Symmetry of superconducting states with two orbitals on a tetragonal lattice:: Application to LaFeAsO1-xFx

We use group theory to classify the superconducting states of systems with two orbitals on a tetragonal lattice. The orbital part of the superconducting gap function can be either symmetric or antisymmetric. For the orbital symmetric state, the parity is even for spin singlet and odd for spin triplet; for the orbital antisymmetric state, the parity is odd for spin singlet and even for spin triplet. The gap basis functions are obtained with the use of the group chain scheme by taking into account the spin-orbit coupling. In the weak pairing limit, the orbital antisymmetric state is only stable for the degenerate orbitals. Possible application to iron-based superconductivity is discussed.