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Information × Registration Number 0224U000729, 0123U102283 , R & D reports Title Electron properties of low-dimensional Dirac and semiconducting materials in the presence of external fields and spacial inhomogeneities. popup.stage_title Head Bryzhyk Larysa S., д.ф.-м.н.Zolotaryuk Yaroslav O., д.ф.-м.н. Registration Date 11-01-2024 Organization М.М.Bogolyubov Institute of Theoretical Physics of the National Academy of Sciences of Ukraine popup.description2  The research subjects of this project are Dirac materials, graphene nanoribbons, nanostructures, heterostructures, crystals, Josephson junctions. The аiм of this project was to study the influence of external fields, structural inhomogeneities and controlled spatially inhomogeneous deformations on the spectral, electronic, and transport properties of low-dimensional materials, in particular, on the single and multilayer Dirac and superconducting materials and heterostructures that are used in modern nanotechnologies. The Landau levels in in graphene nanoribbons with an armchair edge in crossed magnetic and electric fields are analytically considered and the energy spectrum is obtained. Based on the full set of spin invariants of the Dirac equation with Coulomb potential and their algebraic properties, it is shown that it can be solved by a purely algebraic method. The charge distribution and spin orientation of electrons on the atomic orbitals of a hydrogen atom in states corresponding to different spin invariants of the Dirac equation are calculated. Within the framework of Dirac theory and taking into account radiation corrections and polarization of the electron-positron vacuum, the energy spectrum of the hydrogen atom is calculated. The calculated matrix elements of the perturbations determine the value of the Lamb shifts of the electronic levels. The spectrum of a one-dimensional Hamiltonian with pseudospin 1 and a three-component potential is studied. In case when the components of the potential are rectangular, it is shown that the energy spectrum can be one of four essentially different types. It is shown that the dispersion law of a one-dimensional weakly interacting gas of spinless bosons with zero boundary conditions coincides with the known dispersion law of a similar periodic system if the interaction constant or concentration is small. Product Description popup.authors Eremenko Olexandr O. Bryzhyk Larysa S. Husynin Valerii P. Zolotaryuk Olexandr V. Zolotaryuk Yaroslav O. Starodub Ivan O. Tomchenko Maxim D. Sharapov Sergij H. popup.nrat_date 2024-01-11 Close