Novel properties in Josephson junctions involving the cos(kx)cos(ky)-pairing state in iron-pnictides

We propose a trilayer $\pi$-junction that takes advantage of the unconventional $s_{x^2 y^2}=\cos k_x \cos k_y$ pairing symmetry which changes sign between electron and hole Fermi pockets in the iron pnictides. In addition, we also present theoretical results for Andreev bound states in thin superconductor-normal metal (or insulator) iron-pnictide junctions. The presence of nontrivial in-gap states, which uniquely appear in this unconventional pairing state, is a distinct feature in comparison to other singlet pairing states.