In this project, we will continue to investigate the structural, magnetic and quantum transport proper- ties of epitaxial V2VI3 tetradymite layers with a focus on magnetically doped (V,Bi,Sb)2 Te3 layers and heterostructures. These compound layers are ferromagnetic (FM) topological insulators (MTI) with bulk bandgaps of about 0.2 eV and Van-der-Waals bonded quintuple layers (QL), which we deposite by molecular beam epitaxy (MBE) on (111)-oriented Si, III-V or II-VI substrates or buffer layers. The interplay of structural layer and device properties, magnetism, hybridization and strong spin-orbit cou- pling of topological surface states (TSSs) enables us to study various topological quantum transport properties. Beyond the fundamental Quantum Anomalous Hall effect (QAHE), i.e. perfectly quantized edge channel transport we observe reproducidly at zero magnetic field, we have drawn a fundamen- tal distinction of the QAHE in 2D MTI layer systems and axion insulator properties in 3D MTI layers corresponding to the topological magnetoelectric effect (TME). We have further observed an insu- lating bulk with R > 300 GΩ/ at temperatures T . 50 mK, edge channel transport surviving up to the Curie temperature TC ≈ 15 K, AH signals of both signs in MTI/TI heterostructures, and quantum tunneling of the magnetization of individual ferromagnetic domains resulting in telegraph-like noise in transport through nano-Hallbar devices. Based on these results, we want to deepen the understand- ing of the interplay of magnetic exchange coupling and spin-orbit coupling depending on the magnetic and structural properties of layers and (nm-sized) transport devices. In the next funding period we want to continue and expand our methods in fabrication, magne- tometry and magnetotransport studies of various MTI devices. The MBE of layer structures will be further optimized with respect to structural and electronic properties. MTI/TI and MTI/semiconductor multiple layer structures with improved designs promise a control of the magnetic interlayer coupling, the number and topology of TSSs. The fabrication of devices with lateral dimensions in the 100 nm range by optimized e-beam lithography will enable Hallbar, quantum wire, and quantum point contact devices with novel functionality. The magnetometry by SQUID will be expanded to temperatures down to about 20 mK and impedance studies of layer structures with (double) gate or tunneling electrodes will be implemented. We want to address the following main scientific objectives: (A) In multiple layer structures with MTI layers, the ferromagnetic (FM) or antiferromagnetic (AFM) order at low temperatures mediated by exchange coupling or RKKY coupling due to hybridized TSSs or bulk states will be studied in order to realize MTI structures with novel topological properties. (B) The Hall and longitudinal transport in edge channels of QAHE or axion insulator devices will be studied in nano-devices with a controlled, low number of magnetic domains resulting in a discrete switching of magnetic domains and quan- tized resistivity. (C) TI and MTI nano-devices with superconducting (SC) contacts will be studied with respect to induced SC and novel topological phases. (D) The stability and dynamics of the magnetic domains and the TME in MTI structures proven so far in quasi-static magnetotransport will be stud- ied by magnetometry and impedance measurements in constant and transient magnetic or electric fields. While the fabrication of such heterostructures and nanodevices as well as the transport and magnetometry studies are challenging, our vast experiences in these fields make them very attainable goals. Our investigations will promote a deeper understanding of the magnetic, quantum transport, TSS and edge channel properties in advanced MTI layer structures and the development of novel functional topological devices. Besides these studies of fundamental MTI properties, more technical improvements in the stability of quantum transport in devices will be addressed. Complementary to our studies we will continue the investigations of such (M)TI structures by STM, STS, ARPES, Re- sPES, infrared spectroscopy, and specific experimental as well as theoretical support in cooperations with projects A01, A02, A03, A06, A07, B02, B03, B04 and B05.