Computer simulation of periodic nanostructures
https://doi.org/10.17586/2220-8054-2016-7-5-865-868
Abstract
An algorithm and code for spectrum calculation for periodic nanostructures in homogeneous magnetic field are developed. The approach is based on the zero-range potentials model. The mathematical background of the model is based on the theory of self-adjoint extensions of symmetric operators.
Supporting agencies: This work was partially financially supported by the Government of the Russian Federation (grant 074-U01), by Ministry of Science and Education of the Russian Federation (GOSZADANIE 2014/190, Projects No 14.Z50.31.0031 and No. 1.754.2014/K), by DFG Grant NE 1439/3-1, by grant 16-11-10330 of Russian Science Foundation. The authors thanks National Research Ogarev Mordovia State University for the possibility to carry out calculations.
About the Authors
E. N. Grishanov
National Research Ogarev Mordovia State University
Russian Federation
Russian Federation
68 Bolshevistskaya Str., Saransk 430005, Republic of Mordovia
I. Y. Popov
ITMO University
Russian Federation
Russian Federation
Kronverkskiy, 49, St. Petersburg, 197101
References
1. Howard A., McIver J., Collins J. HyperChem. Computational Chemistry. Hypercube, 1996, 350 p.
2. Butyrskaya E.V. Computational Chemistry: Theoretical Foundation and Using of Codes Gaussian and GaussView. М.: Solon Press, 2011, 224 p.
3. Grishanov E.N. Code for spectrum calculation for periodic nanostructures in a magnetic field. Certificate of state registration of code No 2016618953 from 10.08.2016.
4. Geyler V.A., Pavlov B.S., Popov I.Yu. One-particle spectral problem for superlattice with a constant magnetic field. Atti. Sem. Mat. Fis. Univ. Modena., 1998, 46, P. 79—124.
5. Grishanov E.N., Eremin D.A., Ivanov D.A., Popov I.Yu., Smirnov P.I. Periodic chain of disks in a magnetic field: bulk states and edge states. Nanosystems: Phys. Chem. Math., 2015, 6(5), P. 637–643.
6. Albeverio S., Kurasov P. Singular perturbations of differential operators. Solvable Schr¨odinger type operators. London Mathematical Society Lecture Notes 271. Cambridge Univ. Press. Cambridge, 2000.
7. Pavlov B.S. The theory of extensions and explicity-solvable models. Russ. Math. Surv., 1997, 42(6), P. 127–168.
8. Albeverio S., Fassari S., Rinaldi F. Spectral properties of a symmetric three-dimensional quantum dot with a pair of identical attractive d-impurities symmetrically situated around the origin. Nanosystems: Phys. Chem. Math., 2016, 7(2), P. 268–299.
9. Geyler V.A., Demidov V.V. Spectrum of three-dimensional Landau operator perturbed by a periodic point potential, TMF, 1995, 103(2), P. 283-–294.
10. Bateman H., Erd´ elyi A. Higher transcendental functions, V.I. McGraw-Hill, New York, 1953.
11. Geyler V.A. The two-dimensional Scr¨odinger operator with a uniform magnetic field, and its perturbation by periodic zero-range potentials. St. Petersburg Math. J., 1992, 3, P. 489–532.
12. Hofstadter D.R. Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields. Phys.Rev. B., 1976, 14, P. 2239–2249.
13. Pacheco Peter S. Parallel Programming With MPI, Morgan Kaufmann, 1997, 418 p.
14. Grishanov E.N., Popov. I.Yu. Spectral properties of multi-layered graphene in a magnetic field. Superlattices and Microstructures, 2015, 86, P. 68–72.
15. Nemec N., Cuniberti G. Hofstadter butterflies of bilayer graphene. Phys. Rev. B (Rapid Comm.), 2007, 75, P. 201404(R)
Review
For citations:
Grishanov E.N., Popov I.Y. Computer simulation of periodic nanostructures. Nanosystems: Physics, Chemistry, Mathematics. 2016;7(5):865-868. https://doi.org/10.17586/2220-8054-2016-7-5-865-868
Views:
3
Email this article 