Motivated by the studies of the superconducting pairing states in the iron-based superconductors, we analyze the effects of Brillouin zone folding procedure from a space-group symmetry perspective for a general class of materials with the P4/nmm space group. The Brillouin zone folding amounts to working with an effective 1-Fe unit cell, instead of the crystallographic 2-Fe unit cell. We show that the folding procedure can be justified by the validity of a glide reflection symmetry throughout the crystallographic Brillouin zone and by the existence of a minimal double degeneracy along the edges of the latter. We also demonstrate how the folding procedure fails when a local spin-orbit coupling is included although the latter does not break any of the space-group symmetries of the bare Hamiltonian. In light of these general symmetry considerations, we further discuss the implications of the glide reflection symmetry for the superconducting pairing in an effective multiorbital t−J1−J2 model. We find that, for spin-singlet pairing states, the P4/nmm space-group symmetry allows only even parity under the glide reflection and zero total momentum.
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