We performed research in modern directions of condensed-matter systems. The project was focused on the advancement of the analysis of physical phenomena in systems with a macroscopic number of degrees of freedom as well as on the analysis of their potential applications and further use in fundamental research in leading scientific and educational centers worldwide.
We have used the following methods in our research: functional integration in quantum many-body theory, diagrammatics, Lindblad equation, bosonization, renormalization group, perturbative methods, saddle-point approximation; numerical simulations, anomalous diffusion equation, nonlinear sigma-model, semiclassical equations in the theory of superconductivity, Usadel equation; statistical methods, polymer elasticity. Analysis of the energy spectra of 2D electrons was based on the method of resonant inelastic light scattering as well as on magnetooptical photoluminiscence spectroscopy. Modern thin-film techniques using electron beam lithography and plasma etching, dilution cryostats at temperatures below 20 mK, microwave techniques; multi-frequency spectroscopy in magnetic resonance in the microwave domain at low temperatures as well as doping as a method to influence basic properties of the magnet. Experimental ESR studies in a wide range of frequencies, fields, and temperatures. Application of theoretical models and numerical methods for the analysis of the data.
We carried out the planned research and obtained results, which are described in detail in the report. Publications based on the results of the project have been prepared and published in leading scientific journals. In particular, we obtained results that advanced theoretical and experimental investigations of such materials and phenomena as:
- edge states and transport in 2D topological insulators and spin impurities
- 2D crystalline membranes
- phenomena in the regime of the quantum Hall effect
- planar Josephson structures
- hybrid superconductor-ferromagnet systems
- Kitaev honeycomb model
- quantum-Hall ferromagnets
- spin valves
- quantum magnets
- Majorana degrees of freedom in networks
- ionization of Majorana fermions in a Josephson junction