Drude weight anisotropy in the doped iron pnictides: the primary role of orbital weight redistribution along the reconstructed Fermi surfaces

We explore the anisotropy in low frequency conductivity as a function of hole doping in multiorbital models of pnictides by analyzing the Drude weight in the $x$ and $y$ directions of a ($\pi$, 0) spin-density wave state. A reduction in the conductivity anisotropy with increased hole doping, and subsequent sign reversal, both observed in experiments, is found to be a common trend in these models. This behavior arises due to the interplay of low energy orbitally-resolved density of states and the geometrical features of the Fermi surface. An understanding of anisotropy in the electron doped regime, however, would require additional ingredients.