Abstract:
Josephson junctions between a $FeAs$-based superconductor with antiphase s-wave pairing and a conventional s-wave superconductor are studied. The translational invariance in a planar junction between a single crystal pnictide and an aluminum metal greatly enhances the relative weight of electron pockets in the pnictide to the critical current. In a wide doping region of the pnictide, a planar and a point contact junctions have opposite phases, which can be used to design a tri-junction ring with $\pi$ phase to probe the antiphase pairing.

Abstract:
We determine the anisotropy of the spin fluctuation induced pairing gap on the Fermi surface of the FeAs based superconductors as function of the exchange and Hund's coupling $J_{H}$. We find that for sufficiently large $J_{H}$, nearly commensurate magnetic fluctuations yield a fully gapped $s^{\pm}$-pairing state with small anisotropy of the gap amplitude on each Fermi surface sheet, but significant variations of the gap amplitude for different sheets of the Fermi surface. In particular, we obtain the large variation of the gap amplitude on different Fermi surface sheets, as seen in ARPES experiments. For smaller values of Hund's coupling incommensurate magnetic fluctuations yield an $s^{\pm}$-pairing state with line nodes. Such a state is also possible once the anisotropy of the material is reduced and three dimensional effects come into play.

Abstract:
Considering model Hamiltonians that respect the symmetry properties of the pnictides, it is argued that pairing interactions that couple electrons at different orbitals with an orbital-dependent pairing strength inevitably lead to interband pairing matrix elements, at least in some regions of the Brillouin zone. Such interband pairing has not been considered of relevance in multiorbital systems in previous investigations. It is also observed that if, instead, a purely intraband pairing interaction is postulated, this requires that the pairing operator has the form $\Delta^+(k)=f(k) \sum_{\alpha} d^+_{k,\alpha,\uparrow}d^+_{-k, \alpha,\downarrow}$ where $\alpha$ labels the orbitals considered in the model and f(k) arises from the spatial location of the coupled electrons or holes. This means that the gaps at two different Fermi surfaces involving momenta $k_F$ and $k'_F$ can only differ by the ratio $f(k_F)/ f(k'_F)$ and that electrons in different orbitals must be subject to the same pairing attraction, thus requiring fine tuning. These results suggest that previously neglected interband pairing tendencies could actually be of relevance in a microscopic description of the pairing mechanism in the pnictides.

Abstract:
Some of the iron pnictides show coexisting superconductivity and spin-density-wave order. We study the superconducting pairing instability in the spin-density-wave phase. Assuming that the pairing interaction is due to spin fluctuations, we calculate the effective pairing interactions in the singlet and triplet channels by summing the bubble and ladder diagrams taking the reconstructed band structure into account. The leading pairing instabilities and the corresponding superconducting gap structures are then obtained from the superconducting gap equation. We illustrate this approach for a minimal two-band model of the pnictides. Analytical and numerical results show that the existence of propagating magnons in the spin-density-wave phase strongly enhances the pairing in both the singlet and the spin s_z=0 triplet channel. Over a limited parameter range, a spin s_z=0 triplet p_x-wave state is the dominant instability. It competes with various singlet states, which have mostly s^\pm-type structures. We analyze the effect of various symmetry-allowed interactions on the pairing in some detail.

Abstract:
The symmetry of the wave function describing the Cooper pairs is one of the most fundamental quantities in a superconductor but its measurement in the iron-based superconductors has proved to be very difficult. The complex multi-band nature of these materials makes the interplay of superconductivity with spin and orbital dynamics very intriguing, leading to very material dependent magnetic excitations, and pairing symmetries. Here we use first-principles many-body method, including ab initio determined two-particle vertex function, to study the spin dynamics and superconducting pairing symmetry in a large number of iron-based superconductors. In iron compounds with high transition temperature, we find both the dispersive high-energy spin excitations, and very strong low energy commensurate or nearly commensurate spin response, suggesting that these low energy spin excitations play the dominate role in cooper pairing. We find three closely competing types of pairing symmetries, which take a very simple form in the space of active iron $3d$ orbitals, and differ only in the relative quantum mechanical phase of the $xz$, $yz$ and $xy$ orbital contributions. The extensively discussed s$^{+-}$ symmetry appears when contributions from all orbitals have equal sign, while the opposite sign in $xz$ and $yz$ orbitals leads to the $d$ wave symmetry. A novel orbital antiphase $s^{+-}$ symmetry emerges when $xy$ orbital has opposite sign to $xz$ and $yz$ orbitals. We propose that this orbital-antiphase pairing symmetry explains the puzzling variation of the experimentally observed superconducting gaps on all the Fermi surfaces of LiFeAs. This novel symmetry of the order parameter may be realized in other iron superconductors.

Abstract:
We introduce and study an extended "t-U-J" two-orbital model for the pnictides that includes Heisenberg terms deduced from the strong coupling expansion. Including these J terms explicitly allows us to enhance the strength of the (pi, 0)-(0, pi) spin order which favors the presence of tightly bound pairing states even in the small clusters that are here exactly diagonalized. The A1g and B2g pairing symmetries are found to compete in the realistic spin-ordered and metallic regime. The dynamical pairing susceptibility additionally unveils low-lying B1g states, suggesting that small changes in parameters may render any of the three channels stable.

Abstract:
We compare the one-loop functional renormalization group results for the cuprates and the iron pnictides. Interestingly a coherent picture suggesting that antiferromagnetic correlation causes pairing for both materials emerges.

Abstract:
We use the functional renormalization group method to analyze the phase diagram of a 4-band model for the iron-pnictides subject to band interactions with certain A_{1g} momentum dependence. We determine the parameter regimes where an extended s-wave pairing instability with and without nodes emerges. On the electron-doped side, the parameter regime in which a nodal gap appears is found to be much narrower than recently predicted in arXiv:0903.5547. On the hole-doped side, the extended s-wave pairing never becomes nodal: above a critical strength of the intra-band repulsion, the system favors an exotic extended d-wave instability on the enlarged hole pockets at much lower T_c. At half filling, we find that a strong momentum dependence of inter-band pair hopping yields an extended s-wave instability instead of spin-density wave (SDW) ordering. These results demonstrate that an interaction anisotropy around the Fermi surfaces generally leads to a pronounced sensitivity of the pairing state on the system parameters.

Abstract:
We show that the competition between magnetism and superconductivity can be used to determine the pairing state in the iron arsenides. To this end we demonstrate that the itinerant antiferromagnetic phase (AFM) and the unconventional $s^{+-}$ sign-changing superconducting state (SC) are near the borderline of microscopic coexistence and macroscopic phase separation, explaining the experimentally observed competition of both ordered states. In contrast, conventional $s^{++}$ pairing is not able to coexist with magnetism. Expanding the microscopic free energy of the system with competing orders around the multicritical point, we find that static magnetism plays the role of an intrinsic interband Josephson coupling, making the phase diagram sensitive to the symmetry of the Cooper pair wavefunction. We relate this result to the quasiparticle excitation spectrum and to the emergent SO$(5)$ symmetry of systems with particle-hole symmetry. Our results rely on the assumption that the same electrons that form the ordered moment contribute to the superconducting condensate and that the system is close to particle-hole symmetry. We also compare the suppression of SC in different regions of the FeAs phase diagram, showing that while in the underdoped side it is due to the competition with AFM, in the overdoped side it is related to the disappearance of pockets from the Fermi surface.

Abstract:
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.