Condensed Matter Physics (Jun 2014)

Similarities and differences in the construction of dispersion laws for charge carriers in semiconductor crystals and adiabatic potentials in molecules

  • S.A. Bercha,
  • V.M. Rizak

DOI
https://doi.org/10.5488/CMP.17.23701
Journal volume & issue
Vol. 17, no. 2
p. 23701

Abstract

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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 D3d 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 D3d2 symmetry was considered as an example.

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