Cooper Pair Formation from Quantum Magnetism in Iron-Pnictide High-Tc Superconductors

We study how spin fluctuations mediate the formation of Cooper pairs in iron-pnictide high-$T_c$ superconductors via a Schwinger-boson-slave-fermion analysis of a two-orbital $t$-$J$ model for a square lattice of iron atoms that includes magnetic frustration and Hund's Rule coupling. The starting point is a hidden half-metal state across the two-orbitals that recovers correct nested Fermi surfaces at a quantum-critical transition with a commensurate spin density wave (cSDW) metal [1]. A mean-field approximation indicates that hidden spinwaves at zero 2D momentum [2] result in an s-wave Cooper-pair instability on the hole Fermi surface pockets centered at 2D momentum $(0,0)$. Proximity to the quantum-critical transition results, additionally, in a simultaneous s-wave Cooper-pair instability on the electron Fermi surface pockets centered at 2D momenta $(\pi,0)$ and $(0,\pi)$, but with a sign change. This mean-field prediction will be checked by extracting the amplitude for such $s_{+-}$ pairing from exact numerical diagonalizations of the two-orbital $t$-$J$ model over the $4\times 4$ lattice with two holes.\\[4pt] [1] J. Rodriguez, M. Araujo \& P. Sacramento, Phys. Rev. B 84, 224504 (2011).\\[0pt] [2] J. Rodriguez, Phys. Rev. B 82, 014505 (2010).