Preview

Nanosystems: Physics, Chemistry, Mathematics

Advanced search

Quantum graph as a benchmark for persistent current.

https://doi.org/10.17586/2220-8054-2024-14-4-469-472

Abstract

The problem of persistence current in nanosystems is studied. We demonstrate some simple theoretical observation which allows one to construct a benchmark for the persistence current. It can be used for improvement of the persistence current measurement procedure. The consideration is based on the quantum graph model. The benchmark is given by a graph with finite number of rings touching at one point with a lead attached to this point. It is assumed that the graph is plane and there exists a magnetic field orthogonal to the rings.

About the Authors

I. Y. Popov
ITMO University
Russian Federation

Igor Y. Popov – Center of Mathematics

Kroverkskiy, 49, St. Petersburg, 197101



A. I. Popov
ITMO University
Russian Federation

Anton I. Popov – Center of Mathematics

Kroverkskiy, 49, St. Petersburg, 197101



P. A. Gilev
ITMO University
Russian Federation

Pavel A. Gilev – Center of Mathematics

Kroverkskiy, 49, St. Petersburg, 197101



A. Chatterjee
ITMO University; GITAM University
Russian Federation

Ashok Chatterjee – Center of Mathematics

Kroverkskiy, 49, St. Petersburg, 197101

GITAM School of Sciences, Department of Physics

Rudraram, Hyderabad 502329, Telangana



References

1. Lorke A., Luyken R.J., Govorov A.O., Kotthaus J.P., Garcia J.M., Petroff P.M. Spectroscopy of Nanoscopic Semiconductor Rings. Phys. Rev. Lett., 2000, 84, P. 2223.

2. Fuhrer A., Luscher S., Ihn T., Heinzel T., Ensslin K., Wegscheider W., Bichler M. Energy spectra of quantum rings. Nature, 2001, 413, P. 822.

3. Chakraborty T., Pietil¨ainen P. Electron-electron interaction and the persistent current in a quantum ring. Phys. Rev. B, 1994, 50, P. 8460.

4. Halonen V., Pietil¨ainen P., Chakraborty T. Optical absorption spectra of quantum dots and rings with a repulsive scattering centre. Europhys. Lett., 1996, 33, P. 377.

5. Popov I.Y. A model of charged particle on the flat M¨obius strip in a magnetic field. Nanosystems: Phys. Chem. Math., 2023, 14(4), P. 418–420.

6. Popov I.Y. Magnetic Schr¨odinger operator on the flat M¨obius strip. Banach J. Math. Anal., 2024, https://doi.org/10.1007/s43037-024-00360-y.

7. Guo Z.L., Gong Z.R., Dong H., Sun C.P. M¨obius graphene strip as a topological insulator. Phys. Rev. B, 2009, 80, P. 195310.

8. B¨uttiker M., Imry Y., Landauer R. Josephson behavior in small normal one-dimensional rings. Phys. Lett. A, 1983, 96, P. 365.

9. Aharonov Y., Bohm D. Significance of Electromagnetic Potentials in the Quantum Theory. Phys. Rev., 1959, 115, P. 485.

10. Cheung H.F., Gefen Y., Riedel E.K., Shih W.H. Persistent currents in small one-dimensional metal rings. Phys. Rev. B, 1988, 37, P. 6050.

11. Cheung H.F., Gefen Y., Riedel E.K. Isolated rings of mesoscopic dimensions. Quantum coherence and persistent currents. IBM J. Res. Dev., 1988, 32, P. 359.

12. Cheung H.F., Riedel E.K., Gefen Y. Persistent Currents in Mesoscopic Rings and Cylinders. Phys. Rev. Lett., 1989, 62, P. 587.

13. L´evy L.P., Dolan G., Dunsmuir J., Bouchiat H. Magnetization of mesoscopic copper rings: Evidence for persistent currents. Phys. Rev. Lett., 1990, 64, P. 2074.

14. Montambaux G., Bouchiat H., Sigeti D., Friesner R. Persistent currents in mesoscopic metallic rings: Ensemble average. Phys. Rev. B, 1990, 42, P. 7647 (R).

15. Chandrasekhar V., Webb R.A., Brady M.J., Ketchen M.B., Gallagher W.J., Kleinsasser A. Magnetic response of a single isolated gold loop. Phys. Rev. Lett., 1991, 67, P. 3578.

16. Avishai Y., Hatsugai Y., Kohmoto M. Persistent currents and edge states in a magnetic field. Phys. Rev. B, 1993, 47, P. 9501.

17. Bouzerar G., Poilblanc D., Montambaux G. Persistent currents in one-dimensional disordered rings of interacting electrons. Phys. Rev. B, 1994, 49, P. 8258.

18. Mailly D., Chapelier C., Benoit A. Experimental observation of persistent currents in GaAs-AlGaAs single loop. Phys. Rev. Lett., 1993, 70, P. 2020.

19. Sankar I.V., Monisha P.J., Sil S., Ashok Chatterjee. Persistent current and existence of metallic phase in a Holstein-Hubbard quantum ring. Physica E, 2015, 73, P. 175–180.

20. Ashok Chatterjee, Smolkina M.O., Popov I.Y. Persistent current in a chain of two Holstein-Hubbard rings in the presence of Rashba spin-orbit interaction. Nanosystems: Physics, Chemistry, Mathematics, 2019, 10, P. 50–62.

21. Lavanya C. U., Ashok Chatterjee. Persistent Charge and Spin Currents in the 1D Holstein-Hubbard ring at half filling and at away from half filling by Bethe-ansatz approach. J. Mag. Mag. Mat., 2021, 529, P. 167711.

22. Mijanur Islam, Tutul Biswas, Saurabh Basu1. Effect of magnetic field on the electronic properties of an α − T3 ring. Phys. Rev. B, 2023, 108, P. 085423.

23. Hisham M. Fayad, Mazen M. Abadla. Mesoscopic Transport and Persistent Current in the Aharonov-Bohm Rings. Journal of Al Azhar University Gaza (ICBAS Special Issue), 2010, 12, P. 88–94.

24. Bleszynski-Jayich A.C., Shanks W.E., Peaudecerf B., Ginossar E., von Oppen F., Glazman L., Harris J.G.E.. Persistent currents in normal metal rings: comparing high-precision experiment with theory. Science, 2009, 326, P. 272.

25. Berkolaiko G., Kuchment P. Introduction to Quantum Graphs. AMS, Providence, 2012.

26. Lipovsky J. Quantum Graphs And Their Resonance Properties. Acta Physica Slovaca, 2016, 66(4), P. 265–363.

27. Exner P., Keating P., Kuchment P. Sunada T., Teplyaev A. Analysis on graph and its applications. AMS, Providence, 2008.

28. Exner P., Manko S.S. Spectra of magnetic chain graphs: coupling constant perturbations. Journal of Physics A: Mathematical and Theoretical, 2015, 48(12), P. 125302.

29. Popov I.Y., Skorynina A.N., Blinova I.V. On the existence of point spectrum for branching strips quantum graph. Journal of Mathematical Physics, 2014, 55, P. 033504/1-20.

30. Rakhmanov S.Z., Tursunov I.B., Matyokubov Kh.Sh., Matrasulov D.U. Optical high harmonic generation in a quantum graph. Nanosystems: Phys. Chem. Math., 2023, 14(2), P. 164–171.

31. Sabirov K.K., Yusupov J.R., Matyokubov Kh.Sh., Susanto H., Matrasulov D.U. Networks with point-like nonlinearities. Nanosystems: Phys. Chem. Math., 2022, 13(1), P. 30–35.


Review

For citations:


Popov I.Y., Popov A.I., Gilev P.A., Chatterjee A. Quantum graph as a benchmark for persistent current. Nanosystems: Physics, Chemistry, Mathematics. 2024;15(4):469-472. https://doi.org/10.17586/2220-8054-2024-14-4-469-472

Views: 3


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


ISSN 2220-8054 (Print)
ISSN 2305-7971 (Online)