HgTe is a semimetal with an inverted band structure. The degeneracy of the Γ8- bands in this system can be lifted by strain or quantum confinement resulting in three-dimensional (3D) or two-dimensional (2D) topological insulator (TI) structures. These structures can be grown by molecular beam epitaxy (MBE) techniques with a very high crystalline quality, making HgTe based topological insulators an ideal system for quantum transport studies. This project will focus on the further improvement of MBE growth of HgTe quantum well (QW) structures (2D TIs) and HgTe bulk layers (3D TIs) and will supply this kind of layers to the SFB consortium for detailed investigation. In particular, we will focus on (i) the investigation of strain engineering techniques in HgTe layers and (ii) the development of bilayer 2D- and 3D-TI structures. Strain engineering will allow for increased band gap sizes (up to 100 meV) in HgTe QWs. This will increase the robustness of the topological insulator behavior and thereby permit advanced experiments or investigations of TI physics at higher temperatures. For strained bulk HgTe layers it is predicted that compressive strain should lead to the emergence of Weyl-Fermions in the material. The strain engineering will be achieved by using ternary compounds (e.g. Cd1−xZnxTe) or superlattice structures to adjust the lattice constant of the host material and thereby the strain in the HgTe layer. The development of bilayer structures will enable the investigation of correlations between either two coupled HgTe quantum wells or the surfaces of two bulk HgTe layers and provide a convenient route to back-gating of these structures. A main concern will be the optimization of the barrier between the HgTe layers in order to control and adjust the strength of the interaction. The research and development in this project will rely on close collaboration and feedback from several experimental and theoretical groups within the SFB.