The Interaction of Bilayer Graphene with an External Magnetic Field

Yuri Petrovich Rybakov; Abdullahi Bappah Ahmed

doi:doi:10.11648/j.ijamtp.20170303.15

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The Interaction of Bilayer Graphene with an External Magnetic Field

Yuri Petrovich Rybakov, Abdullahi Bappah Ahmed

Published in International Journal of Applied Mathematics and Theoretical Physics (Volume 3, Issue 3)

Received: 14 April 2017 Accepted: 19 May 2017 Published: 16 June 2017

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Abstract

In this phenomenological approach to the study of magnetism in bilayer graphene, the chiral model of graphene was employ to describe the interaction of the bilayer graphene with an external magnetic field. The simplest scalar chiral model of graphene suggested earlier and based on the SU (2) order parameter is generalized by including 8-spinor field as an additional order parameter for the description of spin (magnetic) excitations in the bilayer graphene. As an illustration we study the interaction of the bilayer graphene with the external magnetic field orthogonal to the plane. The Lagrangian density of the model was constructed; The Lagrangian density of the model includes the three interacting terms, the spinor field, chiral field, and the electromagnetic field. The domain wall solution describing the bilayer graphene configuration is introduced for studying the magnetic field behavior in the central domain of the material; the solution to the inhomogeneous equations were found using the Green’s function method, at small radial field, the paramagnetic behavior of the material was revealed and the strengthening of the magnetic intensity inside the material in the central domain of the material was also revealed.

Published in	International Journal of Applied Mathematics and Theoretical Physics (Volume 3, Issue 3)
DOI	10.11648/j.ijamtp.20170303.15
Page(s)	74-77
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Bilayer Graphene, Chiral Model, Domain Wall, 8-Spinor, Green Function, Bessel’s Function

References

[1]	Rybakov Yu P: On chiral model of graphene//Solid State Phenomena, v.190.2012, P.59-62.
[2]	ERJUN KAN, ZHENYU LI and JINLONG YANG YANG MAGNETISM IN GRAPHENE SYSTEMS: NANO, 2008. - Issue 06: Vol. 03.
[3]	Berashevich J. [et al.] Properties of graphene: a theoretical perspective: Advances in Physics, 2010. - 4: Vol. 59.
[4]	Jean Paul Issi, Paulo T. Arauja and Mildred S Dresselhaus Electron and Phonon Transport in Graphene in and out of the Bulk [Book Section] // Physics of Graphene / book auth. Aoki H. and Dresselhaus M. S.: Springer, 2014.
[5]	Castro E.v. et al. Phys. Rev.lett.99,216802(2007).
[6]	Santos J. M. B. Lopes dos, N. M. R. Peres and Neto A. H. Castro Graphene bilayer with a twist: electronic structure: arXiv.org > cond-mat > arXiv:0704.2128, 2007.
[7]	McCann Edward and Vladimir. I. Fal'kovski Weak Localised and Spin-Orbit Coupling in Monolayer and Bilayer Graphene: Spinger, 2014.
[8]	Rybakov Yu PSpin excitations in chiral model of graphene//Solid State Phenomena, v.233-234. 2015, P.16-19.
[9]	Rybakov Yu P, Ahmed A. B, Iskandar M., Magnetic excitations of graphene in 8-spinor realization of chiral model// RUDN Jouranal of Mathematics, Information, Physics[Bulletin of Peoples Friendship Unoversity of Russia], vol. 25. 2017, No. 3.
[10]	Philip Kim Graphene and Relativistic Quantum Physics [Report]. - New york 10027, USA: Saminaire Pointcare, 2004.
[11]	Nat´alia Menezes [et al.] Valley- and spin-splitting due to interactions in graphene [Journal]. - [s.l.]: arxiv.org/pdf/1601.07454., 2016. - Vol. 1.
[12]	Erjun Kan, Zhenyu Li and Jinlong Yang Magnetism in Graphene Systems [Journal]. - [s.l.]: Nano, 2008. - 06: Vol. 03.
[13]	Yuchen Ma [et al.] Magnetic properties of vacancies in graphene//New Journal of Physics, Vol. 6. 2004, P. 68.

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APA Style

Yuri Petrovich Rybakov, Abdullahi Bappah Ahmed. (2017). The Interaction of Bilayer Graphene with an External Magnetic Field. International Journal of Applied Mathematics and Theoretical Physics, 3(3), 74-77. https://doi.org/10.11648/j.ijamtp.20170303.15

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ACS Style

Yuri Petrovich Rybakov; Abdullahi Bappah Ahmed. The Interaction of Bilayer Graphene with an External Magnetic Field. Int. J. Appl. Math. Theor. Phys. 2017, 3(3), 74-77. doi: 10.11648/j.ijamtp.20170303.15

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AMA Style

Yuri Petrovich Rybakov, Abdullahi Bappah Ahmed. The Interaction of Bilayer Graphene with an External Magnetic Field. Int J Appl Math Theor Phys. 2017;3(3):74-77. doi: 10.11648/j.ijamtp.20170303.15

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@article{10.11648/j.ijamtp.20170303.15,
  author = {Yuri Petrovich Rybakov and Abdullahi Bappah Ahmed},
  title = {The Interaction of Bilayer Graphene with an External Magnetic Field},
  journal = {International Journal of Applied Mathematics and Theoretical Physics},
  volume = {3},
  number = {3},
  pages = {74-77},
  doi = {10.11648/j.ijamtp.20170303.15},
  url = {https://doi.org/10.11648/j.ijamtp.20170303.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20170303.15},
  abstract = {In this phenomenological approach to the study of magnetism in bilayer graphene, the chiral model of graphene was employ to describe the interaction of the bilayer graphene with an external magnetic field. The simplest scalar chiral model of graphene suggested earlier and based on the SU (2) order parameter is generalized by including 8-spinor field as an additional order parameter for the description of spin (magnetic) excitations in the bilayer graphene. As an illustration we study the interaction of the bilayer graphene with the external magnetic field orthogonal to the plane. The Lagrangian density of the model was constructed; The Lagrangian density of the model includes the three interacting terms, the spinor field, chiral field, and the electromagnetic field. The domain wall solution describing the bilayer graphene configuration is introduced for studying the magnetic field behavior in the central domain of the material; the solution to the inhomogeneous equations were found using the Green’s function method, at small radial field, the paramagnetic behavior of the material was revealed and the strengthening of the magnetic intensity inside the material in the central domain of the material was also revealed.},
 year = {2017}
}

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TY  - JOUR
T1  - The Interaction of Bilayer Graphene with an External Magnetic Field
AU  - Yuri Petrovich Rybakov
AU  - Abdullahi Bappah Ahmed
Y1  - 2017/06/16
PY  - 2017
N1  - https://doi.org/10.11648/j.ijamtp.20170303.15
DO  - 10.11648/j.ijamtp.20170303.15
T2  - International Journal of Applied Mathematics and Theoretical Physics
JF  - International Journal of Applied Mathematics and Theoretical Physics
JO  - International Journal of Applied Mathematics and Theoretical Physics
SP  - 74
EP  - 77
PB  - Science Publishing Group
SN  - 2575-5927
UR  - https://doi.org/10.11648/j.ijamtp.20170303.15
AB  - In this phenomenological approach to the study of magnetism in bilayer graphene, the chiral model of graphene was employ to describe the interaction of the bilayer graphene with an external magnetic field. The simplest scalar chiral model of graphene suggested earlier and based on the SU (2) order parameter is generalized by including 8-spinor field as an additional order parameter for the description of spin (magnetic) excitations in the bilayer graphene. As an illustration we study the interaction of the bilayer graphene with the external magnetic field orthogonal to the plane. The Lagrangian density of the model was constructed; The Lagrangian density of the model includes the three interacting terms, the spinor field, chiral field, and the electromagnetic field. The domain wall solution describing the bilayer graphene configuration is introduced for studying the magnetic field behavior in the central domain of the material; the solution to the inhomogeneous equations were found using the Green’s function method, at small radial field, the paramagnetic behavior of the material was revealed and the strengthening of the magnetic intensity inside the material in the central domain of the material was also revealed.
VL  - 3
IS  - 3
ER  -

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Author Information

Yuri Petrovich Rybakov

Department of Theoretical Physics and Mechanics, Faculty of Science, Peoples’ Friendship University of Russia, Moscow, Russia
Abdullahi Bappah Ahmed

Department of Physics, Faculty of Science, Gombe State University, Gombe, Nigeria

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Plain Text BibTeX RIS

APA Style

Yuri Petrovich Rybakov, Abdullahi Bappah Ahmed. (2017). The Interaction of Bilayer Graphene with an External Magnetic Field. International Journal of Applied Mathematics and Theoretical Physics, 3(3), 74-77. https://doi.org/10.11648/j.ijamtp.20170303.15

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ACS Style

Yuri Petrovich Rybakov; Abdullahi Bappah Ahmed. The Interaction of Bilayer Graphene with an External Magnetic Field. Int. J. Appl. Math. Theor. Phys. 2017, 3(3), 74-77. doi: 10.11648/j.ijamtp.20170303.15

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AMA Style

Yuri Petrovich Rybakov, Abdullahi Bappah Ahmed. The Interaction of Bilayer Graphene with an External Magnetic Field. Int J Appl Math Theor Phys. 2017;3(3):74-77. doi: 10.11648/j.ijamtp.20170303.15

Copy | Download

@article{10.11648/j.ijamtp.20170303.15,
  author = {Yuri Petrovich Rybakov and Abdullahi Bappah Ahmed},
  title = {The Interaction of Bilayer Graphene with an External Magnetic Field},
  journal = {International Journal of Applied Mathematics and Theoretical Physics},
  volume = {3},
  number = {3},
  pages = {74-77},
  doi = {10.11648/j.ijamtp.20170303.15},
  url = {https://doi.org/10.11648/j.ijamtp.20170303.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20170303.15},
  abstract = {In this phenomenological approach to the study of magnetism in bilayer graphene, the chiral model of graphene was employ to describe the interaction of the bilayer graphene with an external magnetic field. The simplest scalar chiral model of graphene suggested earlier and based on the SU (2) order parameter is generalized by including 8-spinor field as an additional order parameter for the description of spin (magnetic) excitations in the bilayer graphene. As an illustration we study the interaction of the bilayer graphene with the external magnetic field orthogonal to the plane. The Lagrangian density of the model was constructed; The Lagrangian density of the model includes the three interacting terms, the spinor field, chiral field, and the electromagnetic field. The domain wall solution describing the bilayer graphene configuration is introduced for studying the magnetic field behavior in the central domain of the material; the solution to the inhomogeneous equations were found using the Green’s function method, at small radial field, the paramagnetic behavior of the material was revealed and the strengthening of the magnetic intensity inside the material in the central domain of the material was also revealed.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - The Interaction of Bilayer Graphene with an External Magnetic Field
AU  - Yuri Petrovich Rybakov
AU  - Abdullahi Bappah Ahmed
Y1  - 2017/06/16
PY  - 2017
N1  - https://doi.org/10.11648/j.ijamtp.20170303.15
DO  - 10.11648/j.ijamtp.20170303.15
T2  - International Journal of Applied Mathematics and Theoretical Physics
JF  - International Journal of Applied Mathematics and Theoretical Physics
JO  - International Journal of Applied Mathematics and Theoretical Physics
SP  - 74
EP  - 77
PB  - Science Publishing Group
SN  - 2575-5927
UR  - https://doi.org/10.11648/j.ijamtp.20170303.15
AB  - In this phenomenological approach to the study of magnetism in bilayer graphene, the chiral model of graphene was employ to describe the interaction of the bilayer graphene with an external magnetic field. The simplest scalar chiral model of graphene suggested earlier and based on the SU (2) order parameter is generalized by including 8-spinor field as an additional order parameter for the description of spin (magnetic) excitations in the bilayer graphene. As an illustration we study the interaction of the bilayer graphene with the external magnetic field orthogonal to the plane. The Lagrangian density of the model was constructed; The Lagrangian density of the model includes the three interacting terms, the spinor field, chiral field, and the electromagnetic field. The domain wall solution describing the bilayer graphene configuration is introduced for studying the magnetic field behavior in the central domain of the material; the solution to the inhomogeneous equations were found using the Green’s function method, at small radial field, the paramagnetic behavior of the material was revealed and the strengthening of the magnetic intensity inside the material in the central domain of the material was also revealed.
VL  - 3
IS  - 3
ER  -

Copy | Download