najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2016-7-5-865-868najo-950Research ArticleСтатьиComputer simulation of periodic nanostructuresGrishanovE. N.

68 Bolshevistskaya Str., Saransk 430005, Republic of Mordovia

grishanoven@math.mrsu.ruPopovI. Y.

Kronverkskiy, 49, St. Petersburg, 197101

popov1955@gmail.comNational Research Ogarev Mordovia State UniversityRussian FederationITMO UniversityRussian Federation20161508202575865868Copyright © Grishanov E.N., Popov I.Y., 20252025Grishanov E.N., Popov I.Y.Grishanov E.N., Popov I.Y.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/950

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.

Periodic nanostructureMPIparallel computingThis 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.ReferencesHoward A., McIver J., Collins J. HyperChem. Computational Chemistry. Hypercube, 1996, 350 p.Howard A., McIver J., Collins J. HyperChem. Computational Chemistry. Hypercube, 1996, 350 p.Butyrskaya E.V. Computational Chemistry: Theoretical Foundation and Using of Codes Gaussian and GaussView. М.: Solon Press, 2011, 224 p.Butyrskaya E.V. Computational Chemistry: Theoretical Foundation and Using of Codes Gaussian and GaussView. М.: Solon Press, 2011, 224 p.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.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.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.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.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.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.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.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.Pavlov B.S. The theory of extensions and explicity-solvable models. Russ. Math. Surv., 1997, 42(6), P. 127–168.Pavlov B.S. The theory of extensions and explicity-solvable models. Russ. Math. Surv., 1997, 42(6), P. 127–168.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.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.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.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.Bateman H., Erd´ elyi A. Higher transcendental functions, V.I. McGraw-Hill, New York, 1953.Bateman H., Erd´ elyi A. Higher transcendental functions, V.I. McGraw-Hill, New York, 1953.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.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.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.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.Pacheco Peter S. Parallel Programming With MPI, Morgan Kaufmann, 1997, 418 p.Pacheco Peter S. Parallel Programming With MPI, Morgan Kaufmann, 1997, 418 p.Grishanov E.N., Popov. I.Yu. Spectral properties of multi-layered graphene in a magnetic field. Superlattices and Microstructures, 2015, 86, P. 68–72.Grishanov E.N., Popov. I.Yu. Spectral properties of multi-layered graphene in a magnetic field. Superlattices and Microstructures, 2015, 86, P. 68–72.Nemec N., Cuniberti G. Hofstadter butterflies of bilayer graphene. Phys. Rev. B (Rapid Comm.), 2007, 75, P. 201404(R)Nemec N., Cuniberti G. Hofstadter butterflies of bilayer graphene. Phys. Rev. B (Rapid Comm.), 2007, 75, P. 201404(R)

The authors declare that there are no conflicts of interest present.