Gutzwiller Density Functional Studies of FeAs-Based Superconductors: Structure Optimization and Evidence for a Three-Dimensional Fermi Surface

The electronic structures of FeAs compounds are sensitive to FeAs bonding, which is described unsuccessfully by the local density approximation (LDA). Treating the multiorbital fluctuations from ab inito $\mathrm{LDA}+\mathrm{\text{Gutzwiller}}$ method, we can now predict the correct FeAs bond length and bonding strength, which will explain the observed “soft phonon.” The bands are narrowed by a factor of 2 from their LDA widths. The $d_{3z^2-r^2}$ orbital is pushed up to cross the Fermi level, forming a three-dimensional Fermi surface, which reduces the anisotropy. The interorbital Hund’s coupling $J$ rather than $U$ plays a crucial role in obtaining these results.

Figure 1

The optimized (by $\mathrm{LDA}+\mathrm{G}$) FeAs interlayer distance $d_{\mathrm{FeAs}}^z$ and the bandwidth renormalization factor $Z^2$ (averaged through five orbitals) as a function of interactions ($U$ and $J$). The left and right panels are for LaOFeAs and ${\mathrm{BaFe}}_2{\mathrm{As}}_2$, respectively.

Figure 2

(a) The total energy versus As displacement ($\Delta d$) from its equilibrium position. (b) The occupation numbers of five Fe-$3d$ orbitals as a function of $J$ with fixed $U=3.0\mathrm{eV}$. (c) The projected local density of states (PDOS) of the Fe-$3d_{3z^2-r^2}$ orbital for Fe site in the bulk or on the surface. (d) The normalized Lindhard response function ${\chi }_0(q)/{\chi }_0(0)$ for $q$ vector along the $\Gamma \mathrm{\text{−}}M$ line.

Figure 3

The electronic structure of ${\mathrm{LaO}}_{0.9}{\mathrm{F}}_{0.1}\mathrm{FeAs}$. Upper and middle panels: band structures by LDA and $\mathrm{LDA}+\mathrm{G}$, respectively. We plot the fat bands, where the symbol size corresponds to the projected weight of Bloch states onto the Fe-$3d_{3z^2-r^2}$ orbital. Lower panels: Fermi surfaces from LDA (left) and $\mathrm{LDA}+\mathrm{G}$ (right). The $\Gamma$ point is located at the body center of the cubes.

Figure 4

The electronic structure of ${\mathrm{Ba}}_{0.6}{\mathrm{K}}_{0.4}{\mathrm{Fe}}_2{\mathrm{As}}_2$. All notations are the same as in Fig. 3. For the reason of comparison, we plot the band structures in the same high symmetry lines as that in LaOFeAs instead of the Brillouin zone of the body centered structure.