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We investigate an unusual symmetry of Fe-based superconductors (FeSCs) andfind novel superconducting pairing structures. FeSCs have a minimaltranslational unit cell composed of two Fe atoms due to the staggered positionsof anions with respect to the Fe plane. We study the physical consequences ofthe additional glide symmetry that further reduces the unit cell to have onlyone Fe atoms. In the regular momentum space, it not only leads to a particularorbital parity separated spectral function but also dictates orbital paritydistinct pairing structures. Furthermore, it produces accompanying Cooper pairsof $(\pi,\pi,0)$ momentum, which have a characteristic \textit{odd} form factorand break time reversal symmetry. Such novel pairing structures explain theunusual angular modulations of the superconducting gaps on the hole pockets inrecent ARPES and STS experiments.

Orbital-Parity Distinct Superconducting Pairing Structures of Fe-based Superconductors under Glide Symmetry