Thesis presented December 13, 2023

Abstract:
The valley degree of freedom present in some materials like silicon or graphene can be seen as an opportunity for quantum manipulation thanks to many similarities with the spin. However, the observed multi-factorial dependencies of the valley splitting in two-dimensional silicon systems highlight the complexity of the underlying mechanisms behind valley polarization. We can mention the nature and the quality of the interfaces of the confined electronic system, electric fields in the structure, carrier density, and potentially, many-body effects. In this work, we report a study of the valley splitting in a doubly-gated silicon transistors in which we can precisely and electrically control the proximity of electrons to the interfaces. By using different kinds of magneto-transport experiments at low temperatures, we can extract the valley splitting as a function of well-controlled physical parameters.
We report an electrical tunability of the valley splitting close to an interface, in qualitative agreement with theoretical expectations. In addition, we observe an important contribution attributed to many-body interactions, enhanced by the application of a perpendicular magnetic field. A model is proposed and it consists in adding to a “bare” valley splitting an electron-electron interactions contribution depending self-consistently on the degree of valley polarization. This contribution is dominant in the quantum Hall regime where the perpendicular magnetic field acts as a polarization booster by increasing the degeneracy of Landau levels. This approach allows us to understand the existing experimental literature in two dimensionnal silicon, and in particular to predict some complex hierarchies observed between spin and valley gaps. We finally discuss the implications for a possible many-body-induced spontaneous valley polarization in clean dilute silicon systems.

Keywords:
Silicon, Valley, Many-body interactions, Electric field, Polarization, MOSFET