Table 2 MEBRs of P_C4bm (#100.177 in BNS setting) involved in this work, taken from the MBANDREP program on the Bilbao Crystallographic Server⁸⁰

Wyckoff pos.	\(2{{{{{{{\rm{b}}}}}}}}\,(\frac{3}{4}\frac{1}{4}0),(\frac{1}{4}\frac{3}{4}0)\)				\(4{{{{{{{\rm{c}}}}}}}}\,(000),(0\frac{1}{2}0),(\frac{1}{2}00),(\frac{1}{2}\frac{1}{2}0)\)
Site sym.	\(4{m}^{{\prime} }{m}^{{\prime} },4\)				\({2}^{{\prime} }{m}^{{\prime} }m,m\)
MEBR	A_b↑G	B_b↑G	¹E_b↑G	²E_b↑G	\({{{{{{{{\rm{A}}}}}}}}}_{{{{{{{{\rm{c}}}}}}}}}^{{\prime\prime} }\uparrow {{{{{{{\rm{G}}}}}}}}\)
Orbital	1	\({d}_{{x}^{2}-{y}^{2}}+i{d}_{xy}\)	p_x + ip_y	p_x − ip_y	p_y
Irreps at Γ	Γ₁ ⊕ Γ₄	Γ₂ ⊕ Γ₃	Γ₅	Γ₅	Γ₂ ⊕ Γ₄ ⊕ Γ₅
Irreps at M	M₅	M₅	M₂ ⊕ M₃	M₁ ⊕ M₄	M₂ ⊕ M₄ ⊕ M₅
Irreps at X	X₁	X₁	X₁	X₁	2X₁

The real space orbital character of each MEBR is shown in the “Orbital” row. For example, the MEBR B_b↑G can be generated by an \({d}_{{x}^{2}-{y}^{2}}+i{d}_{xy}\) type orbital at the first 2b position \((\frac{3}{4},\frac{1}{4},0)\). Note that \({{{{{{{{\rm{A}}}}}}}}}_{{{{{{{{\rm{c}}}}}}}}}^{{\prime\prime} }\uparrow {{{{{{{\rm{G}}}}}}}}\) is the only decomposable MEBR, although bands with this MEBR are always connected in this work. One should notice that we use a different convention of the origin point as the Bilbao Crystallographic Server.

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