This work deals with the characteristics of platinum metals and problems related to their toxicity and mobility in the environment, especially in the aquatic environment. These metals are released into the environment due to the use of automotive catalysts. Their function is based on the catalytic properties of platinum metals. Because of the high temperatures, these metals can be oxidized in the catalyst and subsequently emitted together with the combustion products into the surrounding atmosphere. The aim of the thesis is to measure real samples of river sediments of the river Svratka on the territory of the city of Brno and to find the possibility of contamination of the aquatic environment with these metals.

This thesis was inspired by the discovery of Bi14Rh3I9, the first so-called weak three-dimensional topological insulator (3D-TI) and has been concerned with the topic of TIs in general. Two aspects were tackled to gain a deeper understanding of this new state of matter. On one hand, the expansion of the material’s basis and on the other hand developing a simple model of the structure and analysing it via density-functional theory (DFT) based methods. To discover new materials, a systematic investigation of the metal-rich parts of the bismuth–platinum-metal–iodine phase systems was conducted. It led to six new phases among the bismuth subiodides. Some of which, e.g. Bi14Rh3I9, share a honeycomb network of platinum-metal-centred bismuth-cubes and are the seed of a family of materials with this structural motive. The others show strand-like structures or layered structures with platinum-platinum bonds. The latter were so far unknown amongst bismuth subiodides. The honeycomb network was separately analysed and shown to host the TI properties. Structurally and electronically it can be seen as a “heavy graphene analogue”, which refers to the fact that graphene with hypothetical strong spin-orbit coupling (“heavy graphene”) was the first TI put forward by theoreticians. Apart from DFT-calculations, physical experiments confirmed the TI properties. Angle-resolved photoelectron spectroscopy (ARPES) was used to verify the electronic structure and scanning tunnelling microscopy and spectroscopy (STM and STS) to reveal the protected 1D edge states present at the cleaving surface of this material. As the arrangement of the honeycomb layer varies between the different known and newly discovered materials within this family of structures, this influence was also investigated. All further materials were also characterised by DFT-calculations and physical experiments, e.g. magnetisation and transport measurements. This thesis might give an experimental and theoretical basis for a deeper understanding of the TI state of matter. The 1D edge states on the surface of Bi14Rh3I9 could be a chance to handle spins and therefore propel spintronic research, or they could host Majorana fermions, which could be used as qubits in quantum computing.