{
  "id": "1407.2427",
  "version": "v1",
  "published": "2014-07-09T10:40:31.000Z",
  "updated": "2014-07-09T10:40:31.000Z",
  "title": "Similarities and differences in the construction of dispersion laws for charge carriers in semiconductor crystals and adiabatic potentials in molecules",
  "authors": [
    "S. A. Bercha",
    "V. M. Rizak"
  ],
  "comment": "8 pages",
  "journal": "Condens. Matter Phys., 2014, vol. 17, No. 2, 23701",
  "doi": "10.5488/CMP.17.23701",
  "categories": [
    "cond-mat.mes-hall"
  ],
  "abstract": "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 $D(\\vec{k})$ 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 $\\Gamma$ point of Brillouin zone of the crystal with $D_{3d}^2$ symmetry was considered as an example.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-09T10:40:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "charge carriers",
      "dispersion law",
      "adiabatic potential",
      "semiconductor crystals",
      "vibronic potential energy"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.2427B"
    }
  }
}