Nanocomposites and Nanomaterials

DISPERSION AND THIN SPIN-DEPENDED SPLITTINGS OF ELECTRONIC PI-BANDS IN TRANSITION METAL DICHALCOGENIDE CRYSTALS AND MONOLAYERS
A.Naumenko, V.Gubanov
Faculty of Physics, Taras Shevchenko National University of Kyiv. 
64/13 Volodymyrska Street, Kyiv-01601, Ukraine. 
E-mail: a_naumenko@univ.kiev.uat 
The projective two-valued representations of spinor states for different points of Brollouin zones of crystalline graphite and single-layered graphene as well as of transition metal dichalcogenides (TMDs) have been constructed for the first time. 
Projective classes, which transform spin-dependent electronic wave functions at the points of high symmetry of the Brillouin zone have been determined for the above-mentioned structures. For the establishment of projective classes we found the method of constructing of factor systems, in particular, the correct factor system for spinor representations; the form of standard factor systems and the phase factors for their conversion to standard factor systems for each projective class have been found.
The dispersion of the electronic states of these structures has been investigated by using the symmetric theoretical group methods. It is shown that the results of the developed methods of theoretical-group analysis are consistent with the data of experimental and computational studies of energy spectra and multiplicities of degeneration of quantum states of pi-electron zones.