Nanocomposites and nanomaterials

Dispersion of Vibrational and Electronic States and 
Fine Spin-Dependent Structure of Their Energy Levels 
in Hexagonal BN Crystals
Gubanov V.O, Naumenko A.P.
 Faculty of Physics, Taras Shevchenko National University of Kyiv, 64/13, Volodymyrs’ka Street, 01601, Kyiv, Ukraine. 
E-mail: a_naumenko@univ.kiev.ua

The dispersion dependences of vibrational modes and electron excitations in BN crystals as well as in nitrid-borene (or BN-monolayer, (BN)L,1) have been studied taking into account the electron spin for electron excitations.
For the first time, projective classes, which transform spin-dependent electronic wave functions at the points of high symmetry of the Brillouin zones have been determined for the above-mentioned structures. For the first time we found the method of the constructing of factor systems, in particular, the correct factor systems for spinor representations.
The dispersion of the electronic states has been investigated by using the symmetric theoretical group methods. Taking into account the symmetry to inversion of time, compulsory spin-depent thin splitting of energy spectra at different points of Brillouin zones.
It is shown that the results of the developed methods of theoretical-group analyses are consistent with the data of experimental and computational studies of energy spectra and multiplicities of degeneration of quantum states.