The main goal of project A07 is to establish the region of parameter space in which realistic thin film samples energetically constitute the clean limit of 3D topological systems, with an insulating bulk, and the conduction being dominated by topologically induced states with predominant surface character. For this purpose, we plan a closely coordinated campaign with the growth (A04, B01), transport (A03, B02) and theory teams (A06, A09, C05). Employing Terahertz (THz) polarimetry and Fourier transform infrared (FTIR) transmission spectroscopy, we cover the entire energetic window from the direct vicinity of the Fermi level and up to two eV above the Fermi level. The optical transmission spectra will be an accurate measure for the underlying bandstructure. Our method complements ARPES studies, which are sensitive only to states below the Fermi level, and together serve as a benchmark for realistic DFT calculations. By the combined action of the interlinked SFB 1170 projects, we will established a comprehensive picture of the band structure in HgTe based 3D TIs and topological semimetals. Two main avenues will be addressed: 1.) By intermixing the HgTe active layer with Cd, the energetic position of the Dirac point can be pushed above the valence band edge into the gap region. We will study the interplay of strain and Cd admixture to identify the region of parameter space that is the best match in a real sample for the idealized 3D TI scenario. In this context we will further investigate, to which extent the material properties can be tuned by reorienting the growth direction. 2.) We will continue the efforts of magnetic doping with Mn, for which we observe an early onset of the -1 Quantum Hall plateau for fields as low as 50 mT in the 2D limit. We plan to reproduce this finding also in the 3D scenario, using very small magnetic fields to stabilize the Quantum Spin Hall phase.