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Information × Registration Number 0223U002186, 0122U002313 , R & D reports Title Effects of external fields and spatial inhomogeneities on the electronic properties of low-dimensional Dirac and superconducting materials popup.stage_title Head Bryzhyk Larysa S., д.ф.-м.н.Zolotariuk Yaroslav O., Доктор фізико-математичних наук Registration Date 12-02-2023 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 purpose 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. For the semi-Dirac model optical conductivity was calculated using a new approach developed in this work. For the dice model with a unit spin, it was shown that in the presence of a gap optical transitions occur between the dispersive and the flat zone and absent between dispersion zones. For the graphene nanoribbons with zigzag and armchair edges it was demonstrated that a combined effect of the crossed electric and magnetic fields breaks the symmetries between the electron and hole energy levels while there symmetries are present if only one of these fields is applied. A new spinor invariant of the Dirac equation was found and with taking it into account the general expression of the spin-orbit interaction is calculated and its features were demonstrated on the example of the quantum well potential that describes quasi-two-dimensional electronic states. An exact solution of the Dirac equation with Coulomb potential was found. In the Dirac equation with potentials in the form of several δ− function the bound state energies were found using two methods (using the Green’s function and transfer matrix). It was shown that these energies are different and the reason for the difference was clarified. An exact wave function was found for the ground state of the Bose crystal at zero temperature. Product Description popup.authors Eremenko Olexandr O. Bryzhyk Larysa S. Husynin Valerii P. Zolotaryuk Yaroslav O. Zolotaryuk Olexandr V. Skrypnyk Yurij V. Starodub Ivan O. Tomchenko Maxym D. Sharapov Sergij H. Shubny Volodymyr O. popup.nrat_date 2023-02-12 Close