Abstract : In this thesis, the non-local effect of local electron-electron interaction upon the transport in low-dimensional quantum models is studied. At zero temperature, the transport through an interacting nano-structure is described by the scattering approach, using an effective scattering matrix. However, when the interactions are important inside the nano-structure, the effective one-body scatterer describing the nano-structure cannot be determined from the internal properties of the nano-structure only, but is influenced also by external scatterers in the leads.
In this thesis, these interaction-induced non-local effects are studied in three different models, using the Hartree-Fock theory to describe the interaction.
Looking at two interacting nano-structures coupled by a non-interacting lead, we show that the scattering matrices of the nano-structures are effectively coupled via Friedel-oscillations in the lead.
It is sufficient to study a single interacting nano-structure in series with an one-body scatterer to obtain non-local contributions to the quantum conductance. Replacing the second nano-structure by an Aharonov-Bohm scatterer, we show that the scattering matrix of the nano-structure depends on the magnetic flux in the Aharonov-Bohm scatterer.
Extending our study to two dimensions, the influence of the non-local effect upon the images obtained by Scanning Gate Microscopy is considered. Using the non-local effect, we show that the importance of electron-electron interactions inside a nano-structure can be detected from the these images.