Topological insulators (TI) are new class of materials exhibiting Dirac-like surface states protected by time reversal symmetry for Z2 TIs or by crystalline symmetries for topological crystalline insulators (TCIs). Functional applications requires thin film heterostructures to control the properties of the topological surface states (TSS) by means of strain, finite size hybridization, composition, as well as by magnetic and non-magnetic doping. Here, we present our recent results on molecular beam epitaxy, photoemission spectroscopy [1-3] and magneto-optical and transport investigations  of bismuth-based TI and PbSnSe(Te) TCI films and quantum well structures grown by molecular beam epitaxy. We compare Mn doping of Bi2Se3 and Bi2Te3, revealing peculiar incorporation sites and a striking difference in the gap opening of the TSS . For non-magnetic doping of IV-VI TCIs with four-fold valley-degeneracy, a gap is opened at one Dirac cone at center of the surface Brillouin zone, whereas the three cones at the M-points remain intact. This is the manifestation of a new topological phase transition between a TCI a TI state controlled by Bi doping . In the case of PbSnTe, however, Bi doping rather leads to a giant Rashba splitting of the surface states that is controlled by changes in the bulk Fermi level . We also show that the topology of TCIs can be effectively tuned by strain imposed in heterostructures and moreover, in the thin-film limit a strong hybridization of the opposite TSS occurs that persist up to large thicknesses of more than 50 monolayers. The resulting quantum well show pronounced multiple 2D subband levels in ARPES due to the quantum confinement that can be further tuned by surface doping. This opens a wide playground for device applications.
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