Density of one-particle states for 2-D electron gas in magnetic field
The density of states of a particle in a 2-D area is independent both of the energy and form of the area only at the region of large values of energy. If energy is small, the density of states in the rectangular potential well essentially depends on the form of the area. If the bottom of the potenti...
Збережено в:
| Дата: | 2013 |
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| Формат: | Стаття |
| Мова: | English |
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Інститут фізики конденсованих систем НАН України
2013
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| Назва видання: | Condensed Matter Physics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/121068 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Density of one-particle states for 2-D electron gas in magnetic field / I.M. Dubrovskyi // Condensed Matter Physics. — 2013. — Т. 16, № 1. — С. 13001:1–10. — Бібліогр.: 7 назв. — англ. |
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irk-123456789-1210682017-06-14T03:05:27Z Density of one-particle states for 2-D electron gas in magnetic field Dubrovskyi, I.M. The density of states of a particle in a 2-D area is independent both of the energy and form of the area only at the region of large values of energy. If energy is small, the density of states in the rectangular potential well essentially depends on the form of the area. If the bottom of the potential well has a potential relief, it can define the small eigenvalues as the discrete levels. In this case, dimensions and form of the area would not have any importance. If the conservation of zero value of the angular momentum is taken into account, the effective one-particle Hamiltonian for the 2-D electron gas in the magnetic field in the circle is the Hamiltonian with the parabolic potential and the reflecting bounds. It is supposed that in the square, the Hamiltonian has the same view. The 2-D density of states in the square can be computed as the convolution of 1-D densities. The density of one-particle states for 2-D electron gas in the magnetic field is obtained. It consists of three regions. There is a discrete spectrum at the smallest energy. In the intervening region the density of states is the sum of the piecewise continuous function and the density of the discrete spectrum. At great energies, the density of states is a continuous function. The Fermi energy dependence on the magnetic field is obtained when the field is small and the Fermi energy is located in the region of continuous spectrum. The Fermi energy oscillates and in the average it increases proportionally to the square of the magnetic induction. Total energy of electron gas in magnetic field also oscillates and increases when the magnetic field increases monotonously. Густина станiв частинки у 2D областi не залежить вiд енергiї i форми областi тiльки при великих значеннях енергiї. При малiй енергiї густина станiв у прямокутнiй потенцiальнiй ямi суттєво залежить вiд форми областi. Якщо дно потенцiальної ями має потенцiальний рельєф, то вiн може визначати малi власнi значення енергiї як дискретнi рiвнi. У цьому випадку розмiри i форма областi не мають значення. Якщо приймати до уваги збереження нульового значення кутового моменту, ефективний одночастинковий Гамiльтонiан для 2D електронного газу у магнiтному полi у колi є Гамiльтонiаном з параболiчним потенцiалом i вiдбиваючими границями. Припускається, що у квадратi Гамiльтонiан має такий самий вигляд. 2D густина станiв у квадратi може бути обчислена як згортка 1D густин. Обчислено густину станiв 2D еле-ктронного газу у магнiтному полi. Вона складається з трьох областей. Коли енергiї малi, спектр є дискретним. У промiжнiй областi густина станiв є сумою промiжково-неперервної функцiї i густини дискретного спектру. При великих значеннях енергiї густина станiв є неперервною функцiєю енергiї. Одержано залежнiсть енергiї Фермi вiд магнiтного поля, коли поле є слабким i енергiя Фермi знаходиться в областi неперервного спектру. Енергiя Фермi має доданок, який осцилює i, в середньому, зростає пропорцiйно квадрату магнiтної iндукцiї. Повна енергiя електронного газу у магнiтному полi також осцилює i зростає, коли магнiтне поле монотонно збiльшується. 2013 Article Density of one-particle states for 2-D electron gas in magnetic field / I.M. Dubrovskyi // Condensed Matter Physics. — 2013. — Т. 16, № 1. — С. 13001:1–10. — Бібліогр.: 7 назв. — англ. 1607-324X PACS: 05.30.Ch, 75.20.-g DOI:10.5488/CMP.16.13001 arXiv:1303.5206 http://dspace.nbuv.gov.ua/handle/123456789/121068 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 |
The density of states of a particle in a 2-D area is independent both of the energy and form of the area only at the region of large values of energy. If energy is small, the density of states in the rectangular potential well essentially depends on the form of the area. If the bottom of the potential well has a potential relief, it can define the small eigenvalues as the discrete levels. In this case, dimensions and form of the area would not have any importance. If the conservation of zero value of the angular momentum is taken into account, the effective one-particle Hamiltonian for the 2-D electron gas in the magnetic field in the circle is the Hamiltonian with the parabolic potential and the reflecting bounds. It is supposed that in the square, the Hamiltonian has the same view. The 2-D density of states in the square can be computed as the convolution of 1-D densities. The density of one-particle states for 2-D electron gas in the magnetic field is obtained. It consists of three regions. There is a discrete spectrum at the smallest energy. In the intervening region the density of states is the sum of the piecewise continuous function and the density of the discrete spectrum. At great energies, the density of states is a continuous function. The Fermi energy dependence on the magnetic field is obtained when the field is small and the Fermi energy is located in the region of continuous spectrum. The Fermi energy oscillates and in the average it increases proportionally to the square of the magnetic induction. Total energy of electron gas in magnetic field also oscillates and increases when the magnetic field increases monotonously. |
| format |
Article |
| author |
Dubrovskyi, I.M. |
| spellingShingle |
Dubrovskyi, I.M. Density of one-particle states for 2-D electron gas in magnetic field Condensed Matter Physics |
| author_facet |
Dubrovskyi, I.M. |
| author_sort |
Dubrovskyi, I.M. |
| title |
Density of one-particle states for 2-D electron gas in magnetic field |
| title_short |
Density of one-particle states for 2-D electron gas in magnetic field |
| title_full |
Density of one-particle states for 2-D electron gas in magnetic field |
| title_fullStr |
Density of one-particle states for 2-D electron gas in magnetic field |
| title_full_unstemmed |
Density of one-particle states for 2-D electron gas in magnetic field |
| title_sort |
density of one-particle states for 2-d electron gas in magnetic field |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/121068 |
| citation_txt |
Density of one-particle states for 2-D electron gas in magnetic field / I.M. Dubrovskyi // Condensed Matter Physics. — 2013. — Т. 16, № 1. — С. 13001:1–10. — Бібліогр.: 7 назв. — англ. |
| series |
Condensed Matter Physics |
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2023-10-18T20:37:53Z |
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1796150707408076800 |