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Using functional renormalization group (FRG) approach, we analyze the $\eta$pairing in a five d-orbital model for iron-pncitides. We find that the $\eta$pairing between two hole pockets is a leading instability at low energy whenthe two hole pockets are close to a nesting condition. The result suggests thatthe system can spontaneously enter into a superconducting state with bothnormal pairing and $\eta$ paring and the $\eta$ pairing is driven by theinter-orbital antiferromagnetic exchange coupling while the normal pairing isdriven by the intra-orbital antiferromagnetic ones. An effective model at lowenergy is proposed to account for the $\eta$ pairing instability.

Functional Renormalization Group Analysis of $\eta$-Pairing in Iron-based Superconductors