Conductance of nano-systems with interactions coupled via conduction electrons: effect of indirect exchange interactions

A nano-system in which electrons interact and in contact with Fermi leads gives rise to an effective one-body scattering which depends on the presence of other scatterers in the attached leads. This non local effect is a pure many-body effect that one neglects when one takes non interacting models for describing quantum transport. This enhances the non-local character of the quantum conductance by exchange interactions of a type similar to the RKKY-interaction between local magnetic moments. A theoretical study of this effect is given assuming the Hartree-Fock approximation for spinless fermions of Fermi momentum k<Subscript>F</Subscript> in an infinite chain embedding two scatterers separated by a segment of length L<Subscript>c</Subscript>. The fermions interact only inside the two scatterers. The dependence of one scatterer onto the other exhibits oscillations of period π/k<Subscript>F</Subscript> which decay as 1/L<Subscript>c</Subscript> and which are suppressed when L<Subscript>c</Subscript> exceeds the thermal length L<Subscript>T</Subscript>. The analytical results given by the Hartree-Fock approximation are compared with exact numerical results obtained with the embedding method and the DMRG algorithm. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006