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

We discuss the sign change of superconducting order parameters in both real and reciprocal spaces when the odd parity spin singlet pairing proposed recently in\cite{huoddparity} is allowed. We show that in this case an nodeless anti-phase $s^\pm$ can be generated. In a 2-Fe Brilliouin zone (BZ), sign change exists between two hole pockets and between two electron pockets. In a 1-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 the electron pockets. This sign change character consistently explains experimental results related to sign change properties measured on both iron-pnictides and iron-chalcogenides.