Model of tunneling through periodic array of quantum dots in a magnetic field

doi:10.1088/1674-1056/21/11/117306

Abstract Two-dimensional periodic array of quantum dots with two laterally coupled leads in a magnetic field is considered. The model of electron transport through the system based on the theory of self-adjoint extensions of symmetric operators is suggested. We obtain the formula for the transmission coefficient and investigate its dependence on the magnetic field.

Keywords: tunneling nanostructure operator extension theory

Received: 19 March 2012
Revised: 26 July 2012
Accepted manuscript online:

PACS:	73.23.Ad	(Ballistic transport)
	02.30.Tb	(Operator theory)

Fund: Project supported by the Federal Targeted Program "Scientific and Educational Human Resources for Innovation-Driven Russia" (Grant Nos. P689 NK-526P, 14.740.11.0879, 16.740.11.0030, and 2012-1.2.2-12-000-1001-047), the Russian Foundation for Basic Researches (Grant No. 11-08-00267), and the Federal Targeted Program "Researches and Development in the Priority Directions Developments of a Scientific and Technological Complex of Russia 2007-2013" (Grant No. 07.514.11.4146).

Corresponding Authors: I. Yu. Popov
E-mail: popov@mail.ifmo.ru

Cite this article:

I. Yu. Popov, S. A. Osipov Model of tunneling through periodic array of quantum dots in a magnetic field 2012 Chin. Phys. B 21 117306

[1]	Hofstadter D R 1976 Phys. Rev. B 14 2239
[2]	Albeverio S, Geyler V A, Grishanov E N and Ivanov D A 2010 Int. J. Theor. Phys. 49 728
[3]	Geyler V A, Popov I Yu, Popov A V and Ovechkina A A 2000 Chaos Soliton. Fract. 11 281
[4]	Jaksch D and Zoller P 2003 New J. Phys. 5 56
[5]	Demkov Yu N and Ostrovskiy V N 1975 Method of Zero-range Potentials in Atomic Physics (Leningrad: Leningrad State Univ. Publishing House)
[6]	Block I, Dalibard J and Zwerger W 2008 Rev. Mod. Phys. 80 885
[7]	Geyler V A 1992 St. Petersburg Math. J. 3 489
[8]	Geyler V A and Popov I Yu 1994 Z. Phys. B 93 437
[9]	Geyler V A and Popov I Yu 1995 Z. Phys. B 98 473
[10]	Sols F 1992 Ann. Phys. 214 386
[11]	Geyler V A and Popov I Yu 1996 Theor. Math. Phys. 107 12
[12]	Martin G, Yafyasov A M and Pavlov B S 2010 Nanosystems: Phys. Chem. Math. 1 (1) 108
[13]	Reed M and Simon B 1972 Methods of Modern Mathematical Physics I: Functional Analysis (New York: Academic Press)
[14]	Malkin I A and Manko V I 1979 Dynamical Symmetries and Coherent States of Quantum Systems (Moscow: Nauka)
[15]	Bateman H and Erdelyi A 1953 Higher Transcendental Functions (vol. 1) (New York: McGraw-Hill)
[16]	Albeverio S, Gesztesy F, Hoegh-Krohn R and Holden H 2005 Solvable Models in Quantum Mechanics 2nd edn. (Providence, R.I.: AMS Chelsea Publishing )

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