Quantum physics and low dimensional systems

Theory of Scanning Gate  Microscopy

Scanning gate microscopy (SGM) is a technique of imaging the change in a physical observable induced by the presence of an Atomic Force Microscope  charged tip.    
The change of the position of the tip leads to the obtaintion of figures of interference effects. Different systems can be studied by this method: Quantum point contacts (QPC), quantum rings ...
The figures of intereference pattern obtained with this technique are studied and explained using theoritical tools such as semiclassical theory of scattering and Green's functions. We also find numerical programs based on recursive Green's function which when combined with simplified models provides interesting answers such as the decay law of the fringes in QPC obtained in 2DEG. The different question we can investigate are:
  •  The decay law of the fringes
  • The dependence on the quantum point contact opening 
  • The foccusing effect and the angular dependence of the fringes.
  • The effect of wider tips.
  • Efect of disorder.
  • Simpler modelisation of the system.
Some of these answers could be found in my articles or in my thesis

Thermal enhancement of the interference effects in quantum point contacts (QPC):

The effect of a charged tip on the conductance of a QPC  depends on the opening of the system. If the QPC is fully open for one mode of conduction (first plateau) the effect decays as 1/x2. If now the system is less open, the  decay  law  of the tip's effect becomes 1/x.  Because of this difference  in the behaviour on the plateau and on the step of the conductance profile, we find that a system  fully open at the edge of the plateau can show a conterintuitive effect of enhancement of the fringes by temperature increase! 
This interesting effect is shown numerically and explained analytically assuming simple resonant level model. More details can be found in Phys. Rev. Lett. 106, 156810 (2011).

This effect of thermal enhancement of the fringes is actually more general and can be seen for the higher plateaus of conduction as it can be seen in the figures. The simulation is done on realistic models using the consept  of recursive Green's functions.

The system which includes the quantum point contact and the charged tip acts as a quantum interferometer. The behavior of this interferometer can be explained by studying the semiclassical paths of the electrons.

These examples show how simple models, taking into account the pertinent 
parameters of a problem can give interesting answers and provide the same
results as the original system with an analytical description at the same time.


From     Phys. Rev. Lett. 106, 156810 (2011).
 
Scanning gate microscopy of the Seebeck coefficent :

In a Quantum point contact, connected to two electronic reservoirs set to  slightly different  temperatures, we can aquire the difference of the potential  induced in order to access to the Seebeck coefficient. Now, with an AFM charged tip, we can image the change in the in the Seebeck coefficient as done in the usual Scanning gate experiment.
Here again , we can try to give the decay law of the fringes as a function of the tip position.

For more details, you can look at the thesis here.