Cooperative Motion of Electrons on the Graphene Surface
Introduction. Today, the development of the graphene theory to control its physical and mechanical properties is a relevant objective. The paper deals with the conducting properties of graphene. In particular, the paper investigates the linear law of electron dispersion and traces its corollaries....
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| Format: | Article |
| Language: | English |
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National Research Mordova State University; MRSU
2019-06-01
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| Series: | Инженерные технологии и системы |
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| Online Access: | http://vestnik.mrsu.ru/index.php/en/articles2-en/82-19-2/699-10-15507-0236-2910-029-201902-6 |
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| author | Aleksey V. Yudenkov Aleksandr M. Volodchenkov Maria A. Iudenkova |
| author_facet | Aleksey V. Yudenkov Aleksandr M. Volodchenkov Maria A. Iudenkova |
| author_sort | Aleksey V. Yudenkov |
| collection | DOAJ |
| description | Introduction. Today, the development of the graphene theory to control its physical and mechanical properties is a relevant objective. The paper deals with the conducting properties of graphene. In particular, the paper investigates the linear law of electron dispersion and traces its corollaries.
Materials and Methods. The development of the theory is based on the verified experimental data and on the foundamental principles of the solid body theory and quantum mechanics. The study follows the universal synergetic principle according to which, there have been developed two split-level mathematical models of the quasi-particle motion in graphene on exposure to the electric field. On the macroscopic level, we suggest that graphene should be analyzed as a crystal consisting of three parallel planes. Two of them are electron gas. The remaining one is the main body of the crystal. On the microscopic level, the quasi-particle motion of the electron wave is described through the Schroedinger equation.
Results. The study has developed the alternative method for the explanation of the linear dispersion law in graphene on the macroscopic level. Basing on the analysis of the model, the paper provides a hypothesis of the cooperative motion of the electron pairs, which make up a boson particle. The given hypothesis is different from the traditional one. In accordance with the latter, quasi-particles in graphene are Dirac fermions. To prove the hypothesis consilience, the study examines Hall’s effect in grapheme. The linear dispersion law for a pair of electrons is also deduced from the Schroedinger equation. Both the macroscopic and microscopic models are in a reasonable agreement with the experimental data.
Discussion and Conclusion. The main result of the research is the development of the multi-level mathematical model which properly features the conducting properties of graphene (linear dispersion law, anomalous Hall effect). The practical relevance consists in revealing the possibility to control the conducting properties of graphene through impacts on electron pairs. |
| first_indexed | 2024-12-14T16:24:09Z |
| format | Article |
| id | doaj.art-e192c6ff89144411889814a8cdb24d8f |
| institution | Directory Open Access Journal |
| issn | 2658-4123 2658-6525 |
| language | English |
| last_indexed | 2024-12-14T16:24:09Z |
| publishDate | 2019-06-01 |
| publisher | National Research Mordova State University; MRSU |
| record_format | Article |
| series | Инженерные технологии и системы |
| spelling | doaj.art-e192c6ff89144411889814a8cdb24d8f2022-12-21T22:54:44ZengNational Research Mordova State University; MRSUИнженерные технологии и системы2658-41232658-65252019-06-0129223424710.15507/2658-4123.029.201902.234-247Cooperative Motion of Electrons on the Graphene SurfaceAleksey V. Yudenkov0https://orcid.org/0000-0001-8329-1146Aleksandr M. Volodchenkov1https://orcid.org/0000-0001-9314-7324Maria A. Iudenkova2https://orcid.org/0000-0003-3226-2403Smolensk State Academy of Physical Culture, Sport and TourismSmolensk Branch of Plekhanov Russian University of EconomicsMoscow Institute of Physics and TechnologyIntroduction. Today, the development of the graphene theory to control its physical and mechanical properties is a relevant objective. The paper deals with the conducting properties of graphene. In particular, the paper investigates the linear law of electron dispersion and traces its corollaries. Materials and Methods. The development of the theory is based on the verified experimental data and on the foundamental principles of the solid body theory and quantum mechanics. The study follows the universal synergetic principle according to which, there have been developed two split-level mathematical models of the quasi-particle motion in graphene on exposure to the electric field. On the macroscopic level, we suggest that graphene should be analyzed as a crystal consisting of three parallel planes. Two of them are electron gas. The remaining one is the main body of the crystal. On the microscopic level, the quasi-particle motion of the electron wave is described through the Schroedinger equation. Results. The study has developed the alternative method for the explanation of the linear dispersion law in graphene on the macroscopic level. Basing on the analysis of the model, the paper provides a hypothesis of the cooperative motion of the electron pairs, which make up a boson particle. The given hypothesis is different from the traditional one. In accordance with the latter, quasi-particles in graphene are Dirac fermions. To prove the hypothesis consilience, the study examines Hall’s effect in grapheme. The linear dispersion law for a pair of electrons is also deduced from the Schroedinger equation. Both the macroscopic and microscopic models are in a reasonable agreement with the experimental data. Discussion and Conclusion. The main result of the research is the development of the multi-level mathematical model which properly features the conducting properties of graphene (linear dispersion law, anomalous Hall effect). The practical relevance consists in revealing the possibility to control the conducting properties of graphene through impacts on electron pairs.http://vestnik.mrsu.ru/index.php/en/articles2-en/82-19-2/699-10-15507-0236-2910-029-201902-6graphenedispersion lawhall effectschroedinger equationdirac fermion |
| spellingShingle | Aleksey V. Yudenkov Aleksandr M. Volodchenkov Maria A. Iudenkova Cooperative Motion of Electrons on the Graphene Surface Инженерные технологии и системы graphene dispersion law hall effect schroedinger equation dirac fermion |
| title | Cooperative Motion of Electrons on the Graphene Surface |
| title_full | Cooperative Motion of Electrons on the Graphene Surface |
| title_fullStr | Cooperative Motion of Electrons on the Graphene Surface |
| title_full_unstemmed | Cooperative Motion of Electrons on the Graphene Surface |
| title_short | Cooperative Motion of Electrons on the Graphene Surface |
| title_sort | cooperative motion of electrons on the graphene surface |
| topic | graphene dispersion law hall effect schroedinger equation dirac fermion |
| url | http://vestnik.mrsu.ru/index.php/en/articles2-en/82-19-2/699-10-15507-0236-2910-029-201902-6 |
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