Periodic chain of disks in a magnetic field: bulk states and edge states
https://doi.org/10.17586/2220-8054-2015-6-5-637-643
Abstract
An explicitly solvable model for periodic chain of coupled disks in orthogonal magnetic field is considered. The spectrum for the Hamiltonian is compared with the spectrum for the corresponding chain of circles. These models are used for the comparison of the bulk and edge states. It is found that for some range of the magnetic field values the lowest band for the circles system lies below the spectrum for the corresponding disks system, i.e. the edge band is below and is separated from the lowest bulk band.
Supporting agencies: This work was partially financially supported by the Government of the Russian Federation (grant 074-U01), by the Ministry of Science and Education of the Russian Federation (GOSZADANIE 2014/190, Project 14.Z50.31.0031), by grants of the President of Russia (state contracts 14.124.13.2045-MK and 14.124.13.1493-MK).
About the Authors
E. N. Grishanov
Department of Mathematics and IT, Ogarev Mordovia State University
Russian Federation
Russian Federation
Bolshevistskaya Str. 68, Saransk
D. A. Eremin
Department of Mathematics and IT, Ogarev Mordovia State University
Russian Federation
Russian Federation
Bolshevistskaya Str. 68, Saransk
D. A. Ivanov
Department of Mathematics and IT, Ogarev Mordovia State University
Russian Federation
Russian Federation
Bolshevistskaya Str. 68, Saransk
I. Yu. Popov
Department of Higher Mathematics, ITMO University
Russian Federation
Russian Federation
Kroverkskiy pr. 49, St. Petersburg, 197101
P. I. Smirnov
Department of Higher Mathematics, ITMO University
Russian Federation
Russian Federation
Kroverkskiy pr. 49, St. Petersburg, 197101
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Review
For citations:
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: Physics, Chemistry, Mathematics. 2015;6(5):637-643. https://doi.org/10.17586/2220-8054-2015-6-5-637-643
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