A band is a band representation exactly when it splits into analytic, topologically trivial unit-rank bands permuted by symmetry, which is used to prove that specific photonic crystals are fragile topological with removable boundary states.
The reduced real-space coordinates of the two pairs of orbitals are (0 , 0, 0), in an orthog- onal basis of Bravais lattice vectors
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Crystallographic splitting theorem for band representations and fragile topological photonic crystals
A band is a band representation exactly when it splits into analytic, topologically trivial unit-rank bands permuted by symmetry, which is used to prove that specific photonic crystals are fragile topological with removable boundary states.