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Information × Registration Number 0224U033008, (0124U004093) , R & D reports Title Electronic and transport properties of Dirac materials and Josephson junctions popup.stage_title Вивчення енергетичних рівнів в системах з бездисперсійними зонами у зовнішніх полях Head Zolotaryuk Yaroslav O., д.ф.-м.н. Registration Date 13-12-2024 Organization М.М.Bogolyubov Institute of Theoretical Physics of the National Academy of Sciences of Ukraine popup.description1 The aim of the project is to study in detail the electronic and transport properties of materials containing dispersionless bands in their energy spectra. These are systems with pseudospin-1, multi-fold semimetals, and ladder-like arrays of Josephson junctions. popup.description2  In this stage of the project, the spectral properties of low-dimensional materials such as graphene and Josephson junction array were studied. The spectrum, density of states, and differential entropy per particle for Dirac electrons in graphene in the presence of perpendicular magnetic field and planar electric field were obtained and analyzed. The study considers ballistic electrons and takes into account the effect of weak scattering on impurities. In the latter case, the zero magnetic field limit and the so-called Landau level collapse in graphene are analytically investigated. The density of states for plasma waves in a quasi-one-dimensional array of Josephson junctions is analytically found. If the array consists of N rows, then there are 3N-2 singularities in the density of states, and one delta-like peak associated with the flat band. The anisotropy of the array, which is the ratio of the critical currents of the horizontal and vertical contacts, causes a significant displacement of the singularities along the frequency axis. The semiclassical Wentzel-Kramers-Brillouin method is formulated for quasiparticles with energy dispersion proportional to the fourth power of momentum, which models a weak energy dispersion on momentum. It is shown that matching of wave functions in the classically forbidden and allowed regions requires the consideration of generalized Airy functions. The asymptotics of these functions are found by the steepest descent method and contain exponentially small terms known in the literature as hyperasymptotics. These terms are critically important for the correct matching of wave functions. The found quantization condition was used to determine bound state energies in systems with harmonic and quartic potentials. Product Description popup.authors Barabash Oleh V. Horbar Eduard V. Husynin Valerii P. Zolotariuk Yaroslav O. Momot Andrii I. Pokalchuk Taras-Hryhorii O. Prykhodko Artem Yu. Starodub Ivan O. Sharapov Serhii Н. popup.nrat_date 2024-12-13 Close