Similarities and differences in the construction of dispersion laws for charge carriers in semiconductor crystals and adiabatic potentials in molecules
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...
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| Дата: | 2014 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут фізики конденсованих систем НАН України
2014
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| Назва видання: | Condensed Matter Physics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/153508 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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 // Condensed Matter Physics. — 2014. — Т. 17, № 2. — С. 23701:1-8. — Бібліогр.: 13 назв. — англ. |
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irk-123456789-1535082019-06-15T01:27:29Z Similarities and differences in the construction of dispersion laws for charge carriers in semiconductor crystals and adiabatic potentials in molecules Bercha, S.A. Rizak, V.M. 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. У роботi показано як, використовуючи теоретико-груповий метод i метод iнварiантiв, можна одержати вiбронний потенцiал, записаний у матричному виглядi, та вiдповiднi адiабатичнi потенцiали. В якостi прикладу розглядається молекула з симетрiєю D₃d . Визначено симетрiю нормальних коливань, активних в ян-теллерiвському ефектi. Розглянуто E − E вiбронний зв’язок для одержання вiбронної потенцiальної енергiї у матричному виглядi та адiабатичний потенцiал. Вказано на iстотнi вiдмiнностi у побудовi секулярної матрицi D(~k) для знаходження закону дисперсiї електронного спектру в кристалах i матрицi вiбронної потенцiальної енергiї, залежної вiд нормальних координат активного в ян-теллерiвському ефектi нормального коливання. В якостi прикладу розглядується закон дисперсiї носiїв струму в околi точки Γ зони Брiллюена кристалу з симетрiєю D ² ₃d . 2014 Article 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 // Condensed Matter Physics. — 2014. — Т. 17, № 2. — С. 23701:1-8. — Бібліогр.: 13 назв. — англ. 1607-324X arXiv:1407.2427 DOI:10.5488/CMP.17.23701 PACS: 71.70.Ej, 71.20.-b, 61.50.Ah, 02.20.-a, 31.15.Hz http://dspace.nbuv.gov.ua/handle/123456789/153508 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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. |
| format |
Article |
| author |
Bercha, S.A. Rizak, V.M. |
| spellingShingle |
Bercha, S.A. Rizak, V.M. Similarities and differences in the construction of dispersion laws for charge carriers in semiconductor crystals and adiabatic potentials in molecules Condensed Matter Physics |
| author_facet |
Bercha, S.A. Rizak, V.M. |
| author_sort |
Bercha, S.A. |
| title |
Similarities and differences in the construction of dispersion laws for charge carriers in semiconductor crystals and adiabatic potentials in molecules |
| title_short |
Similarities and differences in the construction of dispersion laws for charge carriers in semiconductor crystals and adiabatic potentials in molecules |
| title_full |
Similarities and differences in the construction of dispersion laws for charge carriers in semiconductor crystals and adiabatic potentials in molecules |
| title_fullStr |
Similarities and differences in the construction of dispersion laws for charge carriers in semiconductor crystals and adiabatic potentials in molecules |
| title_full_unstemmed |
Similarities and differences in the construction of dispersion laws for charge carriers in semiconductor crystals and adiabatic potentials in molecules |
| title_sort |
similarities and differences in the construction of dispersion laws for charge carriers in semiconductor crystals and adiabatic potentials in molecules |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/153508 |
| citation_txt |
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 // Condensed Matter Physics. — 2014. — Т. 17, № 2. — С. 23701:1-8. — Бібліогр.: 13 назв. — англ. |
| series |
Condensed Matter Physics |
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2023-05-20T17:39:40Z |
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