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Effect of flux-dependent Friedel oscillations upon the effective transmission of an interacting nano-system

We consider a nano-system connected to measurement probes via non interacting leads. When the electrons interact inside the nano-system, the coefficient |ts(E_F)|^2 describing its effective transmission at the Fermi energy E_F ceases to be local. This effect of electron-electron interactions upon |ts(E_F)|^2 is studied using a one dimensional model of spinless fermions and the Hartree-Fock approximation. The non locality of |ts(E_F)|^2 is due to the coupling between the Hartree and Fock corrections inside the nano-system and the scatterers outside the nano-system via long range Friedel oscillations. Using this phenomenon, one can vary |ts(E_F)|^2 by an Aharonov-Bohm flux threading a ring which is attached to one lead at a distance Lc from the nano-system. For small distances Lc, the variation of the quantum conductance induced by this non local effect can exceed 0.1 (e^2/h).