Numerical solution for the Schrodinger equation with potential in graphene structures
https://doi.org/10.17586/2220-8054-2019-10-2-124-130
Abstract
This paper presents a different numerical solution to compute eigenvalues of the Schrodinger equation with the potentials in graphene struc- ¨ tures [1]. The research subjects include the Schrodinger equation and the exchange-correlation energy of the graphene structures in Grachev’s ¨ article. Specifically, we used the pseudospectral method basing on the Chebyshev-Gauss-Lobatto grid to determine the approximate numerical results of the problem. The results are the discrete energy spectra and the corresponding eigenfunctions of the nonlinear spin waves in the graphene structure. Additionally, these results can be applied to create the nonlinear spin waves in the graphene structures.
Keywords
graphene,
kinks,
breathers,
spin,
pseudospectral method,
Schrodinger equation,
Chebyshev,
eigenvalue problems,
nonlinear models
Supporting agencies: The author is greatly indebted to Prof. D. S. Kulaybov and to K. P. Lovetskiy for suggesting the problem and for many stimulating conversations. The publication was prepared with the support of the RUDN University Program 5-100.
About the Author
L. A. Nhat
Peoples’ Friendship University of Russia (RUDN University) ; Tan Trao University
Russian Federation
Russian Federation
6 Miklukho-Maklaya str., 117198, Moscow
22227, Tuyen Quang, Vietnam
References
1. Grachev D.D., Sevastianov L.A., Lovetskiy K.P. Nonlinear spin waves in graphene structures. SPIN, 2014, 4(3), P. 1–13.
2. Grachev D.D., Sevastianov L.A. Method of spin wave formation. Patent of Russia No. 2477907, 2010, 7 pp.
3. Grachev D.D., Sevastianov L.A. Method for generating spin waves. Patent of United States No. US8,779,765 B2, 2014, 6 pp.
4. Grachev D.D., Rybakov Y.P., Sevastianov L.A., Sheka E.F. Ferromagnetism in graphen and fulleren nanostructures. Theory, modelling, experiment. RUDN J. of MIPh, 2010, 1, P. 20–27.
5. Grachev D.D., Sevastianov L.A. Quantum field approach to the ferromagnetic properties of the graphene films. Nanostuctures. Math. phys. Model., 2011, 4(1), P. 5–15.
6. Arzumanyan G.M., Ayrjan E.A., Grachev D.D., Sevastianov L.A. Quantum field model for graphene magnetism, modern trends in nanoscience. In book Balasoiu M., Arzumanyan G. M. Modern trends in nanoscience, Editura Academiei Romane, 2013, 236 pp.
7. Grachev D.D., Sevastianov L.A., Lovetskiy K.P., Gusev A.A., Vinitsky S.I., Derbov V.L. Model for spin waves and lasing in monolayer graphene films. Proc. of the SPIE, 2015, 9448, ID. 94481W, 14 pp.
8. Kulyabov D.S., Lovetskiy K.P., Nhat L.A. Simple model of nonlinear spin waves in graphene structures. RUDN J. of MIPh., 2018, 26(3), P. 244–251.
9. Roldan R., Fuchs J.-N., Goerbig M.O. Spin-flip excitations, spin waves, and magneto-excitons in graphene Landau levels at integer filling factors. Phys. Rev. B, 2010, 82, ID 205418, 13 pp.
10. Culchac F.J., Latge A., Costa A.T. Spin waves in graphene nanoribbon devices. Phys. Rev. B, 2012, 86 ID: 115407, 11 pp.
11. Culchac F.J., Latge A., Costa A. T. Spin waves in zigzag graphene nanoribbons and the stability of edge ferromagnetism. New J. Phys., 2011, 13, ID: 033028, 5 pp.
12. Matthew A., Carsten U. Collective charge and spin excitations in graphene with in-plane magnetic fields. In Abstracts of the Conference APS March Meeting, New Orleans - Louisiana, March 13, 2017, 64(4), Abstract ID: BAPS.2017.MAR.P42.9, P. 1024.
13. Mason J.C., Handscomb D.C. Chebyshev polynomials. CRC Press LLC, 2003, 335 pp.
14. Don W.S., Solomonoff A. Accuracy and speed in computing the Chebyshev collocation derivative. SIAM J. Sci. Comput., 1991, 16(6), P. 1253–1268.
15. Nhat L.A. Pseudospectral methods for nonlinear pendulum equations. Zh. Sib. Fed. Univ. Mat. Fiz., 2019, 12(1), P. 79–84.
16. Martha L.A., James P.B. Differential equations with mathematica, ed. 3rd. Elsevier Inc, 2004, 893 pp.
17. Weideman J.A.C., Trefethen L.N. The eigenvalues of second-order spectral differentiation matrices. SIAM J. Numer. Analys., 1988, 25(6), P. 1279–1298.
Review
For citations:
Nhat L.A. Numerical solution for the Schrodinger equation with potential in graphene structures. Nanosystems: Physics, Chemistry, Mathematics. 2019;10(2):124-130. https://doi.org/10.17586/2220-8054-2019-10-2-124-130
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