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

Abstract

Abstract. 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 kF in an infinite chain embedding two scatterers separated by a segment of length Lc. The fermions interact only inside the two scatterers. The dependence of one scatterer onto the other exhibits oscillations of period π/kF which decay as 1/Lc and which are suppressed when Lc exceeds the thermal length LT.

Scanning Gate Microscopy of a Nanostructure Where Electrons Interact

“…As one moves the tip, this changes the Hartree corrections of the nanostructure. A similar effect also changes the Fock corrections [11][12][13]. When the electrons do not interact inside the nanostructure, the SGM images probe the interferences of electrons which are transmitted by the nanostructure and elastically backscattered by the tip at the Fermi energy E F .…”

“…With interactions inside the nanostructure, the effective nanostructure transmission becomes nonlocal and can be modified by the tip. The origin of this nonlocal effect is easy to explain [11][12][13] if one uses the Hartree-Fock (HF) approximation. The tip induces Friedel oscillations of the electron density, which can modify the density inside the nanostructure.…”

Detection of interaction-induced nonlocal effects using perfectly transmitting nanostructures

“…In generic nanosystems, the effective one-body approaches are challenged by the nonlocal effects arising p-1 from interactions which can be tested by approaching an external scatterer. The nonlocality can be explained already at the Hartree-Fock (HF) level [9][10][11], since the Hartree and Fock corrections are given by nonlocal coupled integral equations. For instance, the effect of an external scatterer upon the Hartree corrections results from the Friedel oscillations of the electron density that the external scatterer induces inside the nanosystem.…”

Effect of Measurement Probes upon the Conductance of an Interacting Nanosystem: Detection of an Attached Ring by Nonlocal Many Body Effects

“…This phenomenon is reminiscent of the RKKY interaction [5] between magnetic moments via conduction electrons. At a temperature T = 0, this non local effect is exponentially suppressed [4] when L c exceeds L T , the scale on which the electrons propagate at the Fermi velocity during a time ∝ 1/T .…”

“…(2,3,4) can be given as a function of v, V and k F , as in Ref. [4]. The self-consistent values of v and V can be obtained analytically if U is small or numerically otherwise, solving the coupled Eqs.…”