Tight-binding model for iron pnictides

We propose a five-band tight-binding model for the Fe-As layers of iron pnictides with the hopping amplitudes calculated within the Slater-Koster framework. The band structure found in density-functional theory, including the orbital content of the bands, is well reproduced using only four fitting parameters to determine all the hopping amplitudes. The model allows to study the changes in the electronic structure caused by a modification of the angle $\alpha$ formed by the Fe-As bonds and the Fe plane and recovers the phenomenology previously discussed in the literature. We also find that changes in $\alpha$ modify the shape and orbital content of the Fermi-surface sheets.

Figure 1

(Color online) Top figure: sketch of the lattice structure. Fe-As bonds form an angle $\alpha$ with the Fe plane which changes among compounds, with doping and with pressure. Bottom figure: on the left, in a top view of the Fe-As layer, the real (extended) and the Fe unit cells are shown in dashed and solid lines, respectively. The $X$ and $Y$ axes of the Fe unit cell, used in the paper, and shown with arrows, are directed along the Fe bonds. On the right the experimental (folded) Brillouin zone is shown with dashed lines. Its symmetry points are denoted with primed letters. The extended Brillouin zone, used in the paper, is delimited by solid lines. It is double sized and rotated $45°$ with respect to the experimental Brillouine zone. Bands and Fermi pockets at $\Gamma$ and $M$ in the extended Brillouin zone and discussed through the text will appear experimentally at ${\Gamma }^{\prime }$.

Figure 2

(Color online) Dependence of the hopping amplitudes on $\alpha$. Experimental values of $\alpha$ are between $29°$ and $38°$. Top (bottom) graphs: first- (second-) nearest-neighbor hopping amplitudes corresponding to $pd\pi =-0.5$, ${\left(dd\sigma \right)}_1=-0.6$, ${\left(dd\pi \right)}_1=0.48$, and ${\left(dd\delta \right)}_1=-0.1$. Direct Fe hopping between second-nearest neighbors via ${\left(dd\sigma \right)}_2$, ${\left(dd\pi \right)}_2$, and ${\left(dd\delta \right)}_2$ is neglected. All the energies are in units of ${\left(pd\sigma \right)}^2/\left|{ϵ}_d-{ϵ}_p\right|$ except $pd\sigma$ and $pd\pi$ which are in units of $pd\sigma$. Here ${ϵ}_p$ and ${ϵ}_d$ are the on-site energies of the pnictogen-$p$ and the $\text{Fe}d$ orbital (see Appendix ). The same fitting parameters and energy units are used through all the text.

Figure 3

Band structure in the unfolded Brillouin zone obtained from the tight-binding Hamiltonian (1) with the hopping amplitudes computed within the Slater-Koster framework as described in Appendix . Values used for the overlap integrals are given in Fig. 2, ${\alpha }^{\text{LaFeAsO}}=33.2°$, as found experimentally in LaFeAsO. For on-site energy values see text. From (a) to (d) the width of each bandline is proportional to its $zx$, $xy$, $3z^2-r^2$, and $x^2-y^2$ weight.

Figure 4

From top to bottom, energy bands corresponding to ${\alpha }^{squashed}=29.9°$ (as found in LaFePO), ${\alpha }^{reg}=35.3°$ (regular tetrahedron), and ${\alpha }^{elong}=37.2°$ (elongated tetrahedron). The width of the curves is proportional to their $xy$ weight.

Figure 5

Fermi surface corresponding to ${\alpha }^{squashed}=29.9°$ (as found in LaFePO), ${\alpha }^{\text{LaFeAsO}}=33.2°$ (as found in LaFeAsO), ${\alpha }^{reg}=35.3°$ (regular tetrahedron), and ${\alpha }^{elong}=37.2°$ (elongated tetrahedron) with the same fitting parameters as in Fig. 3.

Figure 6

(Color online) From left to right: orbital content of the Fermi surface corresponding to orbitals $zx$, $xy$, $3z^2-r^2$, and $x^2-y^2$. From top to bottom, each of the figures is plotted for ${\alpha }^{squashed}=29.9°$ (as found in LaFePO), ${\alpha }^{\text{LaFeAsO}}=33.2°$ (as found in LaFeAsO), ${\alpha }^{reg}=35.3°$ (regular tetrahedron), and ${\alpha }^{elong}=37,2°$ (elongated tetrahedron) and the same fitting parameters used in Fig. 3.