Table 1 Character table of irreps at high symmetry momenta in magnetic space group PC4bm (#100.177 in BNS setting), taken from the COREPRESENTATIONS program on the Bilbao Crystallographic Server80

From: Anderson critical metal phase in trivial states protected by average magnetic crystalline symmetry

 

Γ1

Γ2

Γ3

Γ4

Γ5

 

M1

M2

M3

M4

M5

 

X1

{10, 0, 0}

1

1

1

1

2

{10, 0, 0}

1

1

1

1

2

{10, 0, 0}

2

\({C}_{2z}=\{{2}_{001}| -\frac{1}{2},\frac{1}{2},0\}\)

1

1

1

1

−2

\({C}_{2z}=\{{2}_{001}| -\frac{1}{2},\frac{1}{2},0\}\)

−1

−1

−1

−1

2

\({C}_{2z}=\{{2}_{001}| -\frac{1}{2},\frac{1}{2},0\}\)

0

\({C}_{4z}=\{{4}_{001}^{+}| 0,\frac{1}{2},0\}\)

1

−1

−1

1

0

\({C}_{4z}=\{{4}_{001}^{+}| 0,\frac{1}{2},0\}\)

i

i

i

i

0

\(\{{m}_{100}| 0,\frac{1}{2},0\}\)

0

\({M}_{xy}=\{{m}_{1\bar{1}0}| 0,0,0\}\)

1

−1

1

−1

0

\({M}_{xy}=\{{m}_{1\bar{1}0}| 0,0,0\}\)

−1

1

−1

1

0

\(\{{m}_{010}| \frac{1}{2},0,0\}\)

0

  1. Characters of the listed symmetry operations can uniquely determine the irreps One should notice that we use a different convention of the origin point as the Bilbao Crystallographic Server. Our \({C}_{2z}=\{{2}_{001}| -\frac{1}{2},\frac{1}{2},0\},{C}_{4z}=\{{4}_{001}^{+}| 0,\frac{1}{2},0\},{M}_{xy}=\{{m}_{1\bar{1}0}| 0,0,0\},\{{m}_{100}| 0,\frac{1}{2},0\}\), and \(\{{m}_{010}| \frac{1}{2},0,0\}\) correspond to \(\{{2}_{001}| 0,0,0\},\{{4}_{001}^{+}| 0,0,0\},\{{m}_{1\bar{1}0}| \frac{1}{2},-\frac{1}{2},0\},\{{m}_{100}| \frac{1}{2},\frac{1}{2},0\}\), and \(\{{m}_{010}| \frac{1}{2},-\frac{1}{2},0\}\) in the standard convention of the Bilbao Crystallographic Server, respectively.