Pairing State with a time-reversal symmetry breaking in FeAs based superconductors

We investigate the competition between the extended $s_{\pm}$-wave and $d_{x^2-y^2}$-wave pairing order parameters in the iron-based superconductors. Because of the frustrating pairing interactions among the electron and the hole fermi pockets, a time reversal symmetry breaking $s+id$ pairing state could be favored. We analyze this pairing state within the Ginzburg-Landau theory, and explore the experimental consequences. In such a state, spatial inhomogeneity induces supercurrent near a non-magnetic impurity and the corners of a square sample. The resonance mode between the $s_{\pm}$ and $d_{x^2-y^2}$-wave order parameters can be detected through the $B_{1g}$-Raman spectroscopy.