In the second funding period, project A02 significantly expanded our knowledge on charge transport ], electronic , and magnetic properties of strongly spin-orbit– coupled and topological materials. As far as the spin-dependent propagation of ballistic electrons and holes is concerned, we successfully developed the spin-polarized molecular nanoprobe (SP- MONA), a novel technique which allows for investigations at single-nm length scales and with single- impurity sensitivity. In a proof-of-concept experiment, which will be presented in detail in Sect. 3.3.1, we demonstrated that the spin–momentum locking of Rashba-split surface states in BiAg2 results in a spin-dependent propagation of charge carriers in these bands. In the third funding period of this SFB 1170 we will exploit this expertise to achieve the following project goals: We will apply SP- MONA to investigate (i) the spin-momentum locking for Dirac electrons found on the surface of the freshly cleaved topological insulator (TI) Bi2Se3 . Furthermore, (ii) we will study to what extend the propagation of charge carriers is affected by single defects or deliberately deposited non-magnetic or magnetic adatoms. In the final years of this funding period, (iii) we plan to utilize our knowledge for the design of engineered adatom assemblies for improved quantum transport functionalities. We expect that our progress in (i)-(iii) will allow scrutinizing the fundamental basis of topological solid- state physics, i.e. the topological protection of Dirac cone surface states and their manipulation by the Aharonov-Bohm effect. As another subject we will investigate doping-induced correlation gaps in the topological crys- talline insulator (TCI) (Pb,Sn)Se. In cooperation with project B04, we showed that the topo- logical midgap state characteristic for odd-atomic step edges of this TCI is highly susceptible to flat-band Stoner ferromagnetism. This represents a one-dimensional analogue of quantum Hall fer- romagnetism in the zeroth Landau level of graphene or in twisted bilayer graphene. In the next funding period, we will systematically explore if (iv) the gap opening depends on the chemical species and existence of a finite magnetic moment of the dopant atom. Furthermore, (v) by using functionalized superconducting STM tips we will explore if the split edge state is spin-polarized and the step edges of (Pb,Sn)Se exhibit permanent magnetic oder.