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 |t<Subscript>s</Subscript>(E<Subscript>F</Subscript>)|<Superscript>2</Supe rscript> describing its effective transmission at the Fermi energy E<Subscript>F</Subscript> ceases to be local. This effect of electron-electron interactions upon |t<Subscript>s</Subscript>(E<Subscript>F</Subscript>)|<Superscript>2</Supe rscript> is studied using a one dimensional model of spinless fermions and the Hartree-Fock approximation. The non locality of |t<Subscript>s</Subscript>(E<Subscript>F</Subscript>)|<Superscript>2</Supe rscript> 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 |t<Subscript>s</Subscript>(E<Subscript>F</Subscript>)|<Superscript>2</Supe rscript> by an Aharonov-Bohm flux threading a ring which is attached to one lead at a distance L<Subscript>c</Subscript> from the nano-system. For small distances L<Subscript>c</Subscript>, the variation of the quantum conductance induced by this non local effect can exceed 0.1 (e<Superscript>2</Superscript>/h). Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007