Table 1 The irreducible representations allowed by symmetry and their corresponding basis vectors and moment components.
From: Spin structure and dynamics of the topological semimetal Co3Sn2-xInxS2
No. | Irrep | Basis Vectors | M (x,y,z) | ||
|---|---|---|---|---|---|
(x,y,z) = (1/2,1/2,1/2) | (1/2,0,1/2) | (0,1/2,1/2) | |||
1 | \({{\Gamma }}_1^ +\) | \(\psi _1\) | \({{{\mathbf{M}}}} = \left( {\begin{array}{*{20}{c}} a \\ a \\ 0 \end{array}} \right)\) | \(\left( {\begin{array}{*{20}{c}} { - a} \\ 0 \\ 0 \end{array}} \right)\) | \(\left( {\begin{array}{*{20}{c}} 0 \\ { - a} \\ 0 \end{array}} \right)\) |
2 | \({{\Gamma }}_2^ +\) | \(\psi _2\) | \(\left( { - \begin{array}{*{20}{c}} a \\ a \\ 0 \end{array}} \right)\) | \(\left( {\begin{array}{*{20}{c}} a \\ {2a} \\ 0 \end{array}} \right)\) | \(\left( {\begin{array}{*{20}{c}} { - 2a} \\ { - a} \\ 0 \end{array}} \right)\) |
3 | \(\psi _3\) | \(\left( {\begin{array}{*{20}{c}} 0 \\ 0 \\ 1 \end{array}} \right)\) | \(\left( {\begin{array}{*{20}{c}} 0 \\ 0 \\ 1 \end{array}} \right)\) | \(\left( {\begin{array}{*{20}{c}} 0 \\ 0 \\ 1 \end{array}} \right)\) | |
4 | \({{\Gamma }}_3^ +\) | \(\psi _4\) | \(\left( {\begin{array}{*{20}{c}} 1 \\ 0 \\ 0 \end{array}} \right)\) | \(\left( {\begin{array}{*{20}{c}} 0 \\ {b^ \ast } \\ 0 \end{array}} \right)\) | \(\left( {\begin{array}{*{20}{c}} { - b} \\ { - b} \\ 0 \end{array}} \right)\) |
5 | \(\psi _5\) | \(\left( {\begin{array}{*{20}{c}} 1 \\ 0 \\ 0 \end{array}} \right)\) | \(\left( {\begin{array}{*{20}{c}} 0 \\ b \\ 0 \end{array}} \right)\) | \(\left( {\begin{array}{*{20}{c}} { - b^ \ast } \\ { - b^ \ast } \\ 0 \end{array}} \right)\) | |
6 | \(\psi _6\) | \(\left( {\begin{array}{*{20}{c}} 0 \\ 1 \\ 0 \end{array}} \right)\) | \(\left( {\begin{array}{*{20}{c}} { - b^ \ast } \\ { - b^ \ast } \\ 0 \end{array}} \right)\) | \(\left( {\begin{array}{*{20}{c}} b \\ 0 \\ 0 \end{array}} \right)\) | |
7 | \(\psi _7\) | \(\left( {\begin{array}{*{20}{c}} 0 \\ 1 \\ 0 \end{array}} \right)\) | \(\left( {\begin{array}{*{20}{c}} { - b} \\ { - b} \\ 0 \end{array}} \right)\) | \(\left( {\begin{array}{*{20}{c}} {b^ \ast } \\ 0 \\ 0 \end{array}} \right)\) | |
8 | \(\psi _8\) | \(\left( {\begin{array}{*{20}{c}} 0 \\ 0 \\ 1 \end{array}} \right)\) | \(\left( {\begin{array}{*{20}{c}} 0 \\ 0 \\ {b^ \ast } \end{array}} \right)\) | \(\left( {\begin{array}{*{20}{c}} 0 \\ 0 \\ b \end{array}} \right)\) | |
9 | \(\psi _9\) | \(\left( {\begin{array}{*{20}{c}} 0 \\ 0 \\ { - 1} \end{array}} \right)\) | \(\left( {\begin{array}{*{20}{c}} 0 \\ 0 \\ { - b} \end{array}} \right)\) | \(\left( {\begin{array}{*{20}{c}} 0 \\ 0 \\ { - b^ \ast } \end{array}} \right)\) | |
