We performed research in modern directions of condensed-matter physics. The goal was to advance our understanding of the physics of such systems and phenomena as well as to create the basis for further use of the results of our research in leading scientific and educational centers worldwide, including potential applications.
We have used the following methods in our research. Functional integration and quantum-fileld-theory methods in condensed-matter physics, diagrammtic methods, numerical methods scuh as Monte-Carlo simulations, direct numerical diagonalization, Lindblad equation, bosonization methods, renormalization-group methods; perturbation theory, saddle-point approximation. Semiclassical equations in the theory of superconductivity, boblinbear replica sigma-model, theory of many-body co-tunneling, dynamic-percolation theory, Mott theory of variable-range hopping. Investigation of the strong-interaction phenomena for heavy electrons in two dimensions we applied the method of inelastic light scattering as well as magnetic spectroscopy, based on the analysis of the radiant recombination of 2D electrons with photo-excited holes. X-ray diffraction, kin-situ sample rotation at low temperatures asnd high magnetic fields in the analysis of anisotropy of an electron system, multi-frequency spectroscopy, magnetic resonance in the microwave domain, at low temperatures as well as doping of magnetic materials. Fabrication of Josephson structures was based on modern techn ology, while their investigation was performed at low and ultra-low temperatures.
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:
- transport and edge states in topological insulators
- intyeraction of qubits, coupled to a continuous medium
- ferromagnetic instability in the quantum Hall effect at filling factor 2
- quasi-1D antiferromagnets
- pi-periodic current-phase relation in Josephson junctions
- switching of magnetic Josephson junctions under microwave irradiation
- mesoscopic superconductivity
- localization theory
- topological Josephson junctions
- physics at the surface of chiral p-wave superconductors
- superconducting spin valves
- nematic topological superconductors
- artificially inhomogeneous macroscopic two-dimensional systems
- elastic turbulence
- smectic-hexatic phase transition in a suspended film
- stability of the Sachdev-Ye-Kitaev model
- correlations in the Anderson model on random regular graphs
- scattering of electrons in quasi-1D systems
The results are desribed in the project report. 42 publications in leading scientific journals have appeared in the course of the project; the results have also been presented at conferences, symposia and seminars in Russia and abroad.