Iron-Based Superconductors as Parity Odd Superconductors

Parity is a fundamental quantum number to classify a state of matter. Materials rarely possess ground states with odd parity. We show that the superconducting state in iron-based superconductors is classified as an odd parity s-wave spin-singlet pairing state in a single trilayer FeAs/Se, the building block of the materials. In a low energy effective model constructed on the Fe square bipartite lattice, the superconducting order parameter in this state is a combination of a s-wave normal pairing between two sublattices and a s-wave $\eta$-pairing within the sublattices. Parity conservation was violated in proposed superconducting states in the past. The state has a fingerprint with a real space sign inversion between the top and bottom As/Se layers. The results demonstrate iron-based superconductors being a new quantum state of matter and suggest that the measurement of the odd parity can establish fundamental principles related to high temperature superconducting mechanism.