The dark side of DFT based transport calculations.

We compare the conductance of an interacting ring with six lattice sites threaded by flux π in a two terminal setup with the conductance of the corresponding Kohn-Sham particles. Based on symmetry considerations we can show that even within (lattice) Density Functional Theory employing the exact Kohn-Sham exchange-correlation functional the conductance of the Kohn-Sham particles is exactly zero, while the conductance of the physical system is close to the unitary limit. We provide a clear demonstration that the linear conductance is not given by the conductance of the Kohn-Sham particles. We show that this fundamental problem might be solved by extending the standard DFT scheme.