(Top) Adapted from F. Wang and D.-H. Lee [9]; (Bottom) Adapted from J. Hu and N. Hao [2]

Figure 1:
(Top) Lattice structure of the iron-based superconductors. Note that the atomic positions are symmetric under a rotation by 90 degrees in the ab plane, followed by a reflection c→-c. This is the basic operation of the S_{4} symmetry. (Bottom) The gauge transformation consists of multiplying by a minus sign the electronic creation and annihilation operators on the orange iron sites. The transformation changes the pairing symmetry from s wave to d wave, as shown.