Effects of Fermi-surface shrinking on the optical sum rule in pnictides

In this paper we investigate the effects of the band shifts induced by the interband spin-fluctuation coupling on the optical sum rule in pnictides. We show that, despite the shrinking of the Fermi surfaces with respect to first-principle calculations, the charge-carrier concentration in each band is almost unchanged, with a substantial conservation of the total optical sum rule. However, a significant transfer of spectral weight occurs from low-energy coherent processes to incoherent ones, with practical consequences on the experimental estimate of the sum rule, that is carried out integrating the data up to a finite cut-off. This has profound consequences both on the absolute value of the sum rule and on its temperature dependence, that must be taken into account while discussing optical experiments in these systems.