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 r
esults 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.
We report the results of exact diagonalization studies of Hubbard models on a $4times 4$ square lattice with periodic boundary conditions and various degrees and patterns of inhomogeneity, which are represented by inequivalent hopping integrals $t$ a
nd $t^{prime}$. We focus primarily on two patterns, the checkerboard and the striped cases, for a large range of values of the on-site repulsion $U$ and doped hole concentration, $x$. We present evidence that superconductivity is strongest for $U$ of order the bandwidth, and intermediate inhomogeneity, $0 <t^prime< t$. The maximum value of the ``pair-binding energy we have found with purely repulsive interactions is $Delta_{pb} = 0.32t$ for the checkerboard Hubbard model with $U=8t$ and $t^prime = 0.5t$. Moreover, for near optimal values, our results are insensitive to changes in boundary conditions, suggesting that the correlation length is sufficiently short that finite size effects are already unimportant.
We study a spin $S$ quantum Heisenberg model on the Fe lattice of the rare-earth oxypnictide superconductors. Using both large $S$ and large $N$ methods, we show that this model exhibits a sequence of two phase transitions: from a high temperature sy
mmetric phase to a narrow region of intermediate ``nematic phase, and then to a low temperature spin ordered phase. Identifying phases by their broken symmetries, these phases correspond precisely to the sequence of structural (tetragonal to monoclinic) and magnetic transitions that have been recently revealed in neutron scattering studies of LaOFeAs. The structural transition can thus be identified with the existence of incipient (``fluctuating) magnetic order.
The zero temperature phase diagram of the checkerboard Hubbard model is obtained in the solvable limit in which it consists of weakly coupled square plaquettes. As a function of the on-site Coulomb repulsion U and the density of holes per site, x, we
demonstrate the existence of at least 16 distinct phases. For instance, at zero doping, the ground state is a novel d-wave Mott insulator (d-Mott), which is not adiabatically continuable to a band insulator; by doping the d-Mott state with holes, depending on the magnitude of U, it gives way to a d-wave superconducting state, a two-flavor spin-1/2 Fermi liquid (FL), or a spin-3/2 FL.
