najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2017-8-2-194-201najo-651Research ArticleMATHEMATICSМАТЕМАТИКАModel of tunnelling through double quantum layer in a magnetic fieldMeynsterD. L.

Kronverkskiy, 49, St. Petersburg, 197101

mdldml@gmail.comPopovI. Y.

Kronverkskiy, 49, St. Petersburg, 197101

popov1955@gmail.comPopovA I.

Kronverkskiy, 49, St. Petersburg, 197101

popov239@gmail.comITMO UniversityRussian Federation20171208202582194201Copyright © Meynster D.L., Popov I.Y., Popov A.I., 20252025Meynster D.L., Popov I.Y., Popov A.I.Meynster D.L., Popov I.Y., Popov A.I.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/651

Several explicitly solvable models are constructed for electron tunneling in a system of double two-dimensional periodic arrays of quantum dots with two laterally coupled leads in a homogeneous magnetic field are constructed. The theory of self-adjoint extensions of symmetric operators is used for modelling of electron transport. Dependencies of the transmission coefficient on the magnetic field, the energy of electron and the distance between layers are investigated. The results are compared with those of tunnelling through the corresponding single-layer periodic arrays.

quantum dots arraymagnetic fieldscatteringThis work was partially financially supported by the Government of the Russian Federation (grant 074-U01), by grant MK-5161.2016.1 of the President of the Russian Federation, DFG Grant NE 1439/3-1, by grant 16-11-10330 of Russian Science Foundation.ReferencesHofstadter D.R. Energy levels and wavefunctions of Bloch electrons in rational and irrational magnetic fields. Phys. Rev., 1976, B14, P. 2239–2249.Hofstadter D.R. Energy levels and wavefunctions of Bloch electrons in rational and irrational magnetic fields. Phys. Rev., 1976, B14, P. 2239–2249.Gonzalez A., Capote R. Vertical magneto-tunneling through a quantum dot and the density of states of small electronic systems. Physica E, 2001, 10(4), P. 528–534.Gonzalez A., Capote R. Vertical magneto-tunneling through a quantum dot and the density of states of small electronic systems. Physica E, 2001, 10(4), P. 528–534.Brunner R., Meisels R., et al. 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The authors declare that there are no conflicts of interest present.