:(1,0,0) | $(M)Y_{1}^{S}(2)⊕(M)Y_{4}^{S}(2) $ | |
| R:(0,1/2,1/2) | R:(1/2,1/2,1/2) | $R_{1}^{S}(2)⊕R_{2}^{S}(2) $ | |
| X:(0,1/2,0) | S:(1/2,1/2,0) | $(X)S_{1}^{S}(2)⊕(X)S_{2}^{S}(2) $ | |
| Z:(0,0,1/2) | Z:(0,0,1/2) | $Z_{2}^{S}(2)⊕Z_{3}^{S}(2) $ | |
| Δ:(0,v,0) | P:(v,v,0) | $2(Δ)P_{1}^{S}(2) $ | |
| Λ:(0,0,w) | Λ:(0,0,w) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2) $ | |
| S:(u,u,1/2) | A:(2*u,0,1/2) | $2(S)A_{1}^{S}(1)⊕2(S)A_{2}^{S}(1)$ | Spin Splitting |
| Σ:(u,u,0) | Σ:(2*u,0,0) | $2Σ_{1}^{S}(1)⊕2Σ_{2}^{S}(1)$ | Spin Splitting |
| T:(u,1/2,1/2) | Q:(1/2+u,1/2-u,1/2) | $2(T)Q_{1}^{S}(2) $ | |
| U:(0,v,1/2) | Q:(v,v,1/2) | $2(U)Q_{1}^{S}(2) $ | |
| V:(1/2,1/2,w) | H:(1,0,w) | $(V)H_{1}^{S}(2)⊕(V)H_{2}^{S}(2) $ | |
| W:(0,1/2,w) | D:(1/2,1/2,w) | $(W)D_{1}^{S}(2)⊕(W)D_{2}^{S}(2) $ | |
| Y:(u,1/2,0) | P:(1/2+u,1/2-u,0) | $2(Y)P_{1}^{S}(2) $ | |
| B:(0,v,w) | GP:(v,v,w) | $2(B)GP_{1}^{S}(2) $ | |
| C:(u,u,w) | M:(2*u,0,w) | $4(C)M_{1}^{S}(1)$ | Spin Splitting |
| D:(u,v,0) | P:(u+v,-u+v,0) | $4(D)P_{1}^{S}(1)$ | Spin Splitting |
| E:(u,v,1/2) | Q:(u+v,-u+v,1/2) | $4(E)Q_{1}^{S}(1)$ | Spin Splitting |
| F:(u,1/2,w) | GP:(1/2+u,1/2-u,w) | $2(F)GP_{1}^{S}(2) $ | |
| GP:(u,v,w) | GP:(u+v,-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_{2}^{S}(2) $ | |
| A:(1/2,1/2,1/2) | T:(1,0,1/2) | $(A)T_{1}^{S}(2)⊕(A)T_{2}^{S}(2) $ | |
| M:(1/2,1/2,0) | Y:(1,0,0) | $(M)Y_{1}^{S}(2)⊕(M)Y_{2}^{S}(2) $ | |
| R:(0,1/2,1/2) | R:(1/2,1/2,1/2) | $2 R_{1}^{S}(2) $ | |
| X:(0,1/2,0) | S:(1/2,1/2,0) | $2 (X)S_{1}^{S}(2) $ | |
| Z:(0,0,1/2) | Z:(0,0,1/2) | $Z_{1}^{S}(2)⊕Z_{2}^{S}(2) $ | |
| Δ:(0,v,0) | P:(v,v,0) | $2(Δ)P_{1}^{S}(2) $ | |
| Λ:(0,0,w) | Λ:(0,0,w) | $2 Λ_{1}^{S}(2) $ | |
| S:(u,u,1/2) | A:(2*u,0,1/2) | $2(S)A_{1}^{S}(1)⊕2(S)A_{2}^{S}(1)$ | Spin Splitting |
| Σ:(u,u,0) | Σ:(2*u,0,0) | $2Σ_{1}^{S}(1)⊕2Σ_{2}^{S}(1)$ | Spin Splitting |
| T:(u,1/2,1/2) | Q:(1/2+u,1/2-u,1/2) | $2(T)Q_{1}^{S}(2) $ | |
| U:(0,v,1/2) | Q:(v,v,1/2) | $2(U)Q_{1}^{S}(2) $ | |
| V:(1/2,1/2,w) | H:(1,0,w) | $2 (V)H_{1}^{S}(2) $ | |
| W:(0,1/2,w) | D:(1/2,1/2,w) | $2 (W)D_{1}^{S}(2) $ | |
| Y:(u,1/2,0) | P:(1/2+u,1/2-u,0) | $2(Y)P_{1}^{S}(2) $ | |
| B:(0,v,w) | GP:(v,v,w) | $2(B)GP_{1}^{S}(2) $ | |
| C:(u,u,w) | M:(2*u,0,w) | $4(C)M_{1}^{S}(1)$ | Spin Splitting |
| D:(u,v,0) | P:(u+v,-u+v,0) | $4(D)P_{1}^{S}(1)$ | Spin Splitting |
| E:(u,v,1/2) | Q:(u+v,-u+v,1/2) | $4(E)Q_{1}^{S}(1)$ | Spin Splitting |
| F:(u,1/2,w) | GP:(1/2+u,1/2-u,w) | $2(F)GP_{1}^{S}(2) $ | |
| GP:(u,v,w) | GP:(u+v,-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_{2}^{S}(2)⊕Γ_{3}^{S}(2)⊕Γ_{4}^{S}(2) $ | |
| A:(1/2,1/2,1/2) | T:(1,0,1/2) | $(A)T_{1}^{S}(2)⊕(A)T_{2}^{S}(2)⊕(A)T_{3}^{S}(2)⊕(A)T_{4}^{S}(2) $ | |
| M:(1/2,1/2,0) | Y:(1,0,0) | $(M)Y_{1}^{S}(2)⊕(M)Y_{2}^{S}(2)⊕(M)Y_{3}^{S}(2)⊕(M)Y_{4}^{S}(2) $ | |
| R:(0,1/2,1/2) | R:(1/2,1/2,1/2) | $2R_{1}^{S}(2)⊕2R_{2}^{S}(2) $ | |
| X:(0,1/2,0) | S:(1/2,1/2,0) | $2(X)S_{1}^{S}(2)⊕2(X)S_{2}^{S}(2) $ | |
| Z:(0,0,1/2) | Z:(0,0,1/2) | $Z_{1}^{S}(2)⊕Z_{2}^{S}(2)⊕Z_{3}^{S}(2)⊕Z_{4}^{S}(2) $ | |
| Δ:(0,v,0) | P:(v,v,0) | $4(Δ)P_{1}^{S}(2) $ | |
| Λ:(0,0,w) | Λ:(0,0,w) | $2Λ_{1}^{S}(2)⊕2Λ_{2}^{S}(2) $ | |
| S:(u,u,1/2) | A:(2*u,0,1/2) | $4(S)A_{1}^{S}(1)⊕4(S)A_{2}^{S}(1)$ | Spin Splitting |
| Σ:(u,u,0) | Σ:(2*u,0,0) | $4Σ_{1}^{S}(1)⊕4Σ_{2}^{S}(1)$ | Spin Splitting |
| T:(u,1/2,1/2) | Q:(1/2+u,1/2-u,1/2) | $4(T)Q_{1}^{S}(2) $ | |
| U:(0,v,1/2) | Q:(v,v,1/2) | $4(U)Q_{1}^{S}(2) $ | |
| V:(1/2,1/2,w) | H:(1,0,w) | $2(V)H_{1}^{S}(2)⊕2(V)H_{2}^{S}(2) $ | |
| W:(0,1/2,w) | D:(1/2,1/2,w) | $2(W)D_{1}^{S}(2)⊕2(W)D_{2}^{S}(2) $ | |
| Y:(u,1/2,0) | P:(1/2+u,1/2-u,0) | $4(Y)P_{1}^{S}(2) $ | |
| B:(0,v,w) | GP:(v,v,w) | $4(B)GP_{1}^{S}(2) $ | |
| C:(u,u,w) | M:(2*u,0,w) | $8(C)M_{1}^{S}(1)$ | Spin Splitting |
| D:(u,v,0) | P:(u+v,-u+v,0) | $8(D)P_{1}^{S}(1)$ | Spin Splitting |
| E:(u,v,1/2) | Q:(u+v,-u+v,1/2) | $8(E)Q_{1}^{S}(1)$ | Spin Splitting |
| F:(u,1/2,w) | GP:(1/2+u,1/2-u,w) | $4(F)GP_{1}^{S}(2) $ | |
| GP:(u,v,w) | GP:(u+v,-u+v,w) | $8GP_{1}^{S}(1)$ | Spin Splitting |