On spin flip for electron scattering by several delta-potentials for 1D Hamiltonian with spin-orbit interaction
https://doi.org/10.17586/2220-8054-2023-14-4-413-417
Abstract
One-dimensional Rashba and Dresselhaus Hamiltonians with spin-orbit interaction are studied. It is assumed that there are point-like potentials on the line. The scattering problem is solved and the possibility of spin-flip is discussed.
About the Authors
I. V. Blinova
ITMO University
Russian Federation
Russian Federation
Irina V. Blinova – Center of Mathematics
Kroverkskiy, 49, St. Petersburg, 197101
E. N. Grishanov
Ogarev Mordovia State University
Russian Federation
Russian Federation
Evgeny N. Grishanov – Department of Mathematics and IT
Bolshevistskaya Str. 68, Saransk, 430005
A. I. Popov
ITMO University
Russian Federation
Russian Federation
Anton I. Popov – Center of Mathematics
Kroverkskiy, 49, St. Petersburg, 197101
I. Y. Popov
ITMO University
Russian Federation
Russian Federation
Igor Y. Popov – Center of Mathematics
Kroverkskiy, 49, St. Petersburg, 197101
M. O. Smolkina
ITMO University
Russian Federation
Russian Federation
Maria O. Smolkina – Center of Mathematics
Kroverkskiy, 49, St. Petersburg, 197101
References
1. Wolf S.A., Awschalom D.D., Buhrman R.A., Daughton J.M., S. von Molnar, Roukes M.L., Chtchelkanova A.Y., Treger D.M. Spintronics: A spin-based electronics vision for the future. Science, 2001, 294, P. 1488–1495.
2. Nielsen M.A., Chuang I.L. Quantum Computation and Quantum Information. Cambridge University Press, Cambridge, 2010.
3. Lobanov I.S. Spin Boltzmann machine. Nanosystems: Phys. Chem. Math., 2022, 13(6), P. 593–607.
4. Bychkov Yu.A., Rashba E.I. Properties of a 2D electron gas with a lifted spectrum degeneracy. Sov. Phys. - JETP Lett., 1984, 39, P. 78–81.
5. Dresselhaus G. Spin-orbit coupling effects in Zinc blende structures. Physical Review, 1955, 100(2), P. 580–586.
6. Magarill L.I., Romanov D.A., Chaplik A.V. Ballistic transport and spin-orbit interaction of two-dimensional electrons on cylindrical surface. J. Exper. Theor. Phys., 1998, 113(4), P. 1411–1428.
7. Ambrosetti A., Pederiva F., Lipparini E., Gandolfi S. Quantum Monte Carlo study of the two-dimensional electron gas in presence of Rashba interaction. Phys. Rev. B, 2009, 80, P. 125306.
8. Ishizaka K., et.al. Giant Rashba-type spin splitting in bulk BiTeI, Nature Materials, 2011, 10, P. 521–526.
9. Di Sante D., Barone P., Bertacco R., Picozzi S. Electric Control of the Giant Rashba Effect in Bulk GeTe. Advanced Materials, 2013, 25, P. 509– 513.
10. Bruning J., Geyler V., Pankrashkin K. Explicit Green functions for spin-orbit Hamiltonians. ¨ J. Phys. A: Math. Theor., 2007, 40, P. F697–F704.
11. Jursenas R. Spectrum of a family of spin-orbit coupled Hamiltonians with singular perturbation. J. Phys. A: Math. Theor., 2016, 49(6), P. 065202.
12. Boitsev A.A., Brasche J., Popov I.Y. Point-like perturbation of Rashba Hamiltonian. Complex Variables and Elliptic Equations, 2021, 66(1), P. 154–164.
13. Cacciapuoti C., Carlone R., Figari R. Spin-dependent point potentials in one and three dimensions. J. Phys. A: Math. Theor., 2007, 40, P. 249–261.
14. Kulinskii V.L., Panchenko D.Yu. Point-Like Rashba Interactions as Singular Self-Adjoint Extensions of the Schrodinger Operator in One Dimen- ¨ sion. Front. Phys., 2019, 7, P. 44(1-8).
15. Berkolaiko G., Kuchment P. 2012 Introduction to Quantum Graphs, (AMS, Providence).
16. Lipovsky J. Quantum Graphs And Their Resonance Properties. Acta Physica Slovaca, 2016, 66(4), P. 265–363.
17. Exner P., Keating P., Kuchment P. Sunada T., Teplyaev A. Analysis on graph and its applications, 2008, AMS, Providence.
18. Chatterjee A., Popov I.Y., Smolkina M.O. Persistent current in a chain of two Holstein-Hubbard rings in the presence of Rashba spin-orbit interaction. Nanosystems: Physics, Chemistry, Mathematics., 2019, 10(1), P. 50–62.
19. Monisha P.J., Sankar I.V., Sil S., Chatterjee A. Persistent current in a correlated quantum ring with electron-phonon interaction in the presence of Rashba interaction and Aharonov-Bohm flux. Scientific Reports, 2016, 6, P. 20056.
20. Dehghana E., Khoshnouda D.S., Naeimi A.S. Logical spin-filtering in a triangular network of quanum nanorings with a Rashba spin-orbit interaction. Physica B, 2018, 529, P. 21–26.
21. Maryam Sabzevar, Mohammad Hossien Ehsani, Mehdi Solaimani. Spin-Polarized wave-packets transport through one-dimensional nonlinear multiple barriers: Rashba and Dresselhaus Spin-Orbit Interactions. Philosophical Magazine, 2023, 103(8), P. 791–811.
22. Blinova I.V., Popov I.Y., Smolkina M.O. Scattering, Spectrum and Resonance States Completeness for a Quantum Graph with Rashba Hamiltonian. Operator Theory, Functional Analysis and Applications. Operator Theory: Advances and Applications, 2021, 282, P. 51–62.
23. Popov I.Y., Blinova I.V., Shamionova E.A., Smolkina M.O. On the electron transmission control by a direction of magnetic field. International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, 2021, 34(6), P. e2918.
24. Blinova I.V., Popov A.I., Bosova A.A. Spectral gaps for star-like quantum graph and for two coupled rings. Nanosystems: Phys. Chem. Math., 2022, 13(3), P. 245–249.
25. Oh J.H., Lee K.-J., Hyun-Woo Lee, Shin M. Effects of Rashba and Dresselhaus spin-orbit interactions on the ground state of two-dimensional localized spins. J. Phys.: Condens. Matter, 2014, 26, P. 196005.
26. Umar Farooq M., Lede Xian, Li Huang. Spin Hall effect in two-dimensional InSe: Interplay between Rashba and Dresselhaus spin-orbit couplings. Phys. Rev. B, 2022, 105, P. 245405.
27. Tkach Yu.Ya. Determination of the Rashba and Dresselhaus spin-orbit interaction parameters and g-factor from the critical points of the spectrum in a 2D electron gas in an in-plane magnetic field. Physica Status Solidi (b), 2021, 258(5), P. 2000553.
Review
For citations:
Blinova I.V., Grishanov E.N., Popov A.I., Popov I.Y., Smolkina M.O. On spin flip for electron scattering by several delta-potentials for 1D Hamiltonian with spin-orbit interaction. Nanosystems: Physics, Chemistry, Mathematics. 2023;14(4):413-417. https://doi.org/10.17586/2220-8054-2023-14-4-413-417
Views:
4
Email this article 