Étude de structures de bandes synthétiques dans un dispositif unidimensionnel

Engineering synthetic band structures in materials presents a compelling avenue for tailoring their electronic properties. The band gap is defined as the energy range within a solid where no electronic states are permitted. It plays a critical role in defining a material's electronic properties. Depending on its size, the material can exhibit an insulating, metallic, or semiconducting behavior. The ability to manipulate this gap enables the design of materials with precisely controlled and desirable properties. In this thesis, we engineer a synthetic band structure in a carbon nanotube, evidenced by differential conductance measurements. We use a linear array of 15 gates to define a corresponding array of quantum dots. A quantum dot arises from the confinement of electrons in all spatial directions and exhibits a discrete energy spectrum, effectively behaving like an artificial atom. By applying a staggered gate voltage, we induce a spatial modulation of the electronic potential landscape, effectively opening synthetic band gap in the carbon nanotube's density of states. This tunable periodic potential enables the simulation of physical systems governed by equations such as the Mathieu equation, and allows exploration of phenomena related to periodic potentials. This method allows for the realization of custom systems with tunable properties, opening the possibility to investigate edge states in periodic structures and to engineer topological systems. By precisely controlling the potential landscape, one can explore boundary phenomena and design materials that exhibit topologically protected states, further expanding the scope of quantum device engineering. In particular, we use a coplanar waveguide cavity to probe the charge susceptibility of the system, which provides valuable insights into the electronic transitions in the system.