Title: Similarities and differences in the construction of dispersion laws for charge carriers in semiconductor crystals and adiabatic potentials in molecules
Author(s):

	S.A. Bercha (Uzhgorod National University, 54Voloshyn St., 88000 Uzhgorod, Ukraine) ,
	V.M. Rizak (Uzhgorod National University, 54Voloshyn St., 88000 Uzhgorod, Ukraine)

Using the group theory and the method of invariants, it is shown how the vibronic potential can be written in a matrix form and the corresponding adiabatic potentials can be found. The molecule having D_3d symmetry is considered herein as an example. The symmetries of normal vibrations active in Jahn-Teller's effect were defined. E-E vibronic interaction was considered to obtain vibronic potential energy in a matrix form and thus the adiabatic potential. Significant differences are shown in the construction of a secular matrix D(k) for defining a dispersion law for charge carriers in the crystals and the matrix of vibronic potential energy, which depends on the normal coordinates of normal vibrations active in Jahn-Teller's effect. Dispersion law of charge carriers in the vicinity of Γ point of Brillouin zone of the crystal with D_3d² symmetry was considered as an example.

Key words: Jahn-Teller's effect, method of invariants, dispersion law, adiabatic potential
PACS: 71.70.Ej, 71.20.-b, 61.50.Ah, 02.20.-a, 31.15.Hz

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