Fig. 1 - Thermal enhancement of the SGM image of a QPC: The QPC is opened at the value given by the green arrow in the inset. The left (right) figures give respectively the change of the QPC conductance induced by the tip, at T=0K (T=0.01 EF) where EF is the 2DEG Fermi energy.
The image of a nanostructured quantum contact taken with a scanning gate microscope (SGM) gives the conductance of the interferometer formed in a two dimensional electron gas (2DEG) between this contact and the depletion region induced by the charged SGM tip, as a function of the position of the tip, of the opening of the contact and of the temperature. As first observed by Topinka et al., the SGM images of a quantum point contact (QPC) exhibit Fabry-Pérot interference fringes spaced by half the Fermi wavelength. The SGM images have been more systematically studied later at lower temperatures using 2DEGs of higher mobility at different points of the QPC conductance plateaus as well as between plateaus. Outside Harvard (Westervelt), this was done notably in Stanford (Goldhaber-Gordon), at ETH-Zurich (Ensslin) and now in Grenoble (Sanquer-Sellier). Ensslin reported the existence of unexplained interference rings which are superimposed upon the Fabry-Pérot fringes.
We have first studied the effect of electron-electron interactions inside the contact upon the SGM images . We have later considered the effect of temperature upon the SGM images of a non-interacting contact . In this work, we have shown that around certain contact openings, the interference fringes are not weakened by thermal averaging, as one usually expects, but are on the contrary enhanced with temperature (see Fig. 1). More recently , we have shown that the magnetic moment of a Kondo dot can be measured by electron interferometry from interference rings of the type observed by Ensslin. These rings can be seen in the SGM images of dots biased in the middle of a Kondo valley above the Kondo temperature (see Fig. 2).
These theoretical projects have been partly supported by ANR (Project ITEM-Th), while experiments are now in progress in Grenoble supported also by ANR (Project ITEM-Exp). These theoretical studies were based on the analytical solution of a simplified model where the contact is made of an Anderson impurity connecting two semi-infinite square lattices, and on numerical studies using recursive Green’s function methods.
 A. Freyn, I. Kleftogiannis and J.-L. Pichard, Scanning gate microscopy of a nanostructure where electrons interact, Phys. Rev. Lett. 100 (2008) 226802
 A. Abbout, G. Lemarié and J.-L. Pichard, Thermal enhancement of interference effects in quantum point contact, Phys. Rev. Lett. 106 (2011) 156810
 A. Kleshchonok, G. Fleury, G. Lemarié and J.-L. Pichard, Scanning Gate Microscopy of Kondo Dots: Fabry-Pérot Interferences and Thermally Induced Rings, arXiv:1305.0106 (2013)