Engineering Technologies and Systems - 06. Yudenkov A.V., Volodchenkov A.M., Iudenkova M.A. Cooperative Motion of Electrons on the Graphene Surface

UDK 538.915:661.66

DOI: 10.15507/2658-4123.029.201902.234-247

Cooperative Motion of Electrons on the Graphene Surface

Aleksey V. Yudenkov
Head, Chair of Management, Sciences and Humanities, Smolensk State Academy of Physical Culture, Sport and Tourism (23 Prospekt Gagarina, Smolensk 214000, Russia), D.Sc. (Physics and Mathematics), Professor, Publons: https://publons.com/researcher/2929429/alexey-vitalevich, ORCID: https://orcid.org/0000-0001-8329-1146, This email address is being protected from spambots. You need JavaScript enabled to view it.

Aleksandr M. Volodchenkov
Head, Chair of Humanities and Sciences, Smolensk Branch of Plekhanov Russian University of Economics (21 Normandia-Neman St., Smolensk 214030, Russia), Ph.D. (Physics and Mathematics), Associate Professor, Publons: https://publons.com/researcher/2927666/ aleksandr-volodchenkov, ORCID: https://orcid.org/0000-0001-9314-7324, This email address is being protected from spambots. You need JavaScript enabled to view it.

Maria A. Iudenkova
Student, Moscow Institute of Physics and Technology (9 Institutskiy Pereulok lane, Dolgoprudnyy 141701, Russia), Publons: https://publons.com/researcher/2929527/maria-iudenkova, ORCID: https://orcid.org/0000-0003-3226-2403, This email address is being protected from spambots. You need JavaScript enabled to view it.

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.

Keywords: graphene, dispersion law, Hall effect, Schroedinger equation, Dirac fermion

For citation: Yudenkov A.V., Volodchenkov A.M., Iudenkova M.A. Cooperative Motion of Electrons on the Graphene Surface. Inzhenernyye tekhnologii i sistemy = Engineering Technologies and Systems. 2019; 29(2):234-247. DOI: https://doi.org/10.15507/2658- 4123.029.201902.234-247

Contribution of the authors: A. V. Yudenkov – the scientific guidance, basic concept of research and structure of the article, mathematical description of the models, draft article, conclusion; A. M. Volodchenkov – tasking, analysing research studies and scholarly works, discussion; M. A. Iudenkova – reviewing the literature, editing and desktop publishing.

All authors have read and approved the final version of the paper.

Received 18.03.2019; revised 06.05.2019; published online 28.06.2019

REFERENCES

1. Geim A.K. Random walk: Unpredictable way to graphene. Uspekhi fizicheskikh nauk = Physics– Uspekhi. 2011; 181(12):1284-1298. (In Russ.)

2. Lozovik Yu.E., Merkulova S.P., Sokolik A.A. Collective electron phenomena in graphene. Uspekhi fizicheskikh nauk = Physics–Uspekhi. 2008; 178(7):757-776. (In Russ.)

3. Geim A.K. Graphene prehistory. Physica Scripta. 2012; 146:014003.

4. Morozov S.V., Novosyelov K.S., Geim A.K. Electronic transport in graphene. Uspekhi fizicheskikh nauk = Physics–Uspekhi. 2008; 178(7):776-780. (In Russ.)

5. Rutkov E.V., Gall N.R. Unusual optical properties of graphene on an Rh surface. Pisma v Zhurnal eksperimentalnoy i teoreticheskoy fiziki = JETP Letters. 2014; 100(9-10):708-711. (In Russ.)

6. Yudenkov A.V., Volodchenkov A.M., Yudenkova M.A. Thermodynamic foundations of graphene optical properties. T-Comm. 2018; 12(11):79-83.

7. Kochnev A.S., Ovidko I.A., Semenov B.N., Sevastyanov Ya.A. Mechanical properties of graphene containing elongated tetravacancies (575757-666-5757 defects). Reviews on Advanced Materials Science. 2017; 48(2):142-146.

8. Neto A.H.C., Guinea F., Peres N.M.R., Novoselov K.S., Geim A.K. The electronic properties of graphene. Reviews of Modern Physics. 2009; 81(1):109-162.

9. Rut’kov E.V., Lavrovskaya N.P., Sheshenya E.S., Gall N.R. Optical transparency of graphene layers grown on metal surfaces. Semiconductors. 2017; 51(4):492-497.

10. Young R.J., Kinloch I.A., Gong L., Novoselov K.S. The mechanics of graphene nanocomposites: A review. Composites Science and Technology. 2012; 72(12):1459-1476.

11. Yudenkov A.V., Terentyev S.E., Kovaleva A.E. Informational description of systemic crises. International Journal of Engineering & Technology. 2018; 7(4.36):899-903.

12. Katsnelson M.I. Graphene: Carbon in two dimensions. New York: Cambridge University Press; 2012.

13. Wallace P.R. The band theory of graphite. Physical Review. 1947; 71(9):622-634.

14. Novoselov K.S., Geim A.K. Quantum Hall effect in graphene.In: 2008 Conference on Precision Electromagnetic Measurements Digest. IEEE; 2008. p. 488-489.

15. Neubeck S., Ponomarenko L.A., Freitag F., Novoselov K.S., Giesbers A.J.M., Zeitler U., et al. From one electron to one hole: Quasiparticle counting in graphene quantum dots determined by electrochemical and plasma etching. Small. 2010; 6(14):1469-1473.

16. Kibis O.V. Hall quantum effect. Sorosovskiy obrazovatelnyy zhurnal = Soros Educational Journal. 1999; 9:89-93. (In Russ.)

17. Laughlin R.B. Quantized Hall conductivity in two dimensions.Physical Review B. 1981; 23(10):5632-5633.

18. Gribov L.A. A method to calculate the energy levels of nanoobjects with a periodic framework structure. Zhurnal strukturnoy khimii = Journal of Structural Chemistry. 2010; 51(1):131-136. (In Russ.)

19. Katsnelson M.I., Novoselov K.S. Graphene: New bridge between condensed matter physics and quantum electrodynamics. Solid State Communications. 2007; 143(1-2):3-13.

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