Proximity-induced magnetism, electrodynamics, and impurites in topological insulators and Weyl semimetals

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Due its unique properties three-dimensional topological insulators (TIs) and Weyl semimetals (WSs) have generated a lot of interest in recent years because of the combination of their peculiarproperties and experimental accessibility. Most importantly, they are likely to play a major role as component materials in different types of heterostructures. In particular, proximity effect to different types of ordered media, especially magnetic and superconducting materials, provides an avenue to several interesting novel physical effects that may lead to the development of new spin-based electronic components.Our overall goal is to better understand the magnetic properties and the electron-electron interaction in the strong three-dimensional topological insulators and Weyl semimetals. It is well established that effective one-particle theories are successful in predicting the main features of the band structure of these systems. Nevertheless, it becomes increasingly evident that many-body effects yielding unusual magnetic properties are present and could play an important role.Our main objective is to study magnetization dynamics, phase transitions, and spin Josephson effect due to proximity-inducedmagnetic (ferromagnetic and antiferromagnetic) symmetry breaking in heterostructures, which involve topological insulators and/or Weyl semimetal. The main focus willbe on bilayer and trilayer structures with room temperature proximity-induced magnetism, which have been recently realized experimentally.Our further goal is to investigate the role of magnetic and non-magnetic impurities and their interaction with surface and bulk states in TIs and WSs, resulting in the non-trivial quasiparticle intereference patterns of the electronic wave functions. The special emphasis will be put on the study of the presumably topological Kondo insulator, SmB6, and Weyl semimetals based on the pyrochlore band structure with broken time-reversal symmetry.