In the first funding period we performed detailed atomic-scale investigations of the structural and electronic properties of clean and magnetically doped topological insulators. Furthermore, we studied cleaved Weyl semimetals (WSMs) and identified a robust spin-polarized edge state on the prototypical topological crystalline insulator (TCI) Sn(Pb)Se. Based on this expertise, we intend to execute the following investigations in the second fund- ing period: (i) We will investigate the electronic properties of thins film WSMs prepared in partner project A04 (Buhmann/Molenkamp) by strain-engineering HgTe/CdTe quantum wells. We will com- pare the surface electronic structure and the scattering states identified by STS and QPI, respectively, with bulk materials and differently strained HgTe films in the 3D and 2D TI regime. In particular, we will scrutinize if the Fermi arcs or other well-nested Fermi surface features of WSMs lead to magnetism- induced mesoscopic electron focusing—as previously observed for Mn on Bi2Te3 —or even lead to long-range magnetic order. Similarly, (ii) we will use spin-polarized STM to examine possible 1D spin order of magnetic adatoms induced by the edge state of Pb(Sn)Se. In coopera- tion with the expertise in MBE available in project A05 (Brunner) we will also explore the structural, electronic, and magnetic properties of Sn(Pb)Te thin films. By epitaxial growth numerous low-index surfaces can be created, such as (111) and (110), which cannot be obtained by cleaving bulk crystals. We will explore if step edges of these surface terminations—similar to the (001) surface of Sn(Pb)Se—also exhibit spin-polarized topological edge states and search for states characteristic for higher-order topological insulators (HOTIs). Finally, (iii) we will use the molecular nanoprobe tech- nique newly developed by us to investigate charge carrier transport in topological materials on the atomic scale. We are particularly interested in understanding how single defects (vacancies, anti-sites, interstitials) or surface adatoms impact transport properties between the injection point (defined by the STM tip) and a detector molecule.