Optical Conductivity Anisotropy in the Undoped Three-Orbital Hubbard Model for the Pnictides

The resistivity anisotropy unveiled in the study of detwinned single crystals of the undoped 122 pnictides is here studied using the two-dimensional three-orbital Hubbard model in the mean-field approximation. Calculating the Drude weight in the x and y directions at zero temperature for a Q=(\pi,0) magnetically ordered state, the conductance along the antiferromagnetic direction is shown to be larger than along the ferromagnetic direction. This effect is caused by the suppression of the d_{yz} orbital at the Fermi surface, but additional insight based on the momentum dependence of the transitions induced by the current operator is provided. It is shown that the effective suppression of the inter-orbital hopping d_{xy} and d_{yz} along the y direction is the main cause of the anisotropy.