Gutzwiller density functional calculations of the electronic structure of FeAs-based superconductors: Evidence for a three-dimensional Fermi surface

The electronic structures of FeAs-compounds strongly depend on the Fe-As bonding, which can not be described successfully by the local density approximation (LDA). Treating the multi-orbital fluctuations from $ab$-$initio$ by LDA+Gutzwiller method, we are now able to predict the correct Fe-As bond-length, and find that Fe-As bonding-strength is 30% weaker, which will explain the observed soft phonon. The bands are narrowed by a factor of 2, and the $d_{3z^2-r^2}$ orbital is pushed up to cross the Fermi level, forming 3-dimensional Fermi surfaces, which suppress the anisotropy and the ($pi,pi$) nesting. The inter-orbital Hunds coupling $J$ rather than $U$ plays crucial roles to obtain these results.