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We discuss the sign change of superconducting order parameters in both realand reciprocal spaces when the odd parity spin singlet pairing proposedrecently in\cite{huoddparity} is allowed. We show that in this case an nodelessanti-phase $s^\pm$ can be generated. In a 2-Fe Brilliouin zone (BZ), signchange exists between two hole pockets and between two electron pockets. In a1-Fe BZ which includes two 2-Fe BZs, the sign change is between two 2-Fe BZs,which leads to a d-wave type sign distribution on the electron pockets, namely,an anti-phase $s^\pm$ state with no symmetry protected gapless node on theelectron pockets. This sign change character consistently explains experimentalresults related to sign change properties measured on both iron-pnictides andiron-chalcogenides.

Odd parity pairing and nodeless anti-phase $s^\pm$ in Iron-Based Superconductors