Spontaneous appearance of nonzero momentum Cooper pairing: Possible application to the iron-pnictides

We suggest that an inhomogeneous (non-zero momentum) paired phase can appear in the absence of an external magnetic field in the system with a predominant interband pairing and with separate Fermi-surface sheets. The Fermi wave vector mismatch which appears in such situation can be compensated by nonzero center-of-mass momentum of the Cooper pairs, what can lead to a spontaneous appearance of the Fulde-Ferrell type of superconducting state. The idea is examined using a tight-binding model which emulates the hole-like and the electron-like bands of iron based superconductor. The state can appear for the case of both spin-singlet and -triplet pairing channels.